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 Journal of Logic and Computation %D 2016 %T Adaptive strategies and finite-conditional premise sets %A Straßer, Christian %A Van De Putte, Frederik %B Journal of Logic and Computation %V 26 %P 1517-1539 %G eng %U + http://dx.doi.org/10.1093/logcom/exu044 %R 10.1093/logcom/exu044 %0 Conference Paper %B Deontic Logic and Normative Systems %D 2016 %T Coarse Deontic Logic (short version) %A Van De Putte, Frederik %B Deontic Logic and Normative Systems %I College Publications %G eng %0 Journal Article %J Logique et Analyse %D 2016 %T Splitting and Relevance: Broadening the Scope of Parikh's Concepts %A Van De Putte, Frederik %B Logique et Analyse %V 59 %P 173 -205 %G eng %N 234 %& 173 %0 Journal Article %J Logic Journal of the IGPL %D 2014 %T Adaptive logics: a parametric approach %A Van De Putte, Frederik %A Straßer, Christian %B Logic Journal of the IGPL %V 22 %P 905-932 %G eng %U + http://dx.doi.org/10.1093/jigpal/jzu017 %& 905 %R 10.1093/jigpal/jzu017 %0 Journal Article %J Proceedings of MICAI2013, Lecture Notes in Artificial Intelligence %D 2013 %T Default Assumptions and Selection Functions: A Generic Framework for Non-monotonic Logics %A Van De Putte, Frederik %XWe investigate a generalization of so-called default-assumption consequence relations, obtained by replacing the consequence relation of classical logic with an arbitrary supraclassical, compact Tarski-logic, and using arbitrary selection functions on sets of sets of defaults. Both generalizations are inspired by various approaches in non-monotonic logic and belief revision. We establish some meta-theoretic properties of the resulting systems. In addition, we compare them with two other frameworks from the literature on non-monotonic logic, viz. adaptive logics and selection semantics.

%B Proceedings of MICAI2013, Lecture Notes in Artificial Intelligence %V 8264 %P 54-67 %G eng %R 10.1007/978-3-642-45114-0_5 %0 Journal Article %J Foundations of science %D 2013 %T Induction from a single instance: Incomplete frames %A Urbaniak, Rafal %A Van De Putte, Frederik %XIn this paper we argue that an existing theory of concepts called dynamic frame theory, although not developed with that purpose in mind, allows for the precise formulation of a number of problems associated with induction from a single instance. A key role is played by the distinction we introduce between complete and incomplete dynamic frames, for incomplete frames seem to be very elegant candidates for the format of the background knowledge used in induction from a single instance. Furthermore, we show how dynamic frame theory provides the terminology to discuss the justification and the fallibility of incomplete frames. In the Appendix, we give a formal account of incomplete frames and the way these lead to induction from a single instance.

%B Foundations of science %V 18 %P 641–653 %G eng %R http://dx.doi.org/10.1007/s10699-012-9295-6 %0 Journal Article %J Journal of Philosophical Logic %D 2013 %T Preferential Semantics using Non-smooth Preference Relations %A Van De Putte, Frederik %A Straßer, Christian %XThis paper studies the properties of eight semantic consequence relations defined from a Tarski-logic **L** and a preference relation &\#8826;. They are equivalent to Shohams so-called preferential entailment for smooth model structures, but avoid certain problems of the latter in non-smooth configurations. Each of the logics can be characterized in terms of what we call multi-selection semantics. After discussing this type of semantics, we focus on some concrete proposals from the literature, checking a number of meta-theoretic properties and elaborating on their intuitive motivation. As it turns out, many of their meta-properties only hold in case &\#8826; is transitive. To tackle this problem, we propose slight modifications of each of the systems, showing the resulting logics to behave better at the intuitive level and in metatheoretic terms, for arbitrary &\#8826;.

This article discusses Parikhs axiom of relevance in belief revision, and recalls some results from Kourousias and Makinson (2007, J. Symbolic Logic, **72**, 9941002) in this context. The crucial distinction is emphasized between the uniqueness of the finest splitting of K and the fact that K has several normal forms associated with that finest splitting. The main new result of this article is a new proof for the theorem that the set of prime implicates of K is a normal form for the finest splitting of K. It is explained how this proof avoids a mistake in an earlier proof from Wu and Zhang (2010, Knowledge-Based Syst., **23**, 7076). As a corollary, relevance can be re-defined without reference to the finest splitting, using the notion of path-relevance from Makinson (2009, J. Appl. Logic, **7**, 377387). Finally, a weak yet sufficient condition for irrelevance is presented.

A broad range of defeasible reasoning forms has been explicated by prioritized adaptive logics. However, the relative lack in meta-theory of many of these logics stands in sharp contrast to the frequency of their application. This article presents the first comparative study of a large group of prioritized adaptive logics. Three formats of such logics are discussed: superpositions of adaptive logics, hierarchic adaptive logics from F. Van De Putte (2011, *Log. J. IGPL, doi:10.1093/jigpal/jzr025*) and lexicographic adaptive logics from F. Van De Putte and C. Stra&\#223;er (2012, *Log. Anal., forthcoming*). We restrict the scope to logics that use the strategy Minimal Abnormality. It is shown that the semantic characterizations of these systems are equivalent and that they are all sound with respect to either of these characterizations. Furthermore, sufficient conditions for the completeness and equivalence of the consequence relations of the three formats are established. Some attractive properties, including Fixed Point and the Deduction Theorem, are shown to hold whenever these conditions are obeyed.

Abduction of generalizations is the process in which explanatory hypotheses are formed for generalizations such as pineapples taste sweet or rainbows appear when the sun breaks through the rain. This phenomenon has received little attention in formal logic and philosophy of science. The current paper remedies this lacuna by first giving an overview of some general characteristics of this process, elaborating on its ubiquity in scientific and everyday reasoning. Second, the adaptive logic LA &\#8704; is presented to explicate this process formally

%B Theoria - revista de teoria historia y fundamentos de la ciencia %V 27 %P 345–364 %G eng %0 Journal Article %J Synthese %D 2012 %T The Dynamics of Relevance: Adaptive Belief Revision %A Van De Putte, Frederik %A Verdée, Peter %XThis paper presents eight (previously unpublished) adaptive logics for belief revision, each of which define a belief revision operation in the sense of the AGM framework. All these revision operations are shown to satisfy the six basic AGM postulates for belief revision, and Parikhs axiom of Relevance. Using one of these logics as an example, we show how their proof theory gives a more dynamic flavor to belief revision than existing approaches. It is argued that this turns belief revision (that obeys Relevance) into a more natural undertaking, where analytic steps are performed only as soon as they turn out to be necessary in order to uphold certain beliefs.

%B Synthese %V 187 %P 1-42 %8 May %G eng %R 10.1007/s11229-012-0116-9 %0 Journal Article %J Logique et Analyse %D 2012 %T Extending the standard format of adaptive logics to the prioritized case %A Van De Putte, Frederik %A Straßer, Christian %XThis paper introduces a new format for reasoning with prioritized stan- dards of normality. It is applicable in a broad variety of contexts, e.g. dealing with (possibly conflicting) prioritized belief bases or combining different reasoning methods in a prioritized way. The format is a gener- alization of the standard format of adaptive logics (see [4]). Every logic that is formulated within it has a straightforward semantics in the style of Shohams selection semantics (see [22]) and a dynamic proof theory. Fur- thermore, it can count on a rich meta-theory that inherits the attractive features of the standard format, such as soundness and completeness, re- flexivity, idempotence, cautious monotonicity, and many other properties.

%B Logique et Analyse %V 55 %P 601–641 %G eng %0 Generic %D 2012 %T Generic Formats for Prioritized Adaptive Logics. With Applications in Deontic Logic, Abduction and Belief Revision %A Van De Putte, Frederik %I Ghent University %8 May 24 %9 phd %1Joke Meheus and Peter Verdée

%0 Journal Article %J Logique et Analyse %D 2012 %T Proof Theories for Superpositions of Adaptive Logics %A Straßer, Christian %A Van De Putte, Frederik %XThe standard format for adaptive logics offers a generic and unifying formal framework for defeasible reasoning forms. One of its main distinguishing features is a dynamic proof theory by means of which it is able to explicate actual reasoning. In many applications it has proven very useful to superpose sequences of adaptive logics, such that each logic treats the consequence set of its predecessor as premise set. Although attempts have been made to define dynamic proof theories for some of the resulting logics, no generic proof theory is available yet. Moreover, the existing proof theories for concrete superpositions are suboptimal in various respects: the derivability relations characterized by these proposals are often not adequate with respect to the consequence relation of the superposed adaptive logics and in some cases they even trivialize premise sets. An adequate and generic proof theory is needed in order to meet the requirement of explicating defeasible reasoning in terms of superpositions of adaptive logics. This paper presents two generic proof theories for superpositions of adaptive logics in standard format. By means of simple examples, the basic ideas behind these proof theories are illustrated and it is shown how the older proposals are inadequate.

%B Logique et Analyse %P 1–33 %G eng %0 Journal Article %J Logic Journal of the IGPL %D 2011 %T Hierarchic adaptive logics %A Van De Putte, Frederik %XThis article discusses the proof theory, semantics and meta-theory of a class of adaptive logics, called hierarchic adaptive logics. Their specific characteristics are illustrated throughout the article with the use of one exemplary logic HKx, an explicans for reasoning with prioritized belief bases. A generic proof theory for these systems is defined, together with a less complex proof theory for a subclass of them. Soundness and a restricted form of completeness are established with respect to a non-redundant semantics. It is shown that all hierarchic adaptive logics are reflexive, have the strong reassurance property and that a subclass of them is a fixed point for a broad class of premise sets. Finally, they are compared to a different yet related class of adaptive logics.

%B Logic Journal of the IGPL %V 20 %P 45–72 %G eng %R http://dx.doi.org/10.1093/jigpal/jzr025 %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 %XIn 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