@article {Pawlowski2017d, title = {Many-valued logic of informal provability: a non-deterministic strategy}, journal = {The Review of Symbolic Logic}, year = {In Press}, author = {Pawlowski, Pawel and Urbaniak, Rafal} } @article {4443714, title = {Mathematical proofs in practice: Revisiting the reliability of published mathematical proofs}, journal = {Theoria. Revista de Teor{\'\i}a, Historia y Fundamentos de la Ciencia}, volume = {29}, number = {3}, year = {2015}, pages = {345{\textendash}360}, author = {Frans, Joachim and Kosolosky, Laszlo} } @article {5685708, title = {Mechanistic and non-mechanistic varieties of dynamical models in cognitive science: explanatory power, understanding, and the {\textquoteright}mere description{\textquoteright} worry}, journal = {Synthese}, volume = {192}, number = {1}, year = {2014}, pages = {43{\textendash}66}, abstract = {

In the literature on dynamical models in cognitive science, two issues have recently caused controversy. First, what is the relation between dynamical and mechanistic models? I will argue that dynamical models can be upgraded to be mechanistic as well, and that there are mechanistic and non-mechanistic dynamical models. Second, there is the issue of explanatory power. Since it is uncontested the mechanistic models can explain, I will focus on the non-mechanistic variety of dynamical models. It is often claimed by proponents of mechanistic explanations that such models do not really explain cognitive phenomena (the ‘mere description’ worry). I will argue against this view. Although I agree that the three arguments usually offered to vindicate the explanatory power of non-mechanistic dynamical models (predictive power, counterfactual support, and unification) are not enough, I consider a fourth argument, namely that such models provide understanding. The Voss strong anticipation model is used to illustrate this.

}, doi = {http://dx.doi.org/10.1007/s11229-014-0548-5}, author = {Gervais, Raoul} } @article {frans2014mechanistic, title = {Mechanistic Explanation and Explanatory Proofs in Mathematics}, journal = {Philosophia Mathematica}, volume = {22}, number = {2}, year = {2014}, pages = {231{\textendash}248}, abstract = {

Although there is a consensus among philosophers of mathematics and mathematicians that mathematical explanations exist, only a few authors have proposed accounts of explanation in mathematics. These accounts fit into the unificationist or top-down approach to explanation. We argue that these models can be complemented by a bottom-up approach to explanation in mathematics. We introduce the mechanistic model of explanation in science and discuss the possibility of using this model in mathematics, arguing that using it does not presuppose a Platonist view of mathematics and allows one to gain insight into why a theorem is true by answering what-if-things-had-been-different questions.

}, doi = {10.1093/philmat/nku003}, author = {Frans, Joachim and Weber, Erik} } @article {clarke2014modelling, title = {Modelling mechanisms with causal cycles}, journal = {Synthese}, volume = {191}, number = {8}, year = {2014}, pages = {1651{\textendash}1681}, abstract = {

Mechanistic philosophy of science views a large part of scientific activity as engaged in modelling mechanisms. While science textbooks tend to offer qualitative models of mechanisms, there is increasing demand for models from which one can draw quantitative predictions and explanations. Casini et al. (Theoria 26(1):5–33, 2011) put forward the Recursive Bayesian Networks (RBN) formalism as well suited to this end. The RBN formalism is an extension of the standard Bayesian net formalism, an extension that allows for modelling the hierarchical nature of mechanisms. Like the standard Bayesian net formalism, it models causal relationships using directed acyclic graphs. Given this appeal to acyclicity, causal cycles pose a prima facie problem for the RBN approach. This paper argues that the problem is a significant one given the ubiquity of causal cycles in mechanisms, but that the problem can be solved by combining two sorts of solution strategy in a judicious way.

}, doi = {10.1007/s11229-013-0360-7}, author = {Clarke, Brendan and Leuridan, Bert and Williamson, Jon} } @article {3178933, title = {Modelling abduction in science by means of a modal adaptive logic}, journal = {FOUNDATIONS OF SCIENCE}, volume = {18}, number = {4}, year = {2013}, pages = {611{\textendash}624}, abstract = {

Scientists confronted with multiple explanatory hypotheses as a result of their abductive inferences, generally want to reason further on the different hypotheses one by one. This paper presents a modal adaptive logic MLA (s) that enables us to model abduction in such a way that the different explanatory hypotheses can be derived individually. This modelling is illustrated with a case study on the different hypotheses on the origin of the Moon.

}, issn = {1233-1821}, doi = {http://dx.doi.org/10.1007/s10699-012-9293-8}, author = {Gauderis, Tjerk} } @incollection {Christiaens2012, title = {Metaphysics and Cinema}, booktitle = {Worldviews, Science and Us: Bridging Knowledge and its Implications for our Perpectives on the World.}, year = {2012}, pages = {118-141}, publisher = {World Scientific Publishing Company}, address = {Singapore}, author = {Christiaens, Wim}, editor = {Aerts, Diederik and Broekaert, Jan and D{\textquoteright}Hooghe, Bart and Note, Nicole} } @article {primiero2012modal, title = {A modal type theory for formalizing trusted communications}, journal = {Journal of Applied Logic}, volume = {10}, number = {1}, year = {2012}, pages = {92{\textendash}114}, abstract = {

This paper introduces a multi-modal polymorphic type theory to model epistemic processes characterized by trust, defined as a second-order relation affecting the communication process between sources and a receiver. In this language, a set of senders is expressed by a modal prioritized context, whereas the receiver is formulated in terms of a contextually derived modal judgement. Introduction and elimination rules for modalities are based on the polymorphism of terms in the language. This leads to a multi-modal non-homogeneous version of a type theory, in which we show the embedding of the modal operators into standard group knowledge operators.

}, doi = {10.1016/j.jal.2011.12.002}, author = {Primiero, Giuseppe and Taddeo, Mariarosaria} } @article {1859590, title = {Modelling defeasible reasoning by means of adaptive logic games}, journal = {Logic Journal of the IGPL}, volume = {20}, number = {2}, year = {2012}, pages = {417{\textendash}437}, abstract = {

In this article, I present a dynamic logic game for defeasible reasoning. I argue that, as far as defeasible reasoning is concerned, one should distinguish between practical and ideal rationality. Starting from the adaptive logic framework, I formalize both rationality notions by means of logic games. The presented adaptive logic games are based on (i) standard logic games on the one hand and (ii) dynamic proof procedures for adaptive logic on the other hand. The games are similar to standard logic games, but have the extra property that some moves are revisable. This is handled by means of a main control game, which starts different standard logic games. I argue that the adaptive logic games form intuitive reasoning models for rationality in defeasible reasoning contexts. Moreover, I will also demonstrate that the games give a good insight in the computational complexity of defeasible reasoning forms.

}, issn = {1367-0751}, doi = {http://dx.doi.org/10.1093/jigpal/jzq060}, author = {Verd{\'e}e, Peter} } @article {primiero2011multi, title = {A multi-modal type system and its procedural semantics for safe distributed programming}, year = {2011}, abstract = {

In this paper we present a multi-modal polymorphic type system for a computational interpretation of programs with distributed resources. Polymorphism induces a distinction between programs whose code is safe at location, and programs whose value is safe overall. We formulate judge- mental modalities to express such distinction and use their introduction and elimination rules to express mobility of code and values within a net- work. The syntactic formulation is completed by a procedural semantics interpreted over states of an abstract machine for which a standard sound- ness result is given in the form of a type safety theorem.

}, author = {Primiero, Giuseppe} } @article {924352, title = {Metaphysical explanatory asymmetries}, journal = {Logique et Analyse}, volume = {53}, number = {211}, year = {2010}, pages = {345{\textendash}365}, abstract = {

The general view is that metaphysical explanation is asymmetric. For instance, if resemblance facts can be explained by facts about their relata, then, by the asymmetry of explanation, these latter facts cannot in turn be explained by the former. The question however is: is there any reason to hold on to the asymmetry? If so, what does it consist in? In the paper we approach these questions by comparing them to analogous questions that have been investigated for scientific explanations. Three main asymmetry criteria have been proposed for the latter: (i) causation, (ii) unification, and (iii) explanatory dependence. We argue that the last criterion, but not the former two, can be of help to metaphysical explanation: metaphysical explanations are asymmetric if the explanatory dependence criterion (in modified format) holds of them.

}, issn = {0024-5836}, author = {Wieland, Jan Willem and Weber, Erik} } @phdthesis {PhD_Rogier, title = {Models in Science: Essays on Scientific Virtues, Scientific Pluralism and the Distribution of Labour in Science}, year = {2010}, month = {April 19}, publisher = {Ghent University}, type = {phd}, author = {De Langhe, Rogier} } @conference {primiero2010multi, title = {A Multi-Modal Dependent Type Theory for Representing Data Accessibility in a Network.}, booktitle = {Electronic Proceedings of the Federated Logic Conference 2010 (Proof Systems for Program Logics Workshop)}, year = {2010}, publisher = {Citeseer}, organization = {Citeseer}, abstract = {

In this paper we present a multi-modal polymorphic constructive type theory for a computational interpretation of programs equipped with locations for data accessibility in the context of distributed processing.

}, author = {Primiero, Giuseppe} } @article {663049, title = {Mainstream economics: searching where the light is}, journal = {JOURNAL OF POST KEYNESIAN ECONOMICS}, volume = {32}, number = {1}, year = {2009}, pages = {137{\textendash}150}, abstract = {

The starting point of this paper is the question of how to explain mainstream economics{\textquoteright} great level of acceptance in the face of its poor empirical track record. An explanation is provided in terms of a combination of unification and, most importantly, inference to the best explanation. This paper asks whether the appeal of mainstream economics to inference to the best explanation is justified and as a consequence questions one of the main reasons for the dominance of mainstream economics today. The final section integrates the ideas from the previous sections into a general framework for explanatory pluralism.

}, issn = {0160-3477}, url = {http://dx.doi.org/10.2753/PKE0160-3477320109}, author = {De Langhe, Rogier} } @article {urbaniak2009kaye, title = {The Mathematics of Logic by Richard Kaye (review).}, journal = {Bulletin of Symbolic Logic}, volume = {15}, number = {02}, year = {2009}, pages = {216{\textendash}218}, author = {Urbaniak, Rafal} } @conference {678298, title = {Mathematics through man-computer interaction. A study of the early years of computing.}, booktitle = {Logic, Philosophy and History of Science in Belgium. Proceedings of the Young Researcher Days 2008}, year = {2009}, publisher = {Koninklijke Vlaamse Academie van Belgi{\"e} voor Wetenschappen en Kunsten}, organization = {Koninklijke Vlaamse Academie van Belgi{\"e} voor Wetenschappen en Kunsten}, isbn = {9789065690432}, author = {De Mol, Liesbeth}, editor = {Weber, Erik and Libert, Thierry and Marage, Pierre and Vanpaemel, Geert} } @incollection {WaartvanGulik2009, title = {Menselijke rationaliteit en identiteit.}, booktitle = {Humanismen}, year = {2009}, pages = {163-172}, publisher = {VUB Press}, abstract = {

Wat volgt is een aanzet tot een zuiver beschrijvende analyse van de relatie tussen de ontwikkeling van de menselijke identiteit en de drie sociaal- psychologische fenomenen xenofobie, etnocentrisme en tolerantie. Het werkkader voor deze analyse is een conceptueel, speculatief model van de menselijke rationaliteit.

}, author = {van der Waart van Gulik, Stephan}, editor = {Van den Bossche, M. and Vandemeulebroecke, R.} } @incollection {Urbaniak2009a, title = {Modal Logic and Philosophy. {A} case study.}, booktitle = {Logic, Philosophy and History of Science in Belgium. Proceedings of the Young Researchers Days 2008}, year = {2009}, pages = {79-83}, publisher = {Koninklijke Vlaamse Academie van Belgi{\"e}}, address = {Brussel}, author = {Urbaniak, Rafal and Rostalska, Agnieszka}, editor = {Weber, Erik and Libert, Thierry and Marage, Pierre and Vanpaemel, Geert} } @conference {531125, title = {Mainstream economics: searching where the light is}, booktitle = {Proceedings of the 10th Anniversary Conference of the Association of Heterodox Economics}, year = {2008}, month = {July}, publisher = {Anglia Ruskin University}, organization = {Anglia Ruskin University}, author = {De Langhe, Rogier} } @article {GiJ:mmac, title = {Majority Merging by Adaptive Counting}, journal = {Synthese (KRA Serie)}, volume = {165}, number = {2}, year = {2008}, pages = {203{\textendash}223}, abstract = {

The present paper introduces a belief merging procedure by majority using the standard format of Adaptive Logics. The core structure of the logic ADM(c) (Adaptive Doxastic Merging by Counting) consists in the formulation of the conflicts arising from the belief bases of the agents involved in the procedure. A strategy is then defined both semantically and proof-theoretically which selects the consistent contents answering to a majority principle. The results obtained are proven to be equivalent to a standard majority operator for bases with partial support.

}, doi = {http://dx.doi.org/10.1007/s11229-008-9370-2}, author = {Primiero, Giuseppe and Meheus, Joke} } @incollection {683245, title = {Middeleeuwse en Arabische Wijsbegeerte}, booktitle = {De rivier van Herakleitos: Een eigenzinnige visie op de wijsbegeere}, year = {2008}, pages = {93{\textendash}101}, publisher = {Houtekiet}, isbn = {978 90 8924 035 4}, url = {http://lib.ugent.be/catalog/pug01:683245}, author = {De Mey, Tim}, editor = {Vermeersch, Etienne and Braeckman, Johan} } @article {primieromodel, title = {A model for processing updates with inconsistent information on propositional databases}, year = {2008}, institution = { College Publications}, abstract = {

In the present paper a model for information update on propositional databases is formulated using the standard format of Adaptive Logics. The core structure of the update procedure is represented by the ab- normal expressions of the language that formalize received information contradicting previous contents. The strategy de ned to restrict abnor- malities works by establishing, at each stage of the process, the most re- cent and reliable information, updating constantly the base and removing older data.

}, author = {Primiero, Giuseppe} } @article {428175, title = {Modeling sorites reasoning with adaptive fuzzy logic}, journal = {Fuzzy Sets and Systems}, volume = {159}, number = {14}, year = {2008}, pages = {1869{\textendash}1884}, abstract = {

We present and discuss a new solution for reasoning with sorites series and their related paradoxes.We argue that a suitable logic for sorites series should be able to apply specific classical logic rules like modus ponens until and unless it becomes apparent that these applications generate unacceptable results. When the latter happens, the logic should be able to retract those applications of classical logic rules that are problematic. The formal core of our solution consists of several adaptive logics based on a {\L}ukasiewicz fuzzy logic extended with the Baaz’ △-operator and a non-singleton interval of designated values. The natural dynamics characteristic of adaptive logics allows these logics to perform necessary retractions in an intuitive and elegant manner. {\textcopyright} 2008 Elsevier B.V. All rights reserved.

}, issn = {0165-0114}, doi = {10.1016/j.fss.2008.01.001}, author = {van der Waart van Gulik, Stephan and Verd{\'e}e, Peter} } @article {381861, title = {Mathematics Education Through Lesson Study in the {A}sia-{P}acific Region}, journal = {History and Pedagogy of Mathematics Newsletter}, volume = {66}, year = {2007}, pages = {4{\textendash}6}, issn = {N/A}, author = {Heeffer, Albrecht} } @article {Primiero2007, title = {A modal language for contextual computations}, year = {2007}, month = {June}, abstract = {

In this paper, we present a modal language for contextual computing, corresponding to the fragment of constructive ΚΤ with necessity and pos- sibility operators. We interpret absolute and contextual computations as difierent modes of verifying the truth of propositions. The semantics of the language L cc interprets absolute computations by a direct verification function valid in every state; contextual computations are interpreted in terms of a verification function valid under unverified information. Modal- ities are used to express extensions of contexts in order to de ne local and global validity. This semantics has a (weak) monotonicity property, de- pending on satisfaction of processes in contexts. In the corresponding axiomatic system cΚΤ a restricted version of the deduction theorem for globally valid formulas holds, soundness and completeness are proven and decidability is shown to hold for the necessitation fragment of the language by a restricted finite model property..

}, author = {Primiero, Giuseppe} } @article {demathematics, title = {Mathematics and Pictures. Some popular examples}, year = {2006}, abstract = {

Mathematics is a science that is traditionally known as a highly abstract discipline. Due to its apparent possibility of deducing abstract formulas without the necessity of back-linking to the outside reality, pure mathematics’ status is often experienced as being isolated from and superior to the dubious reality and our evenly ambiguous perception of it. Despite this attitude, several examples can be given of the usefulness of this back-linking. Moreover, since the commercialisation of the computer, new possibilities for mathematical research became available. These possibilities though can only be reached through experimenting. One of the aspects of this experimental approach to mathematics is the use of computer generated images. On the one hand they are used as testing instruments, on the other hand they are necessary tools for certain mathematical theories to be possible - as the outside reality is the object of observation of a physicist, computer generated images are the reality to be observed and perceived by the mathematician.

}, author = {De Mol, Liesbeth} } @conference {353364, title = {The Methodological Relevance of the History of Mathematics for Mathematics Education}, booktitle = {Proceedings of the International Conference on 21st Century Information Technology in Mathematics Education}, year = {2006}, abstract = {

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.

}, author = {Heeffer, Albrecht}, editor = {Dhompongsa, G and Bhatti , F and Kitson , Q} } @article {300874, title = {Mathematical models in {N}ewton{\textquoteright}s Principia: a new view of the {\textquoteright}{N}ewtonian Style{\textquoteright}.}, journal = {International Studies in the Philosophy of Science}, volume = {19}, number = {1}, year = {2005}, pages = {1{\textendash}19}, abstract = {

In this essay I argue against I. Bernard Cohen’s influential account of Newton’s methodology in the Principia: the ‘Newtonian Style’. The crux of Cohen’s account is the successive adaptation of ‘mental constructs’ through comparisons with nature. In Cohen’s view there is a direct dynamic between the mental constructs and physical systems. I argue that his account is essentially hypothetical-deductive, which is at odds with Newton’s rejection of the hypothetical-deductive method. An adequate account of Newton’s methodology needs to show how Newton’s method proceeds differently from the hypothetical-deductive method. In the constructive part I argue for my own account, which is model based: it focuses on how Newton constructed his models in Book I of the Principia. I will show that Newton understood Book I as an exercise in determining the mathematical consequences of certain force functions. The growing complexity of Newton’s models is a result of exploring increasingly complex force functions (intra-theoretical dynamics) rather than a successive comparison with nature (extra-theoretical dynamics). Nature did not enter the scene here. This intra-theoretical dynamics is related to the ‘autonomy of the models’.

}, issn = {0269-8595}, author = {Ducheyne, Steffen} } @incollection {340350, title = {Micro-explanations of laws.}, booktitle = {Structures in Scientific Cognition. {E}ssays in Debate with {T}heo {K}uipers}, year = {2005}, pages = {177{\textendash}186}, publisher = {Rodopi}, address = {Amsterdam/New York}, abstract = {

After a brief introduction to Kuipers{\textquoteright} views on explanations of laws we argue that micro-explanations of laws can have two formats: they work either by aggregation and transformation (as Kuipers suggests) or by means of function ascriptions (Kuipers neglects this possibility). We compare both types from an epistemic point of view (which information is needed to construct the explanation?) and from a means-end perspective (do both types serve the same purposes? are they equally good?).

}, isbn = {9042016485}, author = {Weber, Erik and De Preester, Helena} } @incollection {DeMey2004, title = {Mere Logical Possibility: A Bridge too Far}, booktitle = {Modal Epistemology}, year = {2004}, pages = {53-62}, publisher = {Koninklijke Vlaamse Academie van Belgi{\"e}}, author = {De Mey, Tim}, editor = {Weber, Erik and De Mey, Tim} } @book {322175, title = {Modal epistemology.}, year = {2004}, pages = {106 p.}, publisher = {{Koninklijke {V}laamse {A}cademie van {B}elgi{\"e}}, organization = {{Koninklijke {V}laamse {A}cademie van {B}elgi{\"e}}, isbn = {N/A}, editor = {Weber, Erik and De Mey, Tim} } @article {397668, title = {Models of intentional explanation.}, journal = {Philosophical Explorations}, volume = {7}, number = {3}, year = {2004}, pages = {233{\textendash}247}, abstract = {

The controversy about intentional explanation of action concerns how these explanations work. What kind of model allows us to capture the dependency or relevance relation between the explanans, i.e. the beliefs and desires of the agent, and the explanandum, i.e. the action? In this paper, I argue that the causal mechanical model can do the job. Causal mechanical intentional explanations consist in a reference to the mechanisms of practical reasoning of the agent that motivated the agent to act, i.e. to a causally relevant set of beliefs and desires. Moreover, the causal mechanical model can provide in efficient and unproblematic applications, unlike action explanations using ceteris paribus laws or counterfactuals. The drawback of the latter models of explanation is their modal requirement: the explanans must mention or implies sufficient and/or necessary conditions for the explanandum. Such a requirement is too strong when it comes to intentional explanation of action.

}, issn = {1386-9795}, doi = {10.1080/1386979042000258330}, author = {Vanderbeeken, Robrecht} } @article {D:minmod, title = {Minimally abnormal models in some adaptive logics}, journal = {Synthese}, volume = {125}, year = {2000}, pages = {5{\textendash}18}, abstract = {

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{\textquoteright}s LPm because of its way of measuring the degree of abnormality of a model is incoherent{\textendash}-correcting this delivers the property.

}, author = {Batens, Diderik} } @article {152579, title = {Minimizing Ambiguity and Paraconsistency.}, journal = {Logique et Analyse}, volume = {42}, number = {165-166}, year = {1999}, pages = {39{\textendash}160}, abstract = {

Ambiguity-adaptive logics offer a natural and rich formal solution to (possibly) inconsistent theories. Three views on ambiguities result in three different, intuitively correct ambiguity-adaptive logics with interesting applications. We present their semantics and proof theory, and illustrate that ambiguity-adaptive logics form an excellent alternative to paraconsistent logics that focus on the characteristics of the logical constants.

}, issn = {0024-5836}, author = {Vanackere, Guido} } @incollection {J:mbr, title = {Model-Based Reasoning in Creative Processes}, booktitle = {Model-Based Reasoning in Scientific Discovery}, year = {1999}, pages = {199{\textendash}217}, publisher = {Kluwer/Plenum}, address = {Dordrecht}, abstract = {

Combining a contextual approach to problem solving with results on some recently developed (non-standard) logics, I present in this paper a general frame for the methodological study of model-based reasoning in creative processes. I argue that model-based reasoning does not require that we turn away from logic. I also argue, however, that in order to better understand and evaluate creative processes that involve model-based reasoning, and in order to formulate guidelines for them, we urgently need to extend the existing variety of logics.

}, author = {Meheus, Joke}, editor = {Magnani, Lorenzo and Nersessian, Nancy and Thagard, Paul} } @incollection {257816, title = {Mathematical Experiments and Mathematical Pictures}, booktitle = {Realism in the Sciences}, year = {1996}, pages = {203{\textendash}216}, publisher = {Universitaire Pers}, address = {Leuven}, author = {Van Bendegem, Jean Paul}, editor = {Douven, Igor and Horsten, Leon} } @book {D:mk, title = {Menselijke kennis. {P}leidooi voor een bruikbare rationaliteit}, year = {1992}, publisher = {Garant}, organization = {Garant}, address = {Antwerpen/Apeldoorn}, author = {Batens, Diderik} } @article {241630, title = {Models of explanation: an evaluation of their fruitfulness}, journal = {COMMUNICATION \& COGNITION : MONOGRAPHIES}, volume = {25}, year = {1992}, pages = {339{\textendash}352}, issn = {0378-0880}, author = {Weber, Erik} } @incollection {D:mad, title = {Meaning, Acceptance, and Dialectics}, booktitle = {Change and Progress in Modern Science}, year = {1985}, pages = {333{\textendash}360}, publisher = {Reidel}, author = {Batens, Diderik}, editor = {Pitt, J. C.} }