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Propositional modal logic of programs

Authors:

Michael J. Fischer,

Richard E. LadnerAuthors Info & Claims

STOC '77: Proceedings of the ninth annual ACM symposium on Theory of computing

Pages 286 - 294

https://doi.org/10.1145/800105.803418

Published: 04 May 1977 Publication History

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Abstract

We introduce a fundamental propositional logical system for describing correctness, termination and equivalence of programs. We define a formal syntax and semantics for the propositional modal logic of programs and give several consequences of the definition. Principal conclusions are that deciding satisfiability requires time d^{n/log n}for some d > 1 and that satisfiability, even in an extended system, can be decided in nondeterministic time cⁿfor some c. We provide applications of the decision procedure to regular expressions, Ianov schemes, and classical systems of modal logic.

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Dolgorukov VGalimullin RGladyshev MDastani MSichman JAlechina NDignum V(2024)Dynamic Epistemic Logic of Resource Bounded Information Mining AgentsProceedings of the 23rd International Conference on Autonomous Agents and Multiagent Systems10.5555/3635637.3662898(481-489)Online publication date: 6-May-2024
https://dl.acm.org/doi/10.5555/3635637.3662898
Fervari RMansutti A(2022)Modal Logics and Local Quantifiers: A Zoo in the Elementary HierarchyFoundations of Software Science and Computation Structures10.1007/978-3-030-99253-8_16(305-324)Online publication date: 29-Mar-2022
https://doi.org/10.1007/978-3-030-99253-8_16
Limón YBárcenas EBenítez-Guerrero ECastillo GVelázquez-Mena A(2020)Mu-Calculus Satisfiability with Arithmetic ConstraintsProgramming and Computer Software10.1134/S036176882008013746:8(503-510)Online publication date: 22-Dec-2020
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Index Terms

Propositional modal logic of programs
1. Software and its engineering
  1. Software notations and tools
    1. Formal language definitions
  2. Software organization and properties
    1. Software functional properties
      1. Correctness
2. Theory of computation
  1. Formal languages and automata theory
  2. Logic
    1. Modal and temporal logics
    2. Proof theory

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Published In

STOC '77: Proceedings of the ninth annual ACM symposium on Theory of computing

May 1977

318 pages

ISBN:9781450374095

DOI:10.1145/800105

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 04 May 1977

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STOC '77 Paper Acceptance Rate 31 of 87 submissions, 36%;

Overall Acceptance Rate 1,469 of 4,586 submissions, 32%

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Cited By

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Dolgorukov VGalimullin RGladyshev MDastani MSichman JAlechina NDignum V(2024)Dynamic Epistemic Logic of Resource Bounded Information Mining AgentsProceedings of the 23rd International Conference on Autonomous Agents and Multiagent Systems10.5555/3635637.3662898(481-489)Online publication date: 6-May-2024
https://dl.acm.org/doi/10.5555/3635637.3662898
Fervari RMansutti A(2022)Modal Logics and Local Quantifiers: A Zoo in the Elementary HierarchyFoundations of Software Science and Computation Structures10.1007/978-3-030-99253-8_16(305-324)Online publication date: 29-Mar-2022
https://doi.org/10.1007/978-3-030-99253-8_16
Limón YBárcenas EBenítez-Guerrero ECastillo GVelázquez-Mena A(2020)Mu-Calculus Satisfiability with Arithmetic ConstraintsProgramming and Computer Software10.1134/S036176882008013746:8(503-510)Online publication date: 22-Dec-2020
https://doi.org/10.1134/S0361768820080137
Moanga N(2020)Fischer-Ladner Closure for Many-Sorted Modal Logic with Application for Operational Semantics2020 22nd International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC)10.1109/SYNASC51798.2020.00022(67-74)Online publication date: Sep-2020
https://doi.org/10.1109/SYNASC51798.2020.00022
O'Connor LDarais DGibbons J(2019)Deferring the details and deriving programsProceedings of the 4th ACM SIGPLAN International Workshop on Type-Driven Development10.1145/3331554.3342605(27-39)Online publication date: 18-Aug-2019
https://dl.acm.org/doi/10.1145/3331554.3342605
Kong JLomuscio A(2017)Model checking multi-agent systems against LDLK specificationsProceedings of the 26th International Joint Conference on Artificial Intelligence10.5555/3171642.3171804(1138-1144)Online publication date: 19-Aug-2017
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Primiero G(2017)Algorithmic Iteration for Computational IntelligenceMinds and Machines10.1007/s11023-017-9423-827:3(521-543)Online publication date: 1-Sep-2017
https://dl.acm.org/doi/10.1007/s11023-017-9423-8
Knobbout MDastani MMeyer J(2016)A dynamic logic of norm changeProceedings of the Twenty-second European Conference on Artificial Intelligence10.3233/978-1-61499-672-9-886(886-894)Online publication date: 29-Aug-2016
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Mamouras K(2016)The Hoare Logic of Deterministic and Nondeterministic Monadic Recursion SchemesACM Transactions on Computational Logic10.1145/283549117:2(1-30)Online publication date: 7-Jan-2016
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Vardi M(2014)From Löwenheim to PSL and SVALanguage, Culture, Computation. Computing - Theory and Technology10.1007/978-3-642-45321-2_5(78-102)Online publication date: 2014
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