@unpublished {2070, title = {Pooling Modalities and Pointwise Intersection: Semantics, Expressivity, and Applications}, year = {Submitted}, author = {Van De Putte, Frederik and Klein, Dominik} } @article {2074, title = {Pooling Modalities and Pointwise Intersection: Axiomatization and Decidability}, journal = {Studia Logica}, volume = {online first}, year = {2020}, abstract = {

We establish completeness and the finite model property for logics featuring the pooling modalities that were introduced in Van De\ Putte and Klein (Pooling modalities and pointwise intersection: semantics, expressivity, and applications). The definition of our canonical models combines standard techniques with a so-called {\textquotedblleft}puzzle piece construction{\textquotedblright}, which we first illustrate informally. After that, we apply it to the weakest classical logics with pooling modalities and investigate the technique{\textquoteright}s potential for the axiomatization of stronger logics, obtained by imposing well-known frame conditions on the models.

}, author = {Van De Putte, Frederik and Klein, Dominik} } @unpublished {2051, title = {Pointwise intersection in neighbourhood modal logic}, year = {2018}, author = {Van De Putte, Frederik and Klein, Dominik} } @article {van2013preferential, title = {Preferential Semantics using Non-smooth Preference Relations}, journal = {Journal of Philosophical Logic}, volume = {43}, number = {5}, year = {2013}, pages = {903{\textendash}942}, abstract = {

This paper studies the properties of eight semantic consequence relations defined from a Tarski-logic L and a preference relation \&\#8826;. They are equivalent to Shoham’s 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;.

}, author = {Van De Putte, Frederik and Stra{\ss}er, Christian} } @article {van2013prime, title = {Prime implicates and relevant belief revision}, journal = {Journal of Logic and Computation}, volume = {23}, number = {1}, year = {2013}, pages = {109{\textendash}119}, abstract = {

This article discusses Parikh’s axiom of relevance in belief revision, and recalls some results from Kourousias and Makinson (2007, J. Symbolic Logic, 72, 994–1002) 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, 70–76). 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, 377–387). Finally, a weak yet sufficient condition for irrelevance is presented.

}, doi = {10.1093/logcom/exr040}, author = {Van De Putte, Frederik} } @article {Strasser2012, title = {Proof Theories for Superpositions of Adaptive Logics}, journal = {Logique et Analyse}, year = {2012}, pages = {1{\textendash}33}, abstract = {

The 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.

}, author = {Stra{\ss}er, Christian and Van De Putte, Frederik} }