research-article

Decidability of weak logics with deterministic transitive closure

Authors:

Witold Charatonik,

Emanuel Kieroński,

Filip MazowieckiAuthors Info & Claims

CSL-LICS '14: Proceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)

Article No.: 29, Pages 1 - 10

https://doi.org/10.1145/2603088.2603134

Published: 14 July 2014 Publication History

Abstract

The deterministic transitive closure operator, added to languages containing even only two variables, allows to express many natural properties of a binary relation, including being a linear order, a tree, a forest or a partial function. This makes it a potentially attractive ingredient of computer science formalisms. In this paper we consider the extension of the two-variable fragment of first-order logic by the deterministic transitive closure of a single binary relation, and prove that the satisfiability and finite satisfiability problems for the obtained logic are decidable and ExpSpace-complete. This contrasts with the undecidability of two-variable logic with the deterministic transitive closures of several binary relations, known before. We also consider the class of universal first-order formulas in prenex form. Its various extensions by deterministic closure operations were earlier considered by other authors, leading to both decidability and undecidability results. We examine this scenario in more details.

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Cited By

Benaim SBenedikt MCharatonik WKieroński ELenhardt RMazowiecki FWorrell J(2016)Complexity of Two-Variable Logic on Finite TreesACM Transactions on Computational Logic (TOCL)10.1145/299679617:4(1-38)Online publication date: 11-Nov-2016
https://dl.acm.org/doi/10.1145/2996796
Wu Z(2016)Semipositivity in Separation Logic with Two VariablesDependable Software Engineering: Theories, Tools, and Applications10.1007/978-3-319-47677-3_12(179-196)Online publication date: 6-Oct-2016
https://doi.org/10.1007/978-3-319-47677-3_12
Demri SDeters M(2015)Two-Variable Separation Logic and Its Inner CircleACM Transactions on Computational Logic10.1145/272471116:2(1-36)Online publication date: 21-Apr-2015
https://dl.acm.org/doi/10.1145/2724711
Show More Cited By

Index Terms

Decidability of weak logics with deterministic transitive closure
1. Software and its engineering
  1. Software notations and tools
    1. Formal language definitions
2. Theory of computation

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cover image ACM Conferences

CSL-LICS '14: Proceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)

July 2014

764 pages

ISBN:9781450328869

DOI:10.1145/2603088

Program Chairs:
Thomas Henzinger
Institute of Science and Technology (IST), Austria
,
Dale Miller
INRIA and LIX/Ecole Polytechnique, Palaiseau

Copyright © 2014 ACM.

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SIGLOG: ACM Special Interest Group on Logic and Computation
EACSL: European Association for Computer Science Logic
IEEE-CS\DATC: IEEE Computer Society

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New York, NY, United States

Publication History

Published: 14 July 2014

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Narodowe Centrum Nauki

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CSL-LICS '14

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SIGLOG
EACSL
IEEE-CS\DATC

CSL-LICS '14: JOINT MEETING OF the Twenty-Third EACSL Annual Conference on COMPUTER SCIENCE LOGIC

July 14 - 18, 2014

Vienna, Austria

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CSL-LICS '14 Paper Acceptance Rate 74 of 212 submissions, 35%;

Overall Acceptance Rate 215 of 622 submissions, 35%

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Cited By

Benaim SBenedikt MCharatonik WKieroński ELenhardt RMazowiecki FWorrell J(2016)Complexity of Two-Variable Logic on Finite TreesACM Transactions on Computational Logic (TOCL)10.1145/299679617:4(1-38)Online publication date: 11-Nov-2016
https://dl.acm.org/doi/10.1145/2996796
Wu Z(2016)Semipositivity in Separation Logic with Two VariablesDependable Software Engineering: Theories, Tools, and Applications10.1007/978-3-319-47677-3_12(179-196)Online publication date: 6-Oct-2016
https://doi.org/10.1007/978-3-319-47677-3_12
Demri SDeters M(2015)Two-Variable Separation Logic and Its Inner CircleACM Transactions on Computational Logic10.1145/272471116:2(1-36)Online publication date: 21-Apr-2015
https://dl.acm.org/doi/10.1145/2724711
Demri SDeters M(2015)Separation logics and modalities: a surveyJournal of Applied Non-Classical Logics10.1080/11663081.2015.101880125:1(50-99)Online publication date: Apr-2015
https://doi.org/10.1080/11663081.2015.1018801

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