research-article

A Proof Theory for Model Checking

Authors:

Dale MillerAuthors Info & Claims

Volume 63, Issue 4

Pages 857 - 885

https://doi.org/10.1007/s10817-018-9475-3

Published: 01 December 2019 Publication History

Abstract

While model checking has often been considered as a practical alternative to building formal proofs, we argue here that the theory of sequent calculus proofs can be used to provide an appealing foundation for model checking. Since the emphasis of model checking is on establishing the truth of a property in a model, we rely on additive inference rules since these provide a natural description of truth values via inference rules. Unfortunately, using these rules alone can force the use of inference rules with an infinite number of premises. In order to accommodate more expressive and finitary inference rules, we also allow multiplicative rules but limit their use to the construction of additive synthetic inference rules: such synthetic rules are described using the proof-theoretic notions of polarization and focused proof systems. This framework provides a natural, proof-theoretic treatment of reachability and non-reachability problems, as well as tabled deduction, bisimulation, and winning strategies.

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Cited By

Horne RMauw SYurkov S(2023)When privacy fails, a formula describes an attackTheoretical Computer Science10.1016/j.tcs.2023.113842959:COnline publication date: 30-May-2023
https://dl.acm.org/doi/10.1016/j.tcs.2023.113842
Miller DViel A(2022)The undecidability of proof search when equality is a logical connectiveAnnals of Mathematics and Artificial Intelligence10.1007/s10472-021-09764-090:5(523-535)Online publication date: 1-May-2022
https://dl.acm.org/doi/10.1007/s10472-021-09764-0
Cohen LRowe R(2020)Integrating Induction and Coinduction via Closure Operators and Proof CyclesAutomated Reasoning10.1007/978-3-030-51074-9_21(375-394)Online publication date: 1-Jul-2020
https://dl.acm.org/doi/10.1007/978-3-030-51074-9_21
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Published In

cover image Journal of Automated Reasoning

Journal of Automated Reasoning Volume 63, Issue 4

Dec 2019

317 pages

ISSN:0168-7433

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Copyright © 2019 Springer Nature B.V.

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Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 01 December 2019

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Cited By

Horne RMauw SYurkov S(2023)When privacy fails, a formula describes an attackTheoretical Computer Science10.1016/j.tcs.2023.113842959:COnline publication date: 30-May-2023
https://dl.acm.org/doi/10.1016/j.tcs.2023.113842
Miller DViel A(2022)The undecidability of proof search when equality is a logical connectiveAnnals of Mathematics and Artificial Intelligence10.1007/s10472-021-09764-090:5(523-535)Online publication date: 1-May-2022
https://dl.acm.org/doi/10.1007/s10472-021-09764-0
Cohen LRowe R(2020)Integrating Induction and Coinduction via Closure Operators and Proof CyclesAutomated Reasoning10.1007/978-3-030-51074-9_21(375-394)Online publication date: 1-Jul-2020
https://dl.acm.org/doi/10.1007/978-3-030-51074-9_21
Miller D(2020)A Distributed and Trusted Web of Formal ProofsDistributed Computing and Internet Technology10.1007/978-3-030-36987-3_2(21-40)Online publication date: 9-Jan-2020
https://dl.acm.org/doi/10.1007/978-3-030-36987-3_2

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