Speaker: Guillaume Aucher
Date and Time: Friday, January 13th 2017, 16:00-17:30
Venue: ILLC Seminar Room F1.15, Science Park 107.
Title: Dynamic Epistemic Logic in Update Logic.
Abstract: We generalize the language of substructural logics interpreted over the ternary relational semantics and we introduce a logic called update logic. This is motivated by our intention to capture within the logical framework of substructural logics various logic-based formalisms dealing with common sense reasoning and logical dynamics. This initiative is based on the key observation that an update can be represented abstractly by the ternary relation of the substructural framework. We introduce three triples of connectives which are interconnected by means of cyclic permutations. The usual fusion, implication and co-implication connectives of the Lambek calculus form one of these triples. We define a proper display calculus for our language which generalizes the display calculus for modal logic and a sequent calculus which generalizes the Lambek calculus. Using correspondence results from substructural logics, we also obtain sound and complete display calculi for a wide variety of classical and substructural logics. In particular, we show that Dynamic Epistemic Logic (DEL) is a substructural logic and that it is an extension of update logic. We identify axioms and inference rules that completely characterize the DEL product update and we provide a sequent calculus for DEL. Finally, we show that some substructural connectives of update logic can be interpreted as operators dealing with epistemic planning.