%0 Journal Article %J Public Understanding of Science %D Submitted %T What science is fair? Representations of science in a Dutch creationist campaign %A Blancke, Stefaan %A Kosolosky, Laszlo %X

In the Netherlands, creationists have started up a civil initiative by which they demand “fair science”. This paper offers an analysis of this peculiar notion. Fair science depends on two representations of science, one as an unimpressive label, and one as an authority. Each of these representations hinges on a different conception of the authority of science: on the one hand, science is endowed with authority because it produces technology and is able to make reliable predictions. On the other hand, science’s authority is only a matter of reputation. To the extent that these two conceptions tap into representations of science and its authority among the larger public, the notion of fair science might prove to be a compelling rhetorical tool. Suggestions are made as to how the appeal of the notion can be reduced.

%B Public Understanding of Science %G eng %0 Generic %D In Press %T Adaptive Deontic Logics %A Van De Putte, Frederik %A Beirlaen, Mathieu %A Meheus, Joke %B Handbook of Deontic Logic and Normative Systems %7 1 %I College Publications %V 2 %G eng %0 Generic %D In Press %T The Feasibility of Modeling Hypothetical Reasoning by Formal Logics. Including an Overview of Adaptive Logics for Singular Fact Abduction %A Gauderis, Tjerk %E Magnani, Lorenzo %E Bertolotti, Tommaso %B Handbook of Model-Based Science %I Springer %G eng %0 Journal Article %J Tijdschrift voor Filosofie %D In Press %T Groepsbeslissingen: kwaliteit, autoriteit en vertrouwen %A Baartmans, Tim %A Kosolosky, Laszlo %B Tijdschrift voor Filosofie %G eng %0 Journal Article %J Journal of Logic and Computation %D In Press %T Haskell before Haskell: an alternative lesson in practical logics of the ENIAC %A De Mol, Liesbeth %A Carlé, Martin %A Bullynck, Maarten %X

This article expands on Curry's work on how to implement the problem of inverse interpolation on the ENIAC (1946) and his subsequent work on developing a theory of program composition (1948–1950). It is shown that Curry's hands-on experience with the ENIAC on the one side and his acquaintance with systems of formal logic on the other, were conductive to conceive a compact ‘notation for program construction’ which in turn would be instrumental to a mechanical synthesis of programs. Since Curry's systematic programming technique pronounces a critique of the Goldstine-von Neumann style of coding, his ‘calculus of program composition’ not only anticipates automatic programming but also proposes explicit hardware optimizations largely unperceived by computer history until Backus' famous ACM Turing Award lecture (1977). The cohesion of these findings asks for an integrative historiographical approach. An appendix gives, for the first time, a full description of Curry's arithmetic compiler.

%B Journal of Logic and Computation %G eng %R 10.1093/logcom/exs072 %0 Journal Article %J Synthese %D In Press %T A Logic for the Discovery of Deterministic Causal Regularities %A Mathieu Beirlaen %A Bert Leuridan %A Frederik Van De Putte %B Synthese %P 1–33 %G eng %0 Journal Article %J Journal of Applied Logic %D In Press %T Non-Adjunctive Deontic Logics That Validate Aggregation as Much as Possible %A Meheus, Joke %A Beirlaen, Mathieu %A Van De Putte, Frederik %A Straßer, Christian %B Journal of Applied Logic %G eng %0 Journal Article %J Studia Logica %D 2020 %T Adaptive Fregean Set Theory %A Batens, Diderik %X

This paper defines provably non-trivial theories that characterize Frege's notion of a set, taking into account that the notion is inconsistent. By choosing an adaptive underlying logic, consistent sets behave classically notwithstanding the presence of inconsistent sets. Some of the theories have a full-blown presumably consistent set theory T as a subtheory, provided T is indeed consistent. An unexpected feature is the presence of classical negation within the language.

%B Studia Logica %V 108 %P 903–939 (e-published 10 NOV 2019) %G eng %R https://doi.org/10.1007/s11225-019-09882-1 %0 Journal Article %J Logicheskie Issledovaniya / Logical Investigations %D 2020 %T Devising the Set of Abnormalities for a Given Defeasible Rule %A Batens, Diderik %X

Devising adaptive logics usually starts with a set of abnormalities and a deductive logic. Where the adaptive logic is ampliative, the deductive logic is the lower limit logic, the rules of which are unconditionally valid. Where the adaptive logic is corrective, the deductive logic is the upper limit logic, the rules of which are valid in case the premises do not require any abnormalities to be true. In some cases, the idea for devising an adaptive logic does not relate to a set of abnormalities, but to one or more defeasible rules, and perhaps also to one of the deductive logics. Defeasible rules are not universally valid, but are valid in `normal situations' or for unproblematic parts of premise set.  Where the idea is such, the set of abnormalities has to be delineated in view of the rules. The way in which this task may be tackled is by no means obvious and is the main topic studied in the present paper. The outcome is an extremely simple and transparent recipe. It is shown that, except for very special cases, the recipe leads to an adequate result.

%B Logicheskie Issledovaniya / Logical Investigations %V 26 %P 9–35 %G eng %U https://logicalinvestigations.ru/article/view/557/561?lang=en %R 10.21146/2074-1472-2020-26-1-9-35 %0 Journal Article %J IfCoLog Journal of Logics and their Applications %D 2019 %T Adaptive Deontic Logics: A Survey %A Van De Putte, Frederik %A Beirlaen, Mathieu %A Meheus, Joke %B IfCoLog Journal of Logics and their Applications %V 6 %P 523-608 %G eng %U http://www.collegepublications.co.uk/downloads/ifcolog00032.pdf %& 523 %0 Generic %D 2019 %T Looting Liars Masking Models %A Batens, Diderik %E Başkent, Can %E Ferguson, Thomas Macaulay %X

This paper does not raise objections but spells out problems that I consider at present unsolved within Priest's view on logic. In light of the state of scientific and other theories (§2) and in light of the character of natural languages (§3), Priest's central arguments do not seem convincing. Next, I offer some six independent obstacles for defining consistency, identifying models and describing the semantics and metatheory of LP (§4).

%B Graham Priest on Dialetheism and Paraconsistency %I Springer %P 139--164 %G eng %0 Generic %D 2018 %T Induction %A Urbaniak, Rafal %A Batens, Diderik %E Hansson, Sven Ove %E Hendricks, Vincent F. %K induction %K logic %K probability %B Handbook of Formal Philosophy %I Springer %@ 978-3-319-77433-6 %G eng %R 10.1007/978-3-319-77434-3 %0 Generic %D 2018 %T Kennissystemen selectief wieden %A Batens, Diderik %E Van Kerkhove, Bart %E François, Karen %E Ducheyne, Steffen %E Allo, Patrick %B Laat ons niet ernstig blijven. Huldeboek voor Jean Paul Van Bendegem %I Academia Press %C Gent, België %P 227–244 %@ 978-94-014-5589-3 %G eng %0 Generic %D 2017 %T Abduction Logics Illustrating Pitfalls Of Defeasible Methods %A Batens, Diderik %E Rafał Urbaniak %E Gillman Payette %X On the one hand this paper offers an introduction to adaptive logics, focussing on properties that are imposed upon adaptive logics by the fact that they explicate defeasible reasoning. On the other hand new adaptive logics of abduction are presented and employed to illustrate those properties. These logics were developed in view of the criticism to existing adaptive logics of abduction. %B Applications of formal philosophy: the road less travelled %S Logic argumentation & reasoning %I Springer %C Berlin %V 14 %P 169–193 %@ 978-3-319-58507-9,331958507X,978-3-319-58505-5 %G eng %R 10.1007/978-3-319-58507-9_8 %0 Generic %D 2017 %T Paradoxen in de vrijmetselarij en de relatie met waarden %A Batens, Diderik %E Rik Pinxten %E Jean Swings %B Kappen aan de ruwe steen %I Academic and Scientific Publishers %C Brussel %P 319–336 %G eng %0 Journal Article %J Humana.Mente Journal of Philosophical Studies %D 2017 %T Pluralism In Scientific Problem Solving. Why Inconsistency Is No Big Deal %A Batens, Diderik %B Humana.Mente Journal of Philosophical Studies %V 32 %P 149–177 %G eng %0 Journal Article %J Studia Logica %D 2016 %T Adaptive Logic Characterizations of Input/output Logic %A Straßer, Christian %A Beirlaen, Mathieu %A Van De Putte, Frederik %X

We translate the unconstrained and constrained input/output-logics from [17, 18] to reflexive modal logics, using adaptive logics for the constrained case. The resulting reformulation has various advantages. First, we obtain a proof-theoretic (dynamic) characterization of input/output logics. Second, we demonstrate that our modal framework gives naturally rise to useful variants. Finally, the modal logics display a gain in expressive power over their original counterparts in the input/output framework.

%B Studia Logica %V 104 %P 869-916 %G eng %N 5 %& 869 %0 Journal Article %J Studia Logica %D 2016 %T Nice Embedding in Classical Logic %A Verdée, Peter %A Batens, Diderik %X

It is shown that a set of semi-recursive logics, including many fragments of CL (Classical Logic), can be embedded within CL in an interesting way. A logic belongs
to the set iff it has a certain type of semantics, called nice semantics. The set includes
many logics presented in the literature. The embedding reveals structural properties of the embedded logic. The embedding turns finite premise sets into finite premise sets. The partial decision methods for CL that are goal directed with respect to CL are turned into partial decision methods that are goal directed with respect to the embedded logics.

%B Studia Logica %P 47-78 %G eng %R 10.1007/s11225-015-9622-3 %0 Journal Article %J Journal of Logic and Computation %D 2016 %T Spoiled for Choice? %A Batens, Diderik %X

The transition from a theory that turned out trivial to a consistent replacement need not proceed in terms of inconsistencies, which are negation gluts. Logics that tolerate gluts or gaps (or both) with respect to any logical symbol may serve as the lower limit for adaptive logics that assign a minimally abnormal consequence set to a given premise set. The same obtains for logics that tolerate a combination of kinds of gluts and gaps. This result runs counter to the obsession with inconsistency that classical logicians and paraconsistent logicians share.
All such basic logics will be systematically reviewed, some variants will be outlined, and the claim will be argued for. While those logics tolerate gluts and gaps with respect to logical symbols, ambiguity logic tolerates ambiguities in non-logical symbols. Moreover, forms of tolerance may be combined, with zero logic as an extreme.\İn the baffling plethora of corrective adaptive logics (roads from trivial theories to consistent replacements), adaptive zero logic turns out theoretically interesting as well as practically useful. On the one hand all meaning becomes contingent, depending on the premise set. On the other hand, precisely adaptive zero logic provides one with an excellent analyzing instrument. For example it enables one to figure out which corrective adaptive logics lead, for a specific trivial theory, to a suitable and interesting minimally abnormal consequence set.

%B Journal of Logic and Computation %V 26 %P 65-95 %G eng %N 1 %R 10.1093/logcom/ext019 %0 Generic %D 2015 %T Explicating ways of consensus-making in science and society: distinguishing the academic, the interface and the meta-consensus %A Kosolosky, Laszlo %A Van Bouwel, Jeroen %E Martini, Carlo %E Boumans, Marcel %X

In this paper, we shed new light on the epistemic struggle between establishing consensus and acknowledging plurality, by explicating different ways of consensus-making in science and society and examining the impact hereof on their field of intersection, i.e. consensus conferences (in particular those organized by the National Institute of Health). We draw a distinction between, what we call, academic and interface consensus, to capture the wide appeal to consensus in existing literature. We investigate such accounts - i.e. Solomon (2007), Beatty & Moore (2010) and Miller (2013) – as to put forth a new understanding of consensus-making, focusing on the meta-consensus. We further defend how (NIH) consensus conferences enable epistemic work, through demands of epistemic adequacy and contestability, contrary to the claim that consensus conferences miss a window for epistemic opportunity (Solomon, 2007). Paying attention to this dynamics surrounding consensus, moreover allows us to illustrate how the public understanding of science and the public use of the ideal of consensus could be well modified.

%B Experts and consensus in social science %I Springer %P 71–92 %G eng %0 Generic %D 2015 %T Private epistemic virtue, public vices: moral responsibility in the policy sciences %A Lefevere, Merel %A Schliesser, Eric %E Martini, Carlo %E Boumans, Marcel %B Experts and consensus in social science %I Springer %P 275–295 %G eng %0 Generic %D 2015 %T Some Adaptive Contributions to Logics of Formal Inconsistency %A Batens, Diderik %E Béziau, Jean-Yves %E Chakraborty, Mihir %E Dutta, Soma %X

Some insights were gained from the study of inconsistency-adaptive logics. The aim of the present paper is to put some of these insight to work for the study of logics of formal inconsistency. The focus of attention are application contexts of the aforementioned logics and their theoretical properties in as far as they are relevant for applications. As the questions discussed are difficult but important, a serious attempt was made to make the paper concise but transparent.

%B New Directions in Paraconsistent Logic %I Springer %P 309 -333 %G eng %0 Generic %D 2015 %T Tutorial on Inconsistency-Adaptive Logics %A Batens, Diderik %E Béziau, Jean-Yves %E Chakraborty, Mihir %E Dutta, Soma %X

This paper contains a concise introduction to a few central features of inconsistency-adaptive logics. The focus is on the aim of the program, on logics that may be useful with respect to applications, and on insights that are central for judging the importance of the research goals and the adequacy of results. Given the nature of adaptive logics, the paper may be read as a peculiar introduction to defeasible reasoning.

%B New Directions in Paraconsistent Logic %I Springer %G eng %0 Generic %D 2015 %T Two, Many, And Differently Many %A Batens, Diderik %E Koslow, Arnold %E Buchsbaum, Arthur %X

This paper is a modest contribution to a universal logic approach to many-valued semantic systems. The main focus is on the relation between such systems and two-valued ones. The matter is discussed for usual many-valued semantic systems. These turn out to exist for more logics than expected. A new type of many-valued semantics is devised and its use illustrated. Truth-functionality has a rather central place in the discussion, which leads to philosophical conclusions.

%B The Road to Universal Logic. Festschrift for the 50th Birthday of Jean-Yves Béziau %I Birkhäuser %C Basel %V II %P 213–242 %G eng %0 Generic %D 2014 %T Adaptive Logics as a Necessary Tool for Relative Rationality. Including a Section on Logical Pluralism %A Batens, Diderik %X

In this paper, I show that adaptive logics are required by my epistemological stand. While doing so, I defy the reader to cope with the problems I am able to cope with.

The last section of the paper contains a defense of a specific form of logical pluralism. Although this section is an integral part of the paper, it may be read separately.

%B Logic, Reasoning and Rationality %I Springer %C Dordrecht %P 1-25 %G eng %0 Generic %D 2014 %T The Consistency of Peano Arithmetic. A Defeasible Perspective %A Batens, Diderik %E Allo, Patrick %E Van Kerkhove, Bart %X

This paper proposes to replace \sys{PA}, Peano Arithmetic, by a theory \sys{APA} defined in terms of (i) a set of axioms that is classically equivalent to the Peano axioms and (ii) a defeasible logic that minimizes inconsistency, viz.\ an inconsistency-adaptive logic. If \sys{PA} is consistent, its set of theorems coincides with the set of \sys{APA}-theorems. If \sys{PA} is inconsistent, \sys{APA} is non-trivial and has the following remarkable property: there is a unique non-standard number that is its own successor and every `desirable' \sys{PA}-theorem is retained if restricted to the other numbers. The restriction can be expressed in the language of arithmetic. And there is much more.

%B Modestly Radical or Radically Modest. Festschrift for Jean Paul Van Bendegem on the Occasion of His 60th Birthday %I College Publications %P 11–59 %G eng %0 Journal Article %J Logic and Logical Philosophy %D 2014 %T Propositional Logic Extended With A Pedagogically Useful Relevant Implication %A Batens, Diderik %X

First and foremost, this paper concerns the combination of classical propositional logic with a relevant implication. The proposed combination is simple and transparent from a proof theoretic point of view and at the same time extremely useful for relating formal logic to natural language sentences. A specific system will be presented and studied, also from a semantic point of view. The last sections of the paper contain more general considerations on combining classical propositional logic with a relevant logic that has all classical theorems as theorems.

%B Logic and Logical Philosophy %V 23 %P 245–276 %G eng %R 10.12775/LLP.2013.024 %0 Generic %D 2013 %T 'Argumentandi modus huius scientiae maximè proprius: ' Guidobaldo's mechanics and the question of mathematical principles %A Van Dyck, Maarten %E Becchi, Antonio %E Bertoloni Meli, Domenico %E Gamba, Enrico %B Guidobaldo del Monte (1545-1607) : theory and practice of the mathematical disciplines from Urbino to Europe %I Edition Open Access %P 9–34 %@ 9783844242836 %G eng %U http://www.edition-open-access.de/media/proceedings/4/Proceedings4.pdf %0 Journal Article %J Metascience %D 2013 %T The ICE-theory of technical functions %A Weber, Erik %A Reydon, Thomas %A Boon, Mieke %A Houkes, Wybo %A Vermaas, Pieter %B Metascience %V 22 %P 23–44 %G eng %R 10.1007/s11016-012-9642-9 %0 Journal Article %J Journal of Philosophical Logic %D 2013 %T An Inconsistency-Adaptive Deontic Logic for Normative Conflicts %A Beirlaen, Mathieu %A Straßer, Christian %A Meheus, Joke %X

We present the inconsistency-adaptive deontic logic \sys{DP}$^r$, a nonmonotonic logic for dealing with conflicts between normative statements. On the one hand, this logic does not lead to explosion in view of normative conflicts. On the other hand, \sys{DP}$^r$ still verifies all intuitively reliable inferences valid in Standard Deontic Logic (\sys{SDL}). \sys{DP}$^r$ interprets a given premise set ‘as normally as possible’ with respect to \sys{SDL}. Whereas some \sys{SDL}-rules are verified unconditionally by \sys{DP}$^r$, others are verified conditionally. The latter are applicable unless they rely on formulas that turn out to behave inconsistently in view of the premises. This dynamic process is mirrored by the proof theory of \sys{DP}$^r$

%B Journal of Philosophical Logic %V 42 %P 285–315 %G eng %R http://dx.doi.org/10.1007/s10992-011-9221-3 %0 Journal Article %J Journal of Logic and Computation %D 2013 %T Non-monotonic reasoning with normative conflicts in multi-agent deontic logic %A Beirlaen, Mathieu %A Straßer, Christian %X

We present two multi-agent deontic logics that consistently accommodate various types of normative conflicts. Its language features modal operators for obligation and permission, and for the realization of individual and collective actions. The logic is non-classical since it makes use of a paraconsistent and paracomplete negation connective. Moreover, it is non-monotonic due to its definition within the adaptive logics framework for defeasible reasoning. The logic is equipped with a defeasible proof theory and semantics.

%B Journal of Logic and Computation %V 24 %P 1179–1207 %G eng %R 10.1093/logcom/exs059 %0 Journal Article %J JOURNAL OF APPLIED LOGIC %D 2013 %T Two adaptive logics of norm-propositions %A Beirlaen, Mathieu %A Straßer, Christian %X

We present two defeasible logics of norm-propositions (statements about norms) that (i) consistently allow for the possibility of normative gaps and normative conflicts, and (ii) map each premise set to a sufficiently rich consequence set. In order to meet (i), we define the logic LNP, a conflict- and gap-tolerant logic of norm-propositions capable of formalizing both normative conflicts and normative gaps within the object language. Next, we strengthen LNP within the adaptive logic framework for non-monotonic reasoning in order to meet (ii). This results in the adaptive logics LNPrLNPr and LNPmLNPm, which interpret a given set of premises in such a way that normative conflicts and normative gaps are avoided ‘whenever possible’. LNPrLNPr and LNPmLNPm are equipped with a preferential semantics and a dynamic proof theory.

%B JOURNAL OF APPLIED LOGIC %V 11 %P 147–168 %G eng %R http://dx.doi.org/10.1016/j.jal.2013.02.001 %0 Generic %D 2012 %T Bedoelingen en principes. Een onverwachte relatie %A Batens, Diderik %E Claes, Tom %B Door Denken en Doen. Essays bij het Werk van Ronald Commers %I Academia Press %C Gent %P 93–106 %G eng %0 Generic %D 2012 %T Can economics become a purely experimental science? A comparative study %A Weber, Erik %E Aerts, Diederik %E Broekaert, Jan %E D'Hooghe, Bart %E Note, Nicole %X

The role of experiments in economics is increasing. This paper deals with a philosophical question that is raised by this evolution: can economics become a purely experimental science? I answer this question by comparing economics with a branch of biomedical science.

%B Worldviews, science and us : bridging knowledge and its implications for our perspectives on the world %I World Scientific Publishing Company %@ 9789814383073 %G eng %U http://www.worldscibooks.com/general/8341.html %0 Generic %D 2012 %T History and Philosophy of Science: From Peaceful Coexistence to Golden Age of Interdisciplinarity? %A Ducheyne, Steffen %E Aerts, Diederik %E Broekaert, Jan %E D'Hooghe, Bart %E Note, Nicole %B Worldviews, Science and Us: Bridging Knowledge and its Implications for our Perpectives on the World. %I World Scientific Publishing Company %C Singapore %P 26-36 %G eng %0 Generic %D 2012 %T An Interdisciplinary Focus on the Concept of Causation: What philosophy can learn from psychology %A De Vreese, Leen %E Aerts, Diederik %E Broekaert, Jan %E D'Hooghe, Bart %E Note, Nicole %X

In philosophy of science, it is still a mainstream practice to search for the `truth' about fundamental scientific concepts in isolation, blind to knowledge achieved in other domains of science. I focus on the topic of causation. I argue that it is worthwhile for philosophy of science to leave its metaphysical tower in order to pick up knowledge from other domains where empirical research on causal reasoning is carried out, such as psychology. I will demonstrate what the psychologist Peter White's theory, on the origin and development of causal reasoning, can impart to philosophy of causation. It concerns different but interre- lated subjects with respect to the philosophy of causation: conceptual pluralism, a core causal concept of causation, the analysis of \what cau- sation is", epistemological pluralism, causation as a secondary quality and weak causal realism. The divide between metaphysical and epis- temological approaches to causation|and hence between philosophy and psychology|may be much smaller than is often presupposed. Keywords: philosophy of causation, developmental psychology, causal pluralism, interdisciplinarity

%B Worldviews, Science and Us: Bridging Knowledge and its Implications for our Perpectives on the World. %I World Scientific Publishing Company %C Singapore %P 55-71 %G eng %0 Journal Article %J Logique et Analyse %D 2012 %T It might have been Classical Logic %A Batens, Diderik %X

In this paper, a propositional logic Q is presented. This logic is more attractive than classical propositional logic P for explicating actual proofs. Moreover, while Q and P assign the same consequence set to consistent premise sets, Q assigns a sensible and non-trivial consequence set to in- consistent premise sets.

%B Logique et Analyse %V 55 %P 241–279 %G eng %0 Generic %D 2012 %T Metaphysics and Cinema %A Christiaens, Wim %E Aerts, Diederik %E Broekaert, Jan %E D'Hooghe, Bart %E Note, Nicole %B Worldviews, Science and Us: Bridging Knowledge and its Implications for our Perpectives on the World. %I World Scientific Publishing Company %C Singapore %P 118-141 %G eng %0 Conference Proceedings %B 11th International Conference on Deontic Logic in Computer Science, DEON2012 %D 2012 %T An Andersonian deontic logic with contextualized sanctions %A Straßer, Christian %A Beirlaen, Mathieu %E Agotnes, Thomas %E Broersen, Jan %E Elgesem, Dag %X

We present a refinement of Anderson's reduction of deontic logic to modal logic with only alethic modalities. The refined proposal contextualizes the Andersonian sanction constant s by replacing it with a unary sanction operator S that is dependent on the concrete normative requirement that is violated. A formula S B is then for instance interpreted as ldquo B causes a sanctionrdquo or as ldquo B provides a reason for (the applicability of) a sanctionrdquo. Due to its modified sanction operator, the resulting logic DSL invalidates some instances of the inheritance principle. This gives rise to new interesting features. For instance, DSL consistently allows for the presence of conflicting obligations. Moreover, it provides novel insights in various central `paradoxes' in deontic logic such as the Ross paradox, the paradox of the good Samaritan, and Forrester's `gentle murderer' paradox.

%B 11th International Conference on Deontic Logic in Computer Science, DEON2012 %I Springer %P 151-169 %@ 9783642315695 %G eng %0 Report %D 2012 %T A short history of small machines %A De Mol, Liesbeth %A Bullynck, Maarten %X

One of the most famous results of Alan M. Turing is the so-called universal Tur- ing machine (UTM). Its in uence on (theoretical) computer science can hardly be overestimated. The operations of this machine are of a most elementary na- ture but nonetheless considered to capture all the (human) processes that can be carried out in computing a number. This kind of elementary machine ts into a tradition of `logical minimalism' that looks for simplest sets of operations or axioms. It is part of the more general research programme into the foundations of mathematics and logic that was carried out in the beginning of the 20th cen- tury. In the 1940s and 1950s, however, this tradition was rede ned in the context of `computer science' when computer engineers, logicians and mathematicians re-considered the problem of small(est) and/or simple(st) machines in the con- text of actual engineering practices. This paper looks into this early history of research on small symbolic and physical machines and tie it to this older tradi- tion of logical minimalism. Focus will be on how the transition and translation of symbolic machines into real computers integrates minimalist philosophies as parts of more complex computer design strategies. This contextualizes Turing's machines at the turn from logic to machines.

%B The Turing Centenary Conference CiE 2012: How the World Computes %G eng %0 Journal Article %J Logique et Analyse %D 2012 %T Tolerating Deontic Conflicts by Adaptively Restricting Inheritance %A Straßer, Christian %A Meheus, Joke %A Beirlaen, Mathieu %X

In order to deal with the possibility of deontic conflicts Lou Goble developed a group of logics DPM that are characterized by a restriction of the inheritance principle. While they approximate the deductive power of standard deontic logic, they do so only if the user adds certain statements to the premises. By adaptively strengthening the DPM logics, this paper presents logics that overcome this shortcoming. Furthermore, they are capable of modeling the dynamic and defeasible aspect of our normative reasoning by their dynamic proof theory. This way they enable us to have a better insight in the relations between obligations and thus to localize deontic conflicts.

%B Logique et Analyse %V 219 %P 477-506 %G eng %0 Generic %D 2012 %T Tolerating Normative Conflicts in Deontic Logic. %A Beirlaen, Mathieu %I Ghent University %8 September 13 %9 phd %1

Joke Meheus and Christian Straßer

%0 Generic %D 2012 %T Towards More Conflict-Tolerant Deontic Logics %A Beirlaen, Mathieu %E Van Kerkhove, Bart %E Libert, Thierry %E Vanpaemel, Geert %E Marage, Pierre %X

In Ethical Consistency, Bernard Williams vindicated the possibility of moral conflicts; he proposed to consistently allow for the presence of such conflicts within the logic of ought. In determining the nature of moral conflict, Williams stressed its contingency. In this paper, Williams’ characterization of moral conflict is defended. However, Williams’ solution for consistently allowing for such conflicts within the logic of ought is shown to be too crude. Whereas Williams rejects all applications of the agglomeration rule in the logic of ought, it is shown that a more sophisticated approach is needed. An alternative solution is presented in which the application of the agglomeration rule is made conditional upon the principle that" oughtimplies can."

%B Logic, Philosophy and History of Science in Belgium II %I Koninklijke Vlaamse Academie van België %C Brussel %P 1-8 %G eng %0 Journal Article %J Tijdschrift voor Filosofie %D 2012 %T Understanding Human Agency, by Erasmus Mayr (review; in Dutch) %A Beirlaen, Mathieu %B Tijdschrift voor Filosofie %V 2 %P 383-385 %G eng %0 Generic %D 2012 %T A unifying framework for reasoning about normative conflicts %A Beirlaen, Mathieu %E Pelis, Michal %E Puncochar, Vit %X

First, two context-dependent desiderata are presented for devising calculi of deontic logic that can consistently accommodate normative conflicts. Conflict-tolerant deontic logics (CTDLs) can be evaluated by their treatment of the trade-off between these desiderata. Next, it is argued that CTDLs defined within the standard format for adaptive logics are particularly good at overcoming this trade-off.

%B The logica yearbook 2011 %I College Publications %P 1–14 %@ 9781848900714 %G eng %0 Journal Article %J Tijdschrift voor Filosofie %D 2011 %T Aristotle's Modal Proofs, by Adriane Rini (review; in Dutch) %A Beirlaen, Mathieu %B Tijdschrift voor Filosofie %V 4 %P 749-751 %G eng %0 Journal Article %J Theoretical and applied ethics %D 2011 %T Ethical consistency and the logic of ought %A Beirlaen, Mathieu %X

In Ethical Consistency, Bernard Williams vindicated the possibility of moral conflicts; he proposed to consistently allow for the presence of such conflicts within the logic of 'ought'. In determining the nature of moral conflict, Williams stressed its contingency. In this paper, Williams’ characterization of moral conflict is defended. However, Williams’ solution for consistently allowing for such conflicts within the logic of 'ought' is shown to be too crude. Whereas Williams rejects all applications of the agglomeration rule in the logic of 'ought', it is shown that a more sophisticated approach is needed. An alternative solution is presented in which the application of the agglomeration rule is made conditional upon the principle that ˝ought implies can˝.

%B Theoretical and applied ethics %V 1 %P 45–51 %G eng %0 Journal Article %J Studia Logica %D 2011 %T Logics for Qualitative Inductive Generalization %A Batens, Diderik %X

The paper contains a survey of (mainly unpublished) adaptive logics of inductive generalization. These defeasible logics are precise formulations of certain methods.\\ Some attention is also paid to ways of handling background knowledge, introducing mere conjectures, and the research guiding capabilities of the logics.

%B Studia Logica %V 97 %P 61–80 %G eng %R 10.1007/s11225-010-9297-8 %0 Conference Proceedings %B 12th International Workshop on Computational Logic in Multi-Agent Systems (CLIMA XII) %D 2011 %T A paraconsistent multi-agent framework for dealing with normative conflicts %A Beirlaen, Mathieu %A Straßer, Christian %E Leite, Joao %E Torroni, Paolo %E Agotnes, Thomas %E Boella, Guido %E van der Torre, Leon %X

In a multi-agent deontic setting, normative conflicts can take a variety of different logical forms. In this paper, we present a very general characterization of such conflicts, including both intra- and inter-agent normative conflicts, conflicts between groups of agents, conflicts between obligations and permissions, and conflicts between contradictory norms. In order to account for the consistent possibility of this wide variety of conflict-types, we present a paraconsistent deontic logic, i.e. a logic that invalidates the classical principle of non-contradiction. Next, we strengthen this logic within the adaptive logics framework for defeasible reasoning. The resulting inconsistency-adaptive deontic logic interprets a given set of norms 'as consistently as possible'.

%B 12th International Workshop on Computational Logic in Multi-Agent Systems (CLIMA XII) %I Springer %P 312-329 %@ 9783642223587 %G eng %U http://dx.doi.org/10.1007/978-3-642-22359-4 %0 Journal Article %J Philosophy of Science %D 2011 %T Where the design argument goes wrong: auxiliary assumptions and unification %A Boudry, Maarten %A Leuridan, Bert %X

Sober (2008) has reconstructed the biological design argument in the framework of likelihoodism, purporting to demonstrate that it is defective for intrinsic reasons. We argue that Sober’s restrictions on the introduction of auxiliary hypotheses is too restrictive, as it commits him to rejecting types of everyday reasoning that are clearly valid. Our account shows that the design argument fails, not because it is intrinsically untestable, but because it clashes with the empirical evidence and fails to satisfy certain theoretical desiderata (in particular, unification). Likewise, Sober’s critique of the arguments from imperfections and from evil against design is off the mark.

%B Philosophy of Science %V 78 %P 558–578 %G eng %U http://dx.doi.org/10.1086/661753 %R http://dx.doi.org/10.1086/661753 %0 Journal Article %J Logic and logical philosophy %D 2010 %T An adaptive logic framework for conditional obligations and deontic dilemmas %A Straßer, Christian %E Tanaka, Koji %E Berto, Francesco %E Mares, Edwin %E Paoli, Francesco %B Logic and logical philosophy %V 19 %P 95–128 %G eng %0 Conference Paper %B Proceedings of the 10th International Conference on Deontic Logic in Computer Science (DEON 2010) %D 2010 %T Avoiding Deontic Explosion by Contextually Restricting Aggregation %A Meheus, Joke %A Beirlaen, Mathieu %A Van De Putte, Frederik %E Governatori, Guido %E Sartor, Giovanni %X

In this paper, we present an adaptive logic for deontic conflicts, called \sys{P2.1}$^r$, that is based on Goble's logic \sys{SDL}$a$\sys{P}$e$–-a bimodal extension of Goble's logic \sys{P} that invalidates aggregation for all \emph{prima facie} obligations. The logic \sys{P2.1}$^r$ has several advantages with respect to \sys{SDL}$a$\sys{P}$e$. For consistent sets of obligations it yields the same results as Standard Deontic Logic and for inconsistent sets of obligations, it validates aggregation ``as much as possible''. It thus leads to a richer consequence set than \sys{SDL}$a$\sys{P}$e$. The logic \sys{P2.1}$^r$ avoids Goble's criticisms against other non-adjunctive systems of deontic logic. Moreover, it can handle all the `toy examples' from the literature as well as more complex ones.

%B Proceedings of the 10th International Conference on Deontic Logic in Computer Science (DEON 2010) %I Springer %C Dordrecht %G eng %R http://dx.doi.org/10.1007/978-3-642-14183-6\_12 %0 Journal Article %J Logic and Logical Philosophy %D 2010 %T Inconsistency-adaptive modal logics: on how to cope with modal inconsistency %A Lycke, Hans %E Tanaka, Koji %E Berto, Francesco %E Mares, Edwin %E Paoli, Francesco %X

In this paper, I will characterize a new class of inconsistency–adaptive logics, namely inconsistency–adaptive modal logics. These logics cope with inconsistencies in a modal context. More specifically, when faced with inconsistencies, inconsistency–adaptive modal logics avoid explosion, but still allow the derivation of sufficient consequences to adequately explicate the intended part of human reasoning.

%B Logic and Logical Philosophy %V 19 %P 31–61 %G eng %U http://www.logika.umk.pl/llp/pi.html %0 Journal Article %J The Reasoner %D 2010 %T Report LRR10: Logic, reasoning and rationality %A Beirlaen, Mathieu %A Gauderis, Tjerk %A Gervais, Raoul %A Kosolosky, Laszlo %B The Reasoner %V 4 %P 165–166 %G eng %U http://www.kent.ac.uk/secl/philosophy/jw/TheReasoner/vol4/TheReasoner-4(11).pdf %0 Journal Article %J Archive for Mathematical Logic %D 2010 %T Setting-up early computer programs: D. H. Lehmer's ENIAC computation %A Bullynck, Maarten %A De Mol, Liesbeth %E Beckmann, Arnold %E Dimitracopoulos, Costas %E Löwe, Benedikt %X

A complete reconstruction of Lehmer's ENIAC set-up for computing the exponents of p modulo two is given. This program served as an early test program for the ENIAC (1946). The reconstruction illustrates the difficulties of early programmers to find a way between a man operated and a machine operated computation. These difficulties concern both the content level (the algorithm) and the formal level (the logic of sequencing operations).

%B Archive for Mathematical Logic %V 49 %P 123–146 %G eng %U http://dx.doi.org/10.1007/s00153-009-0169-8 %0 Report %D 2010 %T Towards more conflict-tolerant deontic logics by relaxing the interdefinability between obligations and permissions %A Straßer, Christian %A Beirlaen, Mathieu %X

While conflict-tolerant logics (CTDLs) usually allow for obligation- obligation conflicts, they fall short of tolerating obligation-permission con- flicts (OP-conflicts) of the type OA &\#8743; P&\#172; A. Moreover, for the sake of conflict-tolerance these logics usually do not validate the very intuitive principle (D), OA &\#8835; PA. We demonstrate in this paper that by relaxing the interdefinability between obligations and permission PA =df &\#172;O&\#172;A that is characteristic for most deontic logics, the logics get more conflict-tolerant since they allow for OP-conflicts. Moreover, this way they can be equipped with (D) without the need to sacrifice conflict-tolerance. In this paper we offer a generic procedure that transforms a given CTDL into a logic that tolerates OP-conflicts and validates (D).

%G eng %0 Journal Article %J Algemeen Nederlands Tijdschrift voor Wijsbegeerte %D 2010 %T Waar stoppen? %A Batens, Diderik %B Algemeen Nederlands Tijdschrift voor Wijsbegeerte %V 102 %P 196–198 %G eng %0 Generic %D 2010 %T William Harvey en de ontdekking van de bloedsomloop. %A De Mey, Tim %A Provijn, Dagmar %E Van Speybroeck, Linda %E Braeckman, Johan %B Fascinerend Leven. Markante Figuren en Ideeën uit de Geschiedenis van de Biologie. %I Nieuwezijds %C Amsterdam %G eng %0 Generic %D 2009 %T Adaptive Cn Logics %A Batens, Diderik %E Carnielli, Walter A. %E Coniglio, Marcelo E. %E Loffredo D'Ottaviano, Itala M. %X

This paper solves an old problem: to devise decent inconsistency-adaptive logics that have the \C{n} logics as their lower limit. Two kinds of logics are presented. Those of the first kind offer a maximally consistent interpretation of the premise set in as far as this is possible in view of logical considerations. At the same time, they indicate at which points further choices may be made on extra-logical grounds. The logics of the second kind allow one to introduce those choices in a defeasible way and handle them.

%B The Many Sides of Logic %I College Publications %C London %P 27–45 %G eng %0 Generic %D 2009 %T La métamorphose graçe au cinèma. %A Christiaens, Wim %E Tatham, Anne-Marie %E Bonnecase, Denis %B La métamorphose: définition, formes et thèmes %I Gérard Monfort Editeur %G eng %0 Generic %D 2009 %T Towards a Dialogic Interpretation of Dynamic Proofs %A Batens, Diderik %E Dégremont, Cédric %E Keiff, Laurent %E Rückert, Helge %X

The main result presented in this paper concerns a dialogic or game-theoretical interpretation of dynamic proofs. Dynamic proofs in themselves do not form a demonstration of the derivability of their last formula from a given premise set. Apart from the proof, such a demonstration requires a specific metalevel argument. In a natural and appealing form, the metalevel argument is phrased in terms of the existence of a winning strategy for the proponent.\par The aforementioned point is presented in terms of an approach that is in a sense Hilbertian and anti-Tarskian: the characterization of logical inference in terms of types of proofs, rather than in terms of properties of the consequence relation.

%B Dialogues, Logics and Other Strange Things. Essays in Honour of Shahid Rahman %I College Publications %C London %P 27–51 %G eng %0 Journal Article %J Logique et Analyse %D 2009 %T On the Transparency of Defeasible Logics: Equivalent Premise Sets, Equivalence of Their Extensions, and Maximality of the Lower Limit %A Batens, Diderik %A Straßer, Christian %A Verdée, Peter %X

For Tarski logics, there are simple criteria that enable one to conclude that two premise sets are equivalent. We shall show that the very same criteria hold for adaptive logics, which is a major advantage in comparison to other approaches to defeasible reasoning forms.
A related property of Tarski logics is that the extensions of equivalent premise sets with the same set of formulas are equivalent premise sets. This does not hold for adaptive logics. However a very similar criterion does.
We also shall show that every monotonic logic weaker than an adaptive logic is weaker than the lower limit logic of the adaptive logic or identical to it. This highlights the role of the lower limit for settling the adaptive equivalence of extensions of equivalent premise sets.

%B Logique et Analyse %V 207 %P 281–304 %G eng %0 Journal Article %J Synthese %D 2009 %T Yes Fellows, Most Human Reasoning is Complex %A Batens, Diderik %A De Clercq, Kristof %A Verdée, Peter %A Meheus, Joke %X

This paper answers the philosophical contentions defended in Horsten and Welch (2007, Synthese, 158, 41-60). It contains a description of the standard format of adaptive logics, analyses the notion of dynamic proof required by those logics, discusses the means to turn such proofs into demonstrations, and argues that, notwithstanding their formal complexity, adaptive logics are important because they explicate an abundance of reasoning forms that occur frequently, both in scientific contexts and in common sense contexts.

%B Synthese %V 166 %P 113–131 %G eng %U http://dx.doi.org/10.1007/s11229-007-9268-4 %0 Journal Article %J The Reasoner %D 2008 %T Graham Priest and Diderik Batens Interview Each Other %A Priest, Graham %A Batens, Diderik %B The Reasoner %V 2 %P 2–4 %G eng %0 Generic %D 2008 %T Middeleeuwse en Arabische Wijsbegeerte %A De Mey, Tim %E Vermeersch, Etienne %E Braeckman, Johan %B De rivier van Herakleitos: Een eigenzinnige visie op de wijsbegeere %I Houtekiet %P 93–101 %@ 978 90 8924 035 4 %G eng %U http://lib.ugent.be/catalog/pug01:683245 %0 Generic %D 2008 %T On Possibilities and Thought Experiments %A Batens, Diderik %E Almeder, Robert %X

This paper concerns two related recent books by Nicholas Rescher, Imagining Irreality on possibilities and What If? on thought experiments. Apart from an expository part, the present contribution consist on the one hand of some proposed elaborations, especially of two technical points, and on the other hand of some discussion concerning points where I am in doubt about Rescher's precise stand and of some suggestions for further research.

%B Rescher Studies. A Collection of Essays on the Philosophical Work of Nicholas Rescher %I Ontos Verlag %C Frankfurt %P 29–57 %G eng %0 Journal Article %J Dialectica %D 2008 %T Relata-specific relations: a response to Vallicella %A Wieland, Jan Willem %A Betti, Arianna %X

According to Vallicella's 'Relations, Monism, and the Vindication of Bradley's Regress' (2002), if relations are to relate their relata, some special operator must do the relating. No other options will do. In this paper we reject Vallicella's conclusion by considering an important option that becomes visible only if we hold onto a precise distinction between the following three feature-pairs of relations: internality/externality, universality/particularity, relata-specificity/relata-unspecificity. The conclusion we reach is that if external relations are to relate their relata, they must be relata-specific (and no special operator is needed). As it eschews unmereological complexes, this outcome is of relevance to defenders of the extensionality of composition.

%B Dialectica %V 62 %P 509–524 %G eng %U http://dx.doi.org/10.1111/j.1746-8361.2008.01167.x %0 Generic %D 2008 %T The Role of Logic in Philosophy of Science %A Batens, Diderik %E Psillos, Stathis %E Curd, Martin %B The Routledge Companion to Philosophy of Science %I Routledge %C London, New York %P 47–57 %G eng %0 Conference Paper %B Logic and Theory of Algorithms %D 2008 %T A week-end off: the first extensive number-theoretical computation on the ENIAC %A De Mol, Liesbeth %A Bullynck, Maarten %E Beckmann, Arnold %E Dimitracopoulos, Costas %E Löwe, Benedikt %X

The first extensive number-theoretical computation run on the ENIAC, is reconstructed. The problem, computing the exponent of 2 modulo a prime, was set up on the ENIAC during a week-end in July 1946 by the number-theorist D.H. Lehmer, with help from his wife Emma and John Mauchly. Important aspects of the ENIAC's design are presented-and the reconstruction of the implementation of the problem on the ENIAC is discussed in its salient points.

%B Logic and Theory of Algorithms %I Springer Verlag %@ 978-3-540-69405-2 %G eng %R 10.1007/978-3-540-69407-6_19 %0 Generic %D 2007 %T Content Guidance in Formal Problem Solving Processes %A Batens, Diderik %E Pombo, Olga %E Gerner, Alexander %X

In this paper, a formal framework to problem-solving processes is presented. The framework is not complete. Nevertheless, even its present sophistication allows one to see that it is promising.\par The framework demonstrably allows one to understand scientific change as content-guided. It will be argued that a formal framework is required in order to make definite and precise statements about the content-guided aspects of scientific problem solving.

%B Abduction and the Process of Scientific Discovery %I Centro de Filosofia das Ciências da U. de Lisboa %C Lisboa %P 121–156 %G eng %0 Journal Article %J Logica Universalis %D 2007 %T A Universal Logic Approach to Adaptive Logics %A Batens, Diderik %X

In this paper, adaptive logics are studied from the viewpoint of universal logic (in the sense of the study of common structures of logics). The common structure of a large set of adaptive logics is described. It is shown that this structure determines the proof theory as well as the semantics of the adaptive logics, and moreover that most properties of the logics can be proved by relying solely on the structure, viz. without invoking any specific properties of the logics themselves.

%B Logica Universalis %V 1 %P 221-242 %G eng %0 Report %D 2006 %T An Adaptive Characterization of Signed Systems for Paraconsistent Reasoning %A Batens, Diderik %A Meheus, Joke %A Provijn, Dagmar %X

In this paper we characterize the six (basic) signed systems from \cite{B&S:sspr} in terms of adaptive logics. We prove the characterization correct and show that it has a number of advantages.

%G eng %0 Conference Paper %B Logica 2005 Yearbook %D 2006 %T Belief Revision in Constructive Type Theory %A Primiero, Giuseppe %E Bilkova, M %E Tomala, O %B Logica 2005 Yearbook %I Filosofia Publisher %G eng %0 Generic %D 2006 %T A Diagrammatic Proof Search Procedure as Part of a Formal Approach to Problem Solving %A Batens, Diderik %E Magnani, Lorenzo %X

This paper aims at describing a goal-directed and diagrammatic method for proof search. The method (and one of the logics obtained by it) is particularly interesting in the context of formal problem solving. A typical property is that it consists of attempts to justify so-called bottom boxes by means of premise elements (diagrammatic elements obtained from premises) and logical elements. Premises are not preprocessed, whence most premises lead to a variety of premise elements.

%B Model Based Reasoning in Science and Engineering. Cognitive Science, Epistemology, Logic %I King's College Publications %P 265–284 %G eng %0 Journal Article %J Logic Journal of the IGPL %D 2006 %T A Formal Logic for Abductive Reasoning %A Meheus, Joke %A Batens, Diderik %X

This paper presents and illustrates a formal logic for the abduction of singular hypotheses. The logic has a semantics and a dynamic proof theory that is sound and complete with respect to the semantics. The logic presupposes that, with respect to a specific application, the set of explananda and the set of possible explanantia are disjoint (but not necessarily exhaustive). Where an explanandum can be explained by different explanantia, the logic allows only for the abduction of their disjunction.

%B Logic Journal of the IGPL %V 14 %P 221–236 %G eng %R http://dx.doi.org/1854/5210 %0 Journal Article %J Logic and Philosophy of Science %D 2006 %T On a Logic of Induction %A Batens, Diderik %X

In this paper, I present a simple and straightforward logic of induction: a consequence relation characterized by a proof theory and a semantics. This system will be called LI. The premises will be restricted to, on the one hand, a set of empirical data and, on the other hand, a set of background generalizations. Among the consequences will be generalizations as well as singular statements, some of which may serve as predictions and explanations.

%B Logic and Philosophy of Science %V IV %P 3–32 %G eng %0 Conference Paper %B Proceedings of the International Conference on 21st Century Information Technology in Mathematics Education %D 2006 %T The Methodological Relevance of the History of Mathematics for Mathematics Education %A Heeffer, Albrecht %E Dhompongsa, G %E Bhatti , F %E Kitson , Q %X

Mathematics education benefits from an integration of the history of mathematics within the mathematics curriculum. We provide three basic arguments for such integration. The first is epistemological and addresses a contextual view on mathematical knowledge. The second concerns the phylogenic aspects of the development of mathematics. Conceptual difficulties with teaching children mathematics often correspond with historical periods of conceptual crisis in mathematics. A third, historical argument, draws on the vast repository of experience in mathematics education. We provide examples for each of these arguments from the history of algebra.

%B Proceedings of the International Conference on 21st Century Information Technology in Mathematics Education %G eng %0 Generic %D 2006 %T Narrowing Down Suspicion in Inconsistent Premise Sets %A Batens, Diderik %E Malinowski, Jacek %E Pietruszczak, Andrzej %X

Inconsistency-adaptive logics isolate the inconsistencies that are derivable from a premise set, and restrict the rules of Classical Logic only where inconsistencies are involved. From many inconsistent premise sets, disjunctions of contradictions are derivable no disjunct of which is itself derivable. Given such a disjunction, it is often justified to introduce new premises that state, with a certain degree of confidence, that some of the disjuncts are false. This is an important first step on the road to consistency: it narrows down suspicion in inconsistent premise sets and hence locates the real problems among the possible ones. In this paper I present two approaches for handling such new premises in the context of the original premises. The first approach may apparently be combined with all paraconsistent logics. The second approach does not have the same generality, but is decidedly more elegant.

%B Essays in Logic and Ontology. %S Poznan Studies in the Philosophy of Science and the Humanities %I Rodopi %C Amsterdam/New York %V 91 %P 185–209 %G eng %0 Journal Article %J Journal of Applied Logic %D 2005 %T A Procedural Criterion for Final Derivability in Inconsistency-Adaptive Logics %A Batens, Diderik %X

This paper concerns a (prospective) goal directed proof procedure for the propositional fragment of the inconsistency-adaptive logic ACLuN1. At the propositional level, the procedure forms an algorithm for final derivability. If extended to the predicative level, it provides a \emph{criterion} for final derivability. This is essential in view of the absence of a positive test. The procedure may be generalized to all flat adaptive logics.

%B Journal of Applied Logic %V 3 %P 221–250 %G eng %0 Journal Article %J Synthese %D 2005 %T The Theory of the Process of Explanation Generalized to Include the Inconsistent Case %A Batens, Diderik %X

This paper proposes a generalization of the theory of the process of explanation to include consistent as well as inconsistent situations. The generalization is strong, for example in the sense that, if the background theory and the initial conditions are consistent, it leads to precisely the same results as the theory from the lead paper \cite{H&H:tpe}. The paper presupposes (and refers to arguments for the view that) inconsistencies constitute problems and that scientists try to resolve them.

%B Synthese %V 143 %P 63–88 %G eng %R 10.1007/s11229-005-3114-3 %0 Journal Article %J Logique et Analyse %D 2004 %T The Basic Inductive Schema, Inductive Truisms, and the Research-Guiding Capacities of the Logic of Inductive Generalization %A Batens, Diderik %X

The aim of this paper is threefold. First, the sometimes slightly messy application of the conditional rule RC of the logic of inductive general- ization is clariØed by reducing this rule to a so-called basic schema BS. Next, some common truisms about inductive generalization are shown to be mistaken, but are also shown to be valid in special cases. Finally, and most importantly, it is shown that applications of the adaptive logic of inductive generalization to sets of data, possibly in the presence of background knowledge, invokes certain empirical tests and certain theo- retically justiØed defeasible conjectures, which in a sensible way increase one's empirical and theoretical knowledge about a given domain.

%B Logique et Analyse %V 47 %P 53–84 %G eng %0 Generic %D 2004 %T The Need for Adaptive Logics in Epistemology %A Batens, Diderik %E Rahman, Shahid %E Symons, John %E Gabbay, Dov M. %E Van Bendegem, Jean Paul %X

After it is argued that philosophers of science have lost their interest in logic because they applied the wrong type of logics, examples are given of the forms of dynamic reasoning that are central for philosophy of science and epistemology. Adaptive logics are presented as a means to understand and explicate those forms of reasoning. All members of a specific (large) set of adaptive logics are proved to have a number of properties that warrant their formal decency and their suitability with respect to understanding and explicating dynamic forms of reasoning. Most of the properties extend to other adaptive logics.

%B Logic, Epistemology, and the Unity of Science %I Kluwer %C Dordrecht %P 459–485 %G eng %0 Journal Article %J Logique et Analyse %D 2004 %T A Rich Paraconsistent Extension of Full Positive Logic %A Batens, Diderik %A De Clercq, Kristof %X

In the present paper we devise and study the most natural predicative extension of Schütte's maximally paraconsistent logic. With some of its large fragments, this logic, \sys{CLuNs}, forms the most popular family of paraconsistent logics. Devising the system involves some entanglements, and the system itself raises several interesting questions. As the system and fragments were studied by other authors, we restrict our attention to results that we have not seen in press.

%B Logique et Analyse %V 47 %P 227–257 %G eng %0 Journal Article %J Algemeen Nederlands Tijdschrift voor Wijsbegeerte %D 2003 %T Adaptieve Logica's. Een precieze benadering van vertrouwde maar door logici verwaarloosde redeneervormen %A Batens, Diderik %B Algemeen Nederlands Tijdschrift voor Wijsbegeerte %V 95 %P 174–189 %G eng %0 Journal Article %J Logic and Logical Philosophy %D 2003 %T Criteria Causing Inconsistencies. General Gluts as Opposed to Negation Gluts %A Batens, Diderik %X

This paper studies the question: how should one handle inconsistencies that derive from the inadequacy of the criteria by which one approaches the world. I compare the approaches underlying several inconsistency-adaptive logics. I consider the Rescher–Manor consequence relations as well as adaptive logics defined from CLuN, CLuNs, LP, AN, and AL. The adaptive systems defined from CLuN appear to be superior to the others. They isolate inconsistencies rather than spreading them, and at the same time allow for genuine deductive steps from inconsistent and mutually inconsistent premises.

Nevertheless, the systems based on CLuN introduce an asymmetry between negated and non-negated formulas that seems hard to justify. To clarify and understand the source of the problem, the epistemological presuppositions of CLuN, viz. inadequate criteria, are investigated. This leads to a new type of paraconsistent logic that involves gluts with respect to all other logical constants. The larger part of the paper is devoted to this logic, to the adaptive logics defined from it, and to the study of the properties of these systems.

While this resulting logics are sensible and display interesting features, the search for variants of the justification leads to an unexpected justification for CLuN.

%B Logic and Logical Philosophy %V 11/12 %P 5–37 %G eng %0 Generic %D 2003 %T A Formal Approach to Problem Solving %A Batens, Diderik %E Delrieux, Claudio %E Legris, Javier %B Computer Modeling of Scientific Reasoning %I Universidad Nacional Del Sur. EDIUNS %C Bahia Blanca, Argentinia %P 15–26 %G eng %0 Report %D 2003 %T A Paraconsistent Proof Procedure Based on Classical Logic %A Batens, Diderik %X

Apparently Ex Falso Quodlibet (or Explosion) cannot be isolated within CL (Classical Logic); if Explosion has to go, then so have other inference rules, for example either Addition or Disjunctive Syllogism. This cer- tainly holds according to the standard abstract view on logic. However, as I shall show, it does not hold if a logic is defined by a procedure-a set of instructions to obtain a proof (if there is one) of a given conclusion from a given premise set. In this paper I present a procedure pCL¡ that defines a logic CL¡|a function assigning a consequence set to any premise set. Anything deriv- able by CL from a consistent premise set ¡ is derivable from ¡ by CL¡. If ¡ is (CL-)inconsistent, pCL¡ enables one to demonstrate this (by de- riving a contradiction from ¡). The logic CL¡ validates applications of Disjunctive Syllogism as well as applications of Addition. Nevertheless, this logic is paraconsistent as well as (in a specific sense) relevant. pCL¡ derives from an intuitively attractive proof search procedure. A characteristic semantics for CL¡ will be presented and the central prop- erties of the logic will be mentioned. CL¡ shows that (and clarifies how) adherents of CL may obtain non-trivial consequence sets for inconsistent theories.

%G eng %0 Journal Article %J Logic and Logical Philosophy %D 2003 %T Some Adaptive Logics for Diagnosis %A Batens, Diderik %A Meheus, Joke %A Provijn, Dagmar %A Verhoeven, Liza %X

A logic of diagnosis proceeds in terms of a set of premises and one or more (prioritized) sets of expectancies. In this paper we generalize the logics of diagnosis from \cite{EDa:diag} and present some alternatives. The former operate on the premises and expectancies themselves, the latter on their consequences.

%B Logic and Logical Philosophy %V 11/12 %P 39–65 %G eng %0 Journal Article %J Logique et Analyse %D 2003 %T A Strengthening of the Rescher–Manor Consequence Relations %A Batens, Diderik %X

The flat Rescher–Manor consequence relations–-the Free, Strong, Weak, C-Based, and Argued consequence relation–-are defined in terms of the classical consequences of the maximal consistent subsets of (possibly) inconsistent sets of premises. If the premises are inconsistent, the Free, Strong and C-Based consequence sets are consistent and the Argued consequence set avoids explicit inconsistencies (such as A and  A).

The five consequence relations may be applied to discussive situations as intended by Jaskowski–-the comparison with Jaskowski's D2 is instructive. The method followed by Joke Meheus to extend D2 to an adaptive logic, may also be applied to the Rescher–Manor consequence relations. It leads to an extension of the Free, Strong, Weak, and C-Based consequence relations. The extended consequence sets are consistent and closed under Classical Logic. Applying the method to the Argued consequence relation leads to a different consequence relation, not an extension. Neither the Argued consequence relation nor its extension appear very interesting in the present application context.

%B Logique et Analyse %V 46 %P 289–313 %G eng %0 Journal Article %J Journal of Applied Non-Classical Logics %D 2002 %T Direct Dynamic Proofs For the Rescher–Manor Consequence Relations: The Flat Case %A Batens, Diderik %A Vermeir, Timothy %X

It was shown in \cite{D:unific} that the flat Rescher–Manor consequence relations–-the Free, Strong, Argued, C-Based, and Weak consequence relation–-are all characterized by special applications of inconsistency-adaptive logics defined from the paraconsistent logic CLuN. As as result, these consequence relations are provided with a dynamic proof theory. In the present paper we show that the detour via an inconsistency-adaptive logic is not necessary. We present a direct dynamic proof theory, formulated in the language of Classical Logic, and prove its adequacy.

%B Journal of Applied Non-Classical Logics %V 12 %P 63–84 %G eng %0 Conference Paper %B Proceedings of the Fourtheenth Belgium-Netherlands Conference on Artificial Intelligence, 2002 %D 2002 %T How to obtain elegant Fitch-style proofs from Goal directed ones. %A Provijn, Dagmar %E Blockeel, H. %E Denecker, M. %B Proceedings of the Fourtheenth Belgium-Netherlands Conference on Artificial Intelligence, 2002 %G eng %0 Generic %D 2002 %T In Defence of a Programme for Handling Inconsistencies %A Batens, Diderik %E Meheus, Joke %X

This paper states and defends the philosophical programme underlying the Ghent approach to adaptive logics. Two central arguments are epistemic in nature, one logical. The underlying claim is that even people with rather classical views should see adaptive logics as the only sensible way to handle the inconsistencies that regularly arise in human knowledge, including scientific theories.

%B Inconsistency in Science %I Kluwer %C Dordrecht %P 129–150 %G eng %0 Generic %D 2002 %T On a Partial Decision Method for Dynamic Proofs %A Batens, Diderik %E Dekker, Hendrik %E Villadsen, Jorgen %E Waragai, Toshiharu %X

This paper concerns a goal directed proof procedure for the propositional fragment of the adaptive logic ACLuN1. At the propositional level, it forms an algorithm for final derivability. If extended to the predicative level, it provides a criterion for final derivability. This is essential in view of the absence of a positive test. The procedure may be generalized to all flat adaptive logics.

%B PCL 2002. Paraconsistent Computational Logic %I Roskilde University %V 95 %P 91–108 %G eng %U http://arxiv.org/abs/cs.LO/0207090 %0 Journal Article %J CLE e-Prints %D 2002 %T Some Computational Aspects of Inconsistency-Adaptive logics %A Batens, Diderik %X

This paper concerns a goal directed proof procedure for the propo- sitional fragment of the adaptive logic ACLuN1. The procedure forms an algorithm for final derivability and may easily be generalized for the propositional fragment of all at adaptive logics. The aim is to articulate a procedure that, if extended to the predicative level, provides criteria for final derivability.

%B CLE e-Prints %V 2 %P 15 pp. %G eng %0 Generic %D 2002 %T On some Remarkable Relations between Paraconsistent Logics, Modal Logics, and Ambiguity Logics %A Batens, Diderik %E Carnielli, Walter A. %E Coniglio, Marcelo E. %E Loffredo D'Ottaviano, Itala M. %X

This paper concerns some connections between paraconsistent logics, modal logics (mainly S5), and Ambiguity Logic AL (Classical Logic applied to a language in which all letters are indexed and in which quantifiers over such indices are present). S5 may be defined from AL.

Three kinds of connections are illustrated. First, a paraconsistent logic A is presented that has the same expressive power as S5. Next, I consider the definition of paraconsistent logics from S5 and AL. Such definition is shown to work for some logics, for example Priest's LP. Other paraconsistent logics appear to withstand such definition, typically those that contain a detachable material implication. Finally, I show that some paraconsistent logics and inconsistency-adaptive logics serve exactly the same purpose as some modal logics and ampliative adaptive logics based on S5. However, they serve this purpose along very different roads and the logics cannot be defined from one another.

The paper intends to open lines of research rather than pursuing them to the end. It also contains a poor person's semantics for S5 as well as a description of the simple but useful and powerful AL.

%B Paraconsistency. The Logical Way to the Inconsistent %I Marcel Dekker %C New York %P 275–293 %G eng %0 Generic %D 2002 %T Subject ingebed? Over het methodologisch individualisme in de sociale wetenschappen. %A Van Bouwel, Jeroen %A Verdonck, Barbara %E Devos, Rob %E Braeckman, Antoon %B De terugkeer van het subject? Recente Ontwikkelingen binnen de filosofie %I Universitaire Pers %P 169–179 %@ 90-5867-237-9 %G eng %0 Report %D 2001 %T Aspects of the Dynamics of Discussions and Logics Handling Them %A Batens, Diderik %X

Although we are all familiar with discussions, spelling out their dynamics in a precise way involves many tough logical problems. This paper reports on a set of logical tools that are useful in this respect. Some concern the arguments produced in a discussion, possibly as a result of interventions of different participants, and the many forms of explicit and implicit agreement that are required to understand what is going on. Others concern the changing positions of participants. Nearly all of the tools are adaptive logics.

%G eng %0 Journal Article %J Logique et Analyse %D 2001 %T On Classical Adaptive Logics of Induction %A Batens, Diderik %A Haesaert, Lieven %X

This paper concerns the inference of inductive generalizations and of predictions derived from them. It improves on the adaptive logic of induction from \emph{On a Logic of Induction} (Batens, Logic and Philosophy of Science, IV, 1, 2006, pp. 3-32) by presenting logics that are formulated strictly according to the usual adaptive standards. It moreover extends that paper with respect to background knowledge.

We present logics that handle inductive generalizations as well as logics that handle prioritized background knowledge of three kinds: background generalizations, pragmatic background generalizations (the instances of which may be invoked even after the generalizations are falsified), and background theories. All logics may be combined into a single system.

%B Logique et Analyse %V 44 %P 255–290 %G eng %0 Journal Article %J Journal of Philosophical Logic %D 2001 %T A Dynamic Characterization of the Pure Logic of Relevant Implication %A Batens, Diderik %X

This paper spells out a dynamic proof format for the pure logic of relevant implication. (A proof is dynamic if a formula derived at some stage need not be derived at a later stage.) The paper illustrates three interesting points. (i) A set of properties that characterizes an inference relation on the (very natural) dynamic proof interpretation, need not characterize the same inference relation (or even any inference relation) on the usual set-theoretical interpretation. (ii) A proof format may display an internal dynamics (defeasible conclusions) in the absence of an external dynamics (non-monotonicity). (iii) A monotonic logic may have a non-monotonic characterization.

Keywords: dynamic proofs, relevant implication, non-monotonicity.

%B Journal of Philosophical Logic %V 30 %P 267-280 %G eng %0 Journal Article %J Logique et Analyse %D 2001 %T A General Characterization of Adaptive Logics %A Batens, Diderik %X

This paper contains a unified characterization of adaptive logics. The general structure is presented in the simplest possible guise, both for flat and prioritized adaptive logics. The latter are presented as a special case of combined adaptive logics. The aim of the paper is to provide the general framework underlying several other papers in this volume and to prepare the unified metatheory of adaptive logics.

%B Logique et Analyse %V 44 %P 45–68 %G eng %0 Generic %D 2001 %T On the Logic and Pragmatics of the Process of Explanation %A Batens, Diderik %A Meheus, Joke %E Kiikeri, Mika %E Ylikoski, Petri %X

In this paper, we present mainly two logical systems that clarify pragmatic aspects of the process of explanation. The first concerns a proof theory that leads to the derivation of possible initial conditions from an \emph{explanandum} and a given theory. The second logic concerns the derivation of questions in view of the verification of some possible initial condition, or of one out of several possible initial conditions. It is essential that the latter derivation proceeds in terms of all available knowledge, and not in terms of the explaining theory. It is shown that the second logic provides useful information for explicating further pragmatic aspects of the process of explanation. Several extensions of the logics are argued to be both useful and rather easy to obtain.

%B Explanatory Connections. Electronic Essays Dedicated to Matti Sintonen %I University of Helsinki %G eng %U http://www.valt.helsinki.fi/kfil/matti/ %0 Journal Article %J Mores %D 2001 %T Over de zin van het leven en de zingevende functie van wereldbeelden %A Batens, Diderik %B Mores %V 226 %P 41–63 %G eng %0 Generic %D 2001 %T A Pragmatic Approach to the Explanation of Actions %A Weber, Erik %A Vanderbeeken, Robrecht %E Blasius, Jörg %E Hox, J. %E de Leeuw, E. %E Schmidt, P. %B Social Science Methodology in the New Millenium %S Proceedings of the Fifth International Conference on Logic and Methodology %I Leske & Budrich %C Keulen %G eng %0 Journal Article %J Logique et Analyse %D 2001 %T Pushing the Search Paths in the Proofs. A Study in Proof Heuristics %A Batens, Diderik %A Provijn, Dagmar %X

Introducing techniques deriving from dynamic proofs in proofs for propositional classical logic is shown to lead to a proof format that enables one to push search paths into the proofs themselves. The resulting goal directed proof format is shown to provide a decision method for A1, ..., An vdash B and a positive test for Gamma vdash A.

%B Logique et Analyse %V 44 %P 113–134 %G eng %0 Journal Article %J Studia Logica %D 2001 %T Shortcuts and Dynamic Marking in the Tableau Method for Adaptive logics %A Batens, Diderik %A Meheus, Joke %X

Adaptive logics typically pertain to reasoning procedures for which there is no positive test. In \cite{DJ:tabl1}, we presented a tableau method for two inconsistency-adaptive logics. In the present paper, we first describe these methods (without repeating the meta-theoretic proofs). Next, we present several ways to increase the efficiency of the methods. This culminates in a dynamic marking procedure that indicates which branches have to be extended first, and thus guides one towards a decision–-the conclusion follows or does not follow–-in a very economical way.

%B Studia Logica %V 69 %P 221–248 %G eng %0 Journal Article %J Logical Investigations %D 2001 %T A Universally Abnormality-Adaptive Logic %A Batens, Diderik %X

The present paper presents a logic that allows for the abnormal behaviour of any logical constant and for the ambiguous behaviour of any non-logical constant, but nevertheless offers an interpretation of the premises that is as normal as possible.

%B Logical Investigations %C Moscow, ``NAUKA'' %V 8 %P 256–265 %G eng %0 Journal Article %J Studia Logica %D 2000 %T The Adaptive Logic of Compatibility %A Batens, Diderik %A Meheus, Joke %X

This paper describes the adaptive logic of compatibility and its dynamic proof theory. The results derive from insights in inconsistency-adaptive logic, but are themselves very simple and philosophically unobjectionable. In the absence of a positive test, dynamic proof theories lead, in the long run, to correct results and, in the short run, sometimes to final decisions but always to sensible estimates. The paper contains a new and natural kind of semantics for S5 from which it follows that a specific subset of the standard worlds-models is characteristic for S5.

Keywords: compatibility, adaptive logic, ampliative reasoning, S5-semantics.

%B Studia Logica %V 66 %P 327–348 %G eng %0 Journal Article %J Philosophica %D 2000 %T On the epistemological justification of pluralism and tolerance %A Batens, Diderik %B Philosophica %C Ghent %V 65 %P 33–54 %G eng %0 Generic %D 2000 %T An Extremely Rich Paraconsistent Logic and the Adaptive Logic Based on It %A Meheus, Joke %E Batens, Diderik %E Mortensen, Chris %E Priest, Graham %E Van Bendegem, Jean Paul %B Frontiers of Paraconsistent Logic %I Research Studies Press %C Baldock, UK %P 189–201 %G eng %0 Book %B Frontiers of Paraconsistent Logic %D 2000 %T Frontiers of Paraconsistent Logic %E Batens, Diderik %E Mortensen, Chris %E Priest, Graham %E Van Bendegem, Jean Paul %B Frontiers of Paraconsistent Logic %I Research Studies Press %C Baldock, UK %G eng %0 Journal Article %J Synthese %D 2000 %T Minimally abnormal models in some adaptive logics %A Batens, Diderik %X

In an adaptive logic APL, based on a (monotonic) non-standard logic PL, the consequences of Gamma can be defined in terms of a selection of the PL-models of Gamma. An important property of the adaptive logics ACLuN1, ACLuN2, ACLuNs1, and ACLuNs2 logics is proved: whenever a model is not selected, this is justified in terms of a selected model (Strong Reassurance). The property fails for Priest's LPm because of its way of measuring the degree of abnormality of a model is incoherent–-correcting this delivers the property.

%B Synthese %V 125 %P 5–18 %G eng %0 Generic %D 2000 %T Rich inconsistency-adaptive logics. The clash between heuristic efficiency and realistic reconstruction %A Batens, Diderik %E Grillet, Eric %E Beets, François %B Logique en perspective. Mélanges offerts à Paul Gochet %I Éditions OUSIA %C Brussels %P 513–543 %G eng %0 Generic %D 2000 %T A Survey of Inconsistency-Adaptive Logics %A Batens, Diderik %E Batens, Diderik %E Mortensen, Chris %E Priest, Graham %E Van Bendegem, Jean Paul %X

This paper offers a systematic review of some central philosophical and technical results on adaptive logics. Quite a few of the results are still in print or forthcoming.

%B Frontiers of Paraconsistent Logic %I Research Studies Press %C Baldock, UK %P 49–73 %G eng %0 Generic %D 2000 %T A Tableau Method for Inconsistency-Adaptive Logics %A Batens, Diderik %A Meheus, Joke %E Dyckhoff, Roy %X

We present a tableau method for inconsistency-adaptive logics and illustrate it in terms of the two best studied systems. The method is new in that adaptive logics require a more complex structure of the tableaus and of some rules and conditions. As there is no positive test for derivability in inconsistency-adaptive logics, the tableau method is important for providing criteria for derivability.

%B Automated Reasoning with Analytic Tableaux and Related Methods %S Lecture Notes in Artificial Intelligence %I Springer %V 1847 %P 127–142 %G eng %0 Journal Article %J Logic and Logical Philosophy %D 2000 %T Towards the Unification of Inconsistency Handling Mechanisms %A Batens, Diderik %X

It is shown that the (flat) consequence relations defined from the Rescher-Manor Mechanism (that is: in terms of maximal consistent subsets of the premises) are all inconsistency-adaptive logics combined with a specific interpretation schema for the premises. Each of the adaptive logics is obtained by applying a suitable adaptive strategy to the paraconsistent logic CLuN.

This result provides all those consequence relations with a (dynamic) proof theory and with a static (as well as a dynamic) semantics.

%B Logic and Logical Philosophy %V 8 %P 5–31 %G eng %0 Journal Article %J Philosophica %D 1999 %T Contextual Problem Solving and Adaptive Logics In Creative Processes %A Batens, Diderik %X

Creativity is commonly seen as beyond the scope of rationality. In the present paper, it is argued that available insights in epistemology and available results in logic enable us to incorporate creativity within an independently sensible view on human rationality.

%B Philosophica %V 64 %P 7–31 %G eng %0 Journal Article %J Reports on Mathematical Logic %D 1999 %T Embedding and Interpolation for Some Paralogics. The Propositional Case %A Batens, Diderik %A De Clercq, Kristof %A Kurtonina, Natasha %X

We consider the very weak paracomplete and paraconsistent logics that are obtained by a straightforward weakening of Classical Logic, as well as some of their maximal extensions that are a fragment of Classical Logic. We prove (for the propositional case) that these logics may be faithfully embedded in Classical Logic (as well as in each other), and that the interpolation theorem obtains for them.

%B Reports on Mathematical Logic %V 33 %P 29–44 %G eng %0 Generic %D 1999 %T Inconsistency-Adaptive Logics %A Batens, Diderik %E Orłowska, Ewa %X

After a general description of adaptive logics and their intended applications, I study the proof theory and semantics of two closely related predicative inconsistency-adaptive logics, ACLuN1 and ACLuN2. To this end, I first describe their monotonic basis: the paraconsistent logic CLuN obtained by dropping the consistency requirement from classical logic. The propositional fragments of these inconsistency-adaptive logics have been studied elsewhere. The predicative versions involve several interesting difficulties that lead to new results.

%B Logic at Work. Essays Dedicated to the Memory of Helena Rasiowa %I Physica Verlag (Springer) %C Heidelberg, New York %P 445–472 %G eng %0 Journal Article %J Logique et Analyse %D 1999 %T Linguistic and Ontological Measures for Comparing the Inconsistent Parts of Models %A Batens, Diderik %X

Adaptive logics depend essentially on measures for the degree of abnormality of models. The linguistic approach to such measures compares the sets of abnormal, e.g., inconsistent wffs verified by the models. The ontological approach compares models in terms of `structural' properties that do not depend on the way in which the language is interpreted in the model.

While the linguistic approach has not been questioned up to now, present proposals for an ontological approach are affected by several weaknesses. The present paper argues for the attractiveness of an ontological approach and elaborates on the challenge to adequately define it. The final outcome is rather negative: the only sensible definition attained leads to a logic that does not seem to have any suitable application contexts.

%B Logique et Analyse %V 42 %P 5–33 %G eng %0 Journal Article %J Foundations of Science %D 1999 %T Paraconsistency and its Relation to Worldviews %A Batens, Diderik %X

The paper highlights the import of the paraconsistent movement, list some motivations for its origin, and distinguishes some stands with respect to paraconsistency. It then discusses some sources of inconsistency that are specific for worldviews, and the import of the paraconsistent turn for the worldviews enterprise.

%B Foundations of Science %V 3 %P 259–283 %G eng %0 Generic %D 1999 %T Radicaal Atheïsme %A Batens, Diderik %E Van Kerckhove, Christian %B Wat met God? %I Humanistisch Vrijzinnige Dienst %C Antwerpen %P 129–162 %G eng %0 Journal Article %J Logical Studies %D 1999 %T Zero Logic Adding Up to Classical Logic %A Batens, Diderik %X

The present paper presents a logic that allows for the abnormal behaviour of any logical constant and for the ambiguous behaviour of any non-logical constant, but nevertheless offers an interpretation of the premises that is as normal as possible. If the premises have classical models, the logic assigns them the same consequence set as Classical Logic.

The semantics of the logic is presented, the dynamic proof theory is hinted at, and some comments are added on the philosophical significance of the result.

%B Logical Studies %V 2 %P 15 %G eng %0 Generic %D 1998 %T De zin van Leo Apostels atheïstische religiositeit. Een kennistheoretisch commentaar. Woord vooraf %A Batens, Diderik %B Atheïstische Spiritualiteit %I VUB-Pers %C Brussel %P 9–21 %G eng %0 Journal Article %J Logical Investigations %D 1998 %T Dynamic Semantics Applied to Inconsistency-Adaptive Logics %A Batens, Diderik %B Logical Investigations %C Moscow, ``NAUKA'' %V 5 %P 74–85 %G eng %0 Journal Article %J Bulletin of the Section of Logic %D 1998 %T A Dynamic Semantics for Inconsistency-Adaptive Logics %A Batens, Diderik %B Bulletin of the Section of Logic %V 27 %P 15–18 %G eng %0 Generic %D 1998 %T What, if anything, is an experiment in mathematics? %A Van Bendegem, Jean Paul %E Anapolitanos, Dionysios %E Baltas, Aristides %E Tsinorema, Stavroula %B Philosophy and the Many Faces of Science %I Rowman & Littlefield %P 172–182 %G eng %0 Generic %D 1997 %T Grondslagen van het vrijzinnig humanisme. Een kennistheoretisch pleidooi %A Batens, Diderik %E Van Kerckhove, Christian %B Grondslagen Vrijzinnig Humanisme %I Humanistisch Vrijzinnige Dienst %C Antwerpen %P 75–104 %G eng %0 Journal Article %J Revue Internationale de Philosophie %D 1997 %T Inconsistencies and Beyond. A Logical-Philosophical Discussion %A Batens, Diderik %X

The paper starts off by epistemological arguments for the need of paraconsistent logics. Next it is argued that some contexts require that one allows for other abnormalities, next to or instead of inconsistencies. The feasibility of such moves is defended in terms of a contextual epistemology. Finally, adaptive logics are defended as means to interpret theories `as normally as possible', even if they contain some abnormalities.

%B Revue Internationale de Philosophie %V 200 %P 259–273 %G eng %0 Journal Article %J Mores %D 1997 %T Over het (vermeende) conflict tussen godsgeloof en de wetenschappen %A Batens, Diderik %A Meheus, Joke %B Mores %V 42 %P 401–415 %G eng %0 Book %D 1996 %T Antropinè Gnosè. Mia Ekklèsè gia mia Chrèsimè Ortologikotèta %A Batens, Diderik %X

Greek translation of "Menselijke Kennis" (Diderik Batens, Garant, 1992).

%I Crete University Press %C Athens/Eracleion %G eng %0 Generic %D 1996 %T Een ontroerend intens streven naar kennis, naar beleving en naar de eenheid van beide %A Batens, Diderik %E Batens, Diderik %B Leo Apostel. Tien filosofen getuigen %I Hadewijch %C Antwerpen/Baarn %P 135–157 %G eng %0 Generic %D 1996 %T Functioning and teachings of adaptive logics %A Batens, Diderik %E van Benthem, Johan %E Van Eemeren, F. H. %E Grootendorst, R. %E Veltman, Frank %X

This paper concerns some formal systems, viz. adaptive logics, that display a specific flexibility in the meanings of logical terms. Both the flexibility that occurs within the systems and the question as to how we may arrive at such systems is discussed. Both, it is argued, are relevant for bridging the gap between logic and argumentation.

%B Logic and Argumentation %I North-Holland %P 241–254 %G eng %0 Generic %D 1996 %T In-world realism vs. reflective realism. %A Batens, Diderik %A Meheus, Joke %E Douven, Igor %E Horsten, Leon %B Realism in the Sciences %I Universitaire Pers %C Leuven %P 35–53 %G eng %0 Book %B Leo Apostel. Tien filosofen getuigen %D 1996 %T Leo Apostel. Tien filosofen getuigen %E Batens, Diderik %B Leo Apostel. Tien filosofen getuigen %I Hadewijch %C Antwerpen/Baarn %G eng %0 Generic %D 1996 %T Ook het oneindige is ons werk %A Van Bendegem, Jean Paul %E Batens, Diderik %B Leo Apostel. Tien filosofen getuigen %I Hadewijch %C Antwerpen/Baarn %P 119–134 %G eng %0 Journal Article %J Philosophica %D 1996 %T Steering Problem Solving Between Cliff Incoherence and Cliff Solitude %A Meheus, Joke %A Batens, Diderik %X

Starting from Nickles' constraint-inclusion model, we present five challenges that any rational problem solving model should meet, but that seem to lead to an inextricable riddle. We then introduce the contextual model and show, step by step, that it meets all the challenges and resolves the riddle. This results in a strong argument for the concept of rationality that underlies the model.

%B Philosophica %V 58 %P 153–187 %G eng %0 Journal Article %J Logique et Analyse %D 1995 %T Blocks. The clue to dynamic aspects of logic %A Batens, Diderik %X

The present paper introduces a new approach to formal logic. The block approach is especially useful to grasp dynamic aspects of reasoning, including formal reasoning, that fall beyond the reach of the usual approaches. A block language, the block analysis of proofs, and semantic systems in terms of blocks are articulated. The approach is first applied to classical logic (including proof heuristics). It is used to solve two important problems for adaptive logics (that have a dynamic proof theory). Some further applications are discussed, including meaning change.

%B Logique et Analyse %V 38 %P 285–328 %G eng %0 Generic %D 1995 %T Scientific Arguments and Scientific Prediction. %A Weber, Erik %E Van Eemeren, F. H. %E Grootendorst, R. %E Blair, J. %E Willart, C. %B Special Fields and Cases. Proceedings on the Third ISSA Conference on Argumentation %I SicSat %V IV %P 377-387 %G eng %0 Generic %D 1994 %T Adaptieve logica’s: een aanzet om elkaar te begrijpen %A Batens, Diderik %E Van Bendegem, Jean Paul %E Kornelis, Gustaaf %B Iedereen die niet denkt zoals ik, volge mij. Acta 16de Nederlands-Vlaamse Filosofiedag %I VUB-Pers %P 13–19 %G eng %0 Generic %D 1994 %T Determinisme en indeterminisme %A Batens, Diderik %E Verbeure, Frans %E Apostel, Leo %B Verwijdering of ontmoeting? %I Pelckmans %P 183–202 %G eng %0 Generic %D 1994 %T Explanation, understanding and why-questions %A Weber, Erik %E Halleux, Robert %E Bernés, Anne-Cathérine %B Nieuwe tendenzen in de geschiedenis en de filosofie van de wetenschappen %I Koninklijke Vlaamse Academie van België %P 83-94 %G eng %0 Journal Article %J Logique et Analyse %D 1994 %T Inconsistency-Adaptive Logics and the Foundation of Non-Monotonic Logics %A Batens, Diderik %X

This paper contains the reconstruction of (what I shall call) mixed non-monotonic logics as a combination of a deductive and a preferential component. The first leads from the premises to a possibly inconsistent consequence set; the second weeds out the inconsistencies. Among the candidates for the deductive component inconsistency-adaptive logics prove most suitable. The ensuing preferential component is formulated in terms of models and is itself split into two parts: (i) a transparent, purely logical procedure leads from a set of inconsistent models to a set of associated consistent models and (ii) the choice between the latter relies on the preferences. The real fight between mixed non-monotonic logics should concentrate on this last aspect. The outlined approach has a broader domain of application than mixed non-monotonic logics.

%B Logique et Analyse %V 37 %P 57–94 %G eng %0 Journal Article %J Analysis %D 1994 %T The two-envelope paradox: the infinite case %A Castel, Paul %A Batens, Diderik %B Analysis %V 54 %P 46–49 %G eng %0 Generic %D 1993 %T De inconsistentie-adaptieve logica DDL %A Batens, Diderik %E van Dooren, Wim %E Hoff, Tineke %B Aktueel Filosoferen %I Eburon %P 39–45 %G eng %0 Generic %D 1993 %T Ontdekking en creativiteit in wetenschap en muziek %A Meheus, Joke %E Halleux, Robert %E Bernés, Anne-Cathérine %B Nieuwe tendenzen in de geschiedenis en de filosofie van de wetenschappen %I Nationaal Comité voor Logica, Geschiedenis en Filosofie van de Wetenschappen %P 41–52 %G eng %0 Generic %D 1993 %T Onze huidige kijk op ontdekking en creativiteit vereist een `contextuele' kennistheoretische aanpak %A Batens, Diderik %E Raymaekers, Bart %B Gehelen en fragmenten. De vele gezichten van de filosofie %I Universitaire Pers %P 265–267 %G eng %0 Generic %D 1992 %T Aspecten van ontdekking en creativiteit %A Batens, Diderik %A Meheus, Joke %A Weber, Erik %E Raymaekers, Bart %B Gehelen en Fragmenten. De vele gezichten van de filosofie %I Universitaire Pers %P 59 %8 Leuven, September %G eng %0 Generic %D 1992 %T Do we need a hierarchical model of science? %A Batens, Diderik %E Earman, John %B Inference, Explanation, and Other Frustrations. Essays in the Philosophy of Science %I University of California Press %P 199–215 %G eng %0 Book %D 1992 %T Logicaboek. Praktijk en theorie van het redeneren %A Batens, Diderik %I Garant %C Antwerpen/Apeldoorn %G eng %) 2: 1993; 3: 1996; 4: 1999; 5: 2002; 6: 2004; 7: 2008; 8: 2017 %0 Book %D 1992 %T Menselijke kennis. Pleidooi voor een bruikbare rationaliteit %A Batens, Diderik %I Garant %C Antwerpen/Apeldoorn %G eng %0 Journal Article %J Wijsgerig perspectief op maatschappij en wetenschap %D 1992 %T Paraconsistente en relevante logica's %A Batens, Diderik %B Wijsgerig perspectief op maatschappij en wetenschap %V 32/2 %P 53–59 %G eng %0 Journal Article %J Studies in Soviet Thought %D 1990 %T Against Global Paraconsistency %A Batens, Diderik %B Studies in Soviet Thought %V 39 %P 209–229 %G eng %0 Generic %D 1989 %T Dynamic Dialectical Logics %A Batens, Diderik %E Priest, Graham %E Routley, Richard %E Norman, Jean %B Paraconsistent Logic. Essays on the Inconsistent %I Philosophica Verlag %P 187–217 %G eng %0 Generic %D 1989 %T Een pleidooi voor lokale consistentie %A Batens, Diderik %E Berghs, H. %E Thys, W. %B Congresbundel Filosofiedag Antwerpen 1988 %I Eburon %P 41–46 %G eng %0 Generic %D 1989 %T Kurt Gödel en de wetenschappelijke zekerheid %A Batens, Diderik %E Kint, J. %B Nieuwe visies in de wetenschap %I Acco %P 43–66 %G eng %0 Generic %D 1989 %T Leo Apostel on Dialectical Logic %A Batens, Diderik %E Vandamme, Fernand %E Pinxten, Rik %B The Philosophy of Leo Apostel, vol. 2: Descriptive and Critical Essays %I Communication and Cognition %P 24–55 %G eng %0 Journal Article %J Logique et Analyse %D 1989 %T Natural Heuristics for Proof Construction. Part I: Classical Propositional Logic %A Batens, Diderik %B Logique et Analyse %V 32 %P 337–363 %G eng %0 Generic %D 1989 %T Over de kloof tussen feit en norm, bekeken vanuit de hedendaagse wetenschapsfilosofie %A Batens, Diderik %E Van den Enden, Hugo %B Dwarsdenken. Omtrent Jaap Kruithof %I EPO %P 165–177 %G eng %0 Book %D 1988 %T Theory and Experiment. Recent Insights and New Perspectives on Their Relation %E Batens, Diderik %E Van Bendegem, Jean Paul %I Reidel %C Dordrecht %G eng %0 Journal Article %J Philosophica %D 1987 %T Action science and the reunification of the social sciences and epistemology %A Batens, Diderik %B Philosophica %V 40 %P 109–134 %G eng %0 Generic %D 1987 %T A contextual approach to meaning and knowledge %A Batens, Diderik %E Gosselin, M. %E Demeyere, F. %B Science and Society %I VUB-Uitgaven %P 84–110 %G eng %0 Journal Article %J Studia Logica %D 1987 %T Relevant Implication and the Weak Deduction Theorem %A Batens, Diderik %B Studia Logica %V 46 %P 239–245 %G eng %0 Generic %D 1987 %T The structure of our knowledge system %A Batens, Diderik %E Vandamme, Fernand %B Communication and Cognition. Applied Epistemology %I Communication and Cognition %P 101 %G eng %0 Generic %D 1987 %T Two semantically motivated enrichments of relevant logics %A Batens, Diderik %E Perzanowski, Jerzy %B Essays in Philosophical Logic %I Jagiellonian University Press %P 65–74 %G eng %0 Generic %D 1986 %T Creativiteit in wetenschap en muziek %A Batens, Diderik %E De Hen, Ferdinand J. %E Riessauw, Anne-Marie %E Sabbe, Herman %B Liber Amicorum J.L. Broeckx %I Grafisch Bureau M & Team %P 29–55 %G eng %0 Journal Article %J Logique et Analyse %D 1986 %T Dialectical dynamics within formal logics %A Batens, Diderik %B Logique et Analyse %V 29 %P 161–173 %G eng %0 Journal Article %J Logique et Analyse %D 1986 %T Rich relevant logics based on a simple type of semantics %A Batens, Diderik %B Logique et Analyse %V 29 %P 437–457 %G eng %0 Generic %D 1986 %T Some remarks on the structural similarity between music and logic %A Batens, Diderik %E Apostel, Leo %E Sabbe, Herman %E Vandamme, Fernand %B Reason, Emotion and Music. Towards a Common Structure for Arts, Sciences and Philosophies, Based on a Conceptual Framework for the Description of Music %I Communication & Cognition %P 127–143 %G eng %0 Journal Article %J Communication and Cognition %D 1986 %T Some remarks on the structural similarity between music and logic %A Batens, Diderik %B Communication and Cognition %I Communication & Cognition %V 19 %P 135–151 %G eng %0 Journal Article %J CC-AI %D 1986 %T Static and dynamic paraconsistent logics and their use in expert systems %A Batens, Diderik %B CC-AI %V 3 %P 33–50 %G eng %0 Generic %D 1986 %T Wetenschap en Vrijzinnige Waarden %A Batens, Diderik %B De specificiteit van Vrijzinnig Humanistische Waarden %I UPV %P 1–14 %G eng %0 Generic %D 1985 %T Dynamic Dialectical Logics as a Tool to Deal with and Partly Eliminate Unexpected Inconsistencies %A Batens, Diderik %E Hintikka, Jaakko %E Vandamme, Fernand %B The Logic of Discovery and the Logic of Discourse %I Plenum Press %P 263–271 %G eng %0 Generic %D 1985 %T Meaning, Acceptance, and Dialectics %A Batens, Diderik %E Pitt, J. C. %B Change and Progress in Modern Science %I Reidel %P 333–360 %G eng %0 Journal Article %J Logique et Analyse %D 1985 %T Relevant derivability and classical derivability in Fitch-style and axiomatic formulations of relevant logics %A Batens, Diderik %A Van Bendegem, Jean Paul %B Logique et Analyse %V 28 %P 21–31 %G eng %0 Journal Article %J Philosophica %D 1983 %T Incommensurability is not a threat to the rationality of science or to the anti-dogmatic tradition %A Batens, Diderik %B Philosophica %V 32 %P 117–132 %G eng %0 Journal Article %J Proceedings of the 12th International Symposium on Multiple-Valued Logic %D 1982 %T A bridge between two-valued and many-valued semantic systems: n-tuple semantics %A Batens, Diderik %B Proceedings of the 12th International Symposium on Multiple-Valued Logic %V IEEE %P Los Angeles, 318–322 %G eng %0 Journal Article %J Logique et Analyse %D 1982 %T Russell's Set versus the Universal Set in Paraconsistent Set Theory %A Arruda, Ayda I. %A Batens, Diderik %B Logique et Analyse %V 25 %P 121–133 %G eng %0 Journal Article %J Tijdschrift voor de studie van de Verlichting en het Vrije denken %D 1981 %T Progress, rationality and the philosophy of science %A Batens, Diderik %B Tijdschrift voor de studie van de Verlichting en het Vrije denken %V 8–9 %P 83–102 %G eng %0 Journal Article %J Notre Dame Journal of Formal Logic %D 1980 %T A completeness-proof method for extensions of the implicational fragment of the propositional calculus %A Batens, Diderik %B Notre Dame Journal of Formal Logic %V 21 %P 509–517 %G eng %0 Journal Article %J Logique et Analyse %D 1980 %T Paraconsistent extensional propositional logics %A Batens, Diderik %B Logique et Analyse %V 23 %P 195–234 %G eng %0 Generic %D 1979 %T An empirical investigation on scientific observation %A Apostel, Leo %A Batens, Diderik %A Breusegem, Erwin %A De Coninck, Jan %A De Waele, Danny %A Pinxten, Rik %A Swings, Jean %A Van Bendegem, Jean Paul %A Vandamme, Fernand %E Callebaut, Werner %E De Mey, Marc %E Pinxten, Rik %E Vandamme, Fernand %B Theory of Knowledge and Science Policy %I Communication & Cognition %P 3–36 %G eng %0 Journal Article %J Philosophica %D 1978 %T Rationality and ethical rationality %A Batens, Diderik %B Philosophica %V 22 %P 23–45 %G eng %0 Generic %D 1977 %T Bijna alle–veel–weinig %A Batens, Diderik %B Contactgroepen Humane en Politieke Wetenschappen %I NFWO %P 6–14 %G eng %0 Generic %D 1977 %T Inductie %A Batens, Diderik %E De Block, A. %E Ten Have, T.T. %E De Keyser, C.C. %B Standaard Encyclopedia voor Opvoeding en Onderwijs %I Standaard %P 180 %G eng %0 Generic %D 1977 %T Inferentie %A Batens, Diderik %E De Block, A. %E Ten Have, T.T. %E De Keyser, C.C. %B Standaard Encyclopedie voor Opvoeding en Onderwijs %I Standaard %P 382–383 %G eng %0 Journal Article %J Philosophica %D 1977 %T Outline of a theory of meaning: semantical and contextual %A Batens, Diderik %B Philosophica %V 19 %P 137–154 %G eng %0 Generic %D 1977 %T Verisimilitude and meaning relations %A Batens, Diderik %E De Mey, Marc %E Pinxten, Rik %E Poriau, M. %E Vandamme, Fernand %B CC77. International Workshop on the Cognitive Viewpoint %I Ghent University %P 321–328 %G eng %0 Journal Article %J Communication and Cognition %D 1976 %T Some contributions to the logic of action %A Batens, Diderik %B Communication and Cognition %V 9 %P 347–376 %G eng %0 Journal Article %J Philosophica %D 1976 %T Some remarks on the relations between science and values %A Batens, Diderik %B Philosophica %V 17 %P 13–46 %G eng %0 Journal Article %J Communication and Cognition %D 1975 %T Deduction and contextual information %A Batens, Diderik %B Communication and Cognition %V 8 %P 243–277 %G eng %0 Book %B Werken uitgegeven door de Faculteit van de Letteren en Wijsbegeerte, Rijksuniversiteit Gent %D 1975 %T Studies in the Logic of Induction and in the Logic of Explanation. Containing a New Theory of Meaning Relations %A Batens, Diderik %B Werken uitgegeven door de Faculteit van de Letteren en Wijsbegeerte, Rijksuniversiteit Gent %I De Tempel %C Brugge %V 161 %G eng %0 Journal Article %J Philosophica %D 1974 %T Rationality and justification %A Batens, Diderik %B Philosophica %V 14 %P 83–103 %G eng %0 Journal Article %J Communication and Cognition %D 1973 %T De rol van ontische factoren in de kennisverzameling %A Batens, Diderik %B Communication and Cognition %V 6 %P 51–69 %G eng %0 Journal Article %J Logique et Analyse %D 1973 %T Nicholas Rescher's coherence theory of truth %A Batens, Diderik %B Logique et Analyse %V 16 %P 393–411 %G eng %0 Journal Article %J Revue internationale de philosophie %D 1971 %T The paradoxes of confirmation %A Batens, Diderik %B Revue internationale de philosophie %V 95–96 %P 101–118 %G eng %0 Journal Article %J The British Journal for the Philosophy of Science %D 1971 %T Some objections to Keith Lehrer's rule IR %A Batens, Diderik %B The British Journal for the Philosophy of Science %V 22 %P 357–362 %G eng %0 Journal Article %J Communicatie en Cognitie %D 1969 %T Inductieve logica. Een inleiding tot enkele basisproblemen %A Batens, Diderik %B Communicatie en Cognitie %V 3 %P 128–154 %G eng %0 Journal Article %J Communicatie en Cognitie %D 1969 %T Over de stand van zaken in de Carnapiaanse inductieve logica %A Batens, Diderik %B Communicatie en Cognitie %V 6 %P 29–57 %G eng %0 Journal Article %J Studia Philosophica Gandensia %D 1968 %T Some proposals for the solution of the Carnap-Popper discussion on `inductive logic' %A Batens, Diderik %B Studia Philosophica Gandensia %V 6 %P 5–25 %G eng