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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| Published in | Journal of logical and algebraic methods in programming Vol. 120; p. 100642 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
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Elsevier Inc
01.04.2021
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| Abstract | 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. |
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| AbstractList | 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. |
| ArticleNumber | 100642 |
| Author | Ziliani, Beta Fervari, Raul Trucco, Francisco |
| Author_xml | – sequence: 1 givenname: Raul orcidid: 0000-0003-0360-0725 surname: Fervari fullname: Fervari, Raul email: rfervari@unc.edu.ar organization: Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Argentina – sequence: 2 givenname: Francisco orcidid: 0000-0003-2493-023X surname: Trucco fullname: Trucco, Francisco email: franciscoctrucco@gmail.com organization: TU Wien, Austria – sequence: 3 givenname: Beta surname: Ziliani fullname: Ziliani, Beta email: beta@mpi-sws.org organization: Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Argentina |
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| Cites_doi | 10.1017/S1755020310000389 10.1093/jigpal/jzt030 10.2307/2695090 10.1080/11663081.2015.1018801 10.1017/CBO9781107050884 10.1145/3236773 10.1017/S1755020311000189 10.1093/jigpal/jzv020 10.1002/malq.19630090502 10.1007/s13347-018-0312-8 10.3166/jancl.17.157-182 10.1093/logcom/exz019 10.1007/s11229-007-9168-7 10.1093/logcom/exx034 10.1080/11663081.2019.1647653 10.1016/j.jlamp.2019.06.005 10.1017/fmp.2017.1 |
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| Keywords | Dynamic logics Modal logics Proof mechanization Bisimulation |
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| Title | Verification of dynamic bisimulation theorems in Coq |
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