Admissibility and unifiability in contact logics

Contact logics are logics for reasoning about the contact relations between regular subsets in a topological space. Admissible inference rules can be used to improve the performance of any algorithm that handles provability within the context of contact logics. The decision problem of unifiability can be seen as a special case of the decision problem of admissibility. In this paper, we examine the decidability of admissibility problems and unifiability problems in contact logics

Definability and canonicity for Boolean logic with a binary relation

International audienceThis paper studies the concepts of definability and canonicity in Boolean logic with a binary relation. Firstly, it provides formulas defining first-order or second-order conditions on frames. Secondly, it proves that all formulas corresponding to compatible first-order conditions on frames are canonical

Boolean logics with relations

AbstractThe language of our Boolean logic with relations is a Boolean language to which relation symbols have been added. Such a language turns out to be a useful tool for describing relational structures and algebraic structures. This paper introduces the concepts of Kripke semantics and Boolean semantics for our language. It addresses the traditional issues of decidability/complexity and axiomatization/completeness but it also defines the new concepts of weak canonicity and strong canonicity

Boolean logics with relations

Special issue : Relations and Kleene Algebras in Computer Science (RelMiCS/AKA 08), edited by Rudolf Berghammer, Bernhard Möller, Georg StruthInternational audienceThe language of our Boolean logic with relations is a Boolean language to which relation symbols have been added. Such a language turns out to be a useful tool for describing relational structures and algebraic structures. This paper introduces the concepts of Kripke semantics and Boolean semantics for our language. It addresses the traditional issues of decidability/complexity and axiomatization/completeness but it also defines the new concepts of weak canonicity and strong canonicity

Boolean Logics with Relations (RelMiCS 2008)

Theoretical Computer Science and General Issues (LNTCS)International audienceWe study a fragment of propositional modal logics using the universal modality given by a restriction on the modal depth of modal formulas