Invited SpeakerILLC, The Netherlands
Assistant Professor at the Institute for Logic, Language and Computation (ILLC) of the University of Amsterdam.
Website: https://www.mariannagirlando.com/Girlando.html
Research Interests
proof theorymodal logicssequent calculuscyclic proofsdeep inferenceconditional and epistemic logicsdevelopment of automated provers
Cyclic proofs for Transitive Closure Logic via Hypersequents
"Propositional Dynamic Logic (PDL) is a modal logic for reasoning about the iterative execution of programs. Via the standard translation, PDL can be embedded into Transitive Closure Logic (TCL), an extension of first-order logic with a recursive operator expressing the transitive closure of binary relations. Cyclic proof systems based on Gentzen-style sequents have been developed for both PDL and TCL in the literature, but cyclic proofs for PDL do not directly translate into cyclic proofs for TCL. Therefore, the standard translation does not lift to the level of Gentzen-style cyclic proofs. Motivated by this observation, we introduce a hypersequent-style cyclic proof system for TCL, which enriches Gentzen-style sequents with additional structural connectives. We prove that this system is sound and that it simulates cyclic proofs for PDL, thereby establishing cut-free completeness for a fragment of TCL.
This talk is based on joint work with Anupam Das: https://link.springer.com/article/10.1007/s10817-023-09675-1"