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Computability and completeness in logics of programs (Preliminary Report)

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V. R. PrattAuthors Info & Claims

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

Pages 261 - 268

https://doi.org/10.1145/800105.803416

Published: 04 May 1977 Publication History

Abstract

Dynamic logic is a generalization of first order logic in which quantifiers of the form “for all χ...” are replaced by phrases of the form “after executing program α...”. This logic subsumes most existing first-order logics of programs that manipulate their environment, including Floyd's and Hoare's logics of partial correctness and Manna and Waldinger's logic of total correctness, yet is more closely related to classical first-order logic than any other proposed logic of programs. We consider two issues: how hard is the validity problem for the formulae of dynamic logic, and how might one axiomatize dynamic logic? We give bounds on the validity problem for some special cases, including a Π⁰₂-completeness result for the partial correctness theories of uninterpreted flowchart programs. We also demonstrate the completeness of an axiomatization of dynamic logic relative to arithmetic.

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Cited By

Beckert BBubel RDrodt DHähnle RLanzinger FPfeifer WUlbrich MWeigl A(2024)The Java Verification Tool KeY:A TutorialFormal Methods10.1007/978-3-031-71177-0_32(597-623)Online publication date: 9-Sep-2024
https://dl.acm.org/doi/10.1007/978-3-031-71177-0_32
Hähnle R(2022)Dijkstra’s Legacy on Program VerificationEdsger Wybe Dijkstra10.1145/3544585.3544593(105-140)Online publication date: 12-Jul-2022
https://dl.acm.org/doi/10.1145/3544585.3544593
Finkbeiner BHeim PPassing N(2022)Temporal Stream Logic modulo TheoriesFoundations of Software Science and Computation Structures10.1007/978-3-030-99253-8_17(325-346)Online publication date: 29-Mar-2022
https://doi.org/10.1007/978-3-030-99253-8_17
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Computability and completeness in logics of programs (Preliminary Report)

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cover image ACM Conferences

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

May 1977

318 pages

ISBN:9781450374095

DOI:10.1145/800105

Copyright © 1977 ACM.

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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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

Beckert BBubel RDrodt DHähnle RLanzinger FPfeifer WUlbrich MWeigl A(2024)The Java Verification Tool KeY:A TutorialFormal Methods10.1007/978-3-031-71177-0_32(597-623)Online publication date: 9-Sep-2024
https://dl.acm.org/doi/10.1007/978-3-031-71177-0_32
Hähnle R(2022)Dijkstra’s Legacy on Program VerificationEdsger Wybe Dijkstra10.1145/3544585.3544593(105-140)Online publication date: 12-Jul-2022
https://dl.acm.org/doi/10.1145/3544585.3544593
Finkbeiner BHeim PPassing N(2022)Temporal Stream Logic modulo TheoriesFoundations of Software Science and Computation Structures10.1007/978-3-030-99253-8_17(325-346)Online publication date: 29-Mar-2022
https://doi.org/10.1007/978-3-030-99253-8_17
Pratt V(2018)Dynamic Logic: A Personal PerspectiveDynamic Logic. New Trends and Applications10.1007/978-3-319-73579-5_10(153-170)Online publication date: 3-Jan-2018
https://doi.org/10.1007/978-3-319-73579-5_10
Platzer A(2015)Differential Game LogicACM Transactions on Computational Logic10.1145/281782417:1(1-51)Online publication date: 14-Nov-2015
https://dl.acm.org/doi/10.1145/2817824
Platzer A(2012)The Complete Proof Theory of Hybrid SystemsProceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science10.1109/LICS.2012.64(541-550)Online publication date: 25-Jun-2012
https://dl.acm.org/doi/10.1109/LICS.2012.64
Platzer A(2012)Logics of Dynamical SystemsProceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science10.1109/LICS.2012.13(13-24)Online publication date: 25-Jun-2012
https://dl.acm.org/doi/10.1109/LICS.2012.13
Platzer A(2012)Logical analysis of hybrid systemsProceedings of the 14th international conference on Descriptional Complexity of Formal Systems10.1007/978-3-642-31623-4_3(43-49)Online publication date: 23-Jul-2012
https://dl.acm.org/doi/10.1007/978-3-642-31623-4_3
Enjalbert P(2011)Systèmes de déduction pour les arbres et les schémas de programmes (I)RAIRO. Informatique théorique10.1051/ita/198014030247114:3(247-278)Online publication date: 8-Jan-2011
https://doi.org/10.1051/ita/1980140302471
Kozen D(2010)Halting and equivalence of program schemes in models of arbitrary theoriesFields of logic and computation10.5555/1983702.1983726(463-469)Online publication date: 1-Jan-2010
https://dl.acm.org/doi/10.5555/1983702.1983726
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