

Workshop on Proof Theory, Modal Logic and Reflection Principles
October 19, 2017 14:00–14:25, Moscow, Steklov Mathematical Institute





Student session


Relationchanging modal logics: some model and proof theoretic aspects
M. Martel^{} 
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Abstract:
We can fairly say that Logic (whichever you want to choose, be it propositional or firstorder, classical or nonclassical) is the mathematical tool used, par excellence, to describe a structure. Modal logics, for example, are particularly well suited to describe relational structures, specially if one is interested in computationally well behaved formalisms. But why can a logic only describe a structure? In this talk we introduce relationchanging modal logics, a family of modal logics that can change the accessibility relation of a model during the evaluation of a formula. We consider some model and proof theoretic aspects of relationchanging modal logics. We start by illustrating some inexpressible properties such as the tree and finite model properties, and we show that these logics can be seen as fragments of hybrid logics by providing satisfiabilitypreserving translations. Then, we present sound and complete tableau methods using hybrid logic tools, and we conclude with some open questions aiming at integrating relationchanging modal logics within the current landscape of logics of model update.
Language: English

