Verification of dynamic bisimulation theorems in Coq

Over the last years, the study of logics that can update a model while evaluating a formula has gained in interest. Motivated by many examples in practice such as hybrid logics, separation logics and dynamic epistemic logics, the ability to update a model has been investigated from a more general po...

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Bibliographic Details
Published inJournal of logical and algebraic methods in programming Vol. 120; p. 100642
Main Authors Fervari, Raul, Trucco, Francisco, Ziliani, Beta
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.04.2021
Subjects
Bisimulation
Dynamic logics
Modal logics
Proof mechanization
Dynamic logics
Modal logics
Proof mechanization
Bisimulation
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Summary:Over the last years, the study of logics that can update a model while evaluating a formula has gained in interest. Motivated by many examples in practice such as hybrid logics, separation logics and dynamic epistemic logics, the ability to update a model has been investigated from a more general point of view. In this work, we formalize and verify in the proof assistant Coq, the bisimulation theorems for a particular family of dynamic logics that can change the structure of a relational model while evaluating a formula. Our framework covers update operators to perform different kinds of modifications on the accessibility relation, the valuation and the evaluation point of a model. The benefits of this formalization are twofold. First, our results apply for a wide variety of dynamic logics. Second, we argue that this is the first step towards the development of a modal logic library in Coq, which allows us to mechanize many relevant results.
ISSN:2352-2208
DOI:10.1016/j.jlamp.2021.100642