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Back and forth between guarded and modal logics

Authors:

Martin OttoAuthors Info & Claims

ACM Transactions on Computational Logic (TOCL), Volume 3, Issue 3

Pages 418 - 463

https://doi.org/10.1145/507382.507388

Published: 01 July 2002 Publication History

Abstract

Guarded fixed-point logic μGF extends the guarded fragment by means of least and greatest fixed points, and thus plays the same role within the domain of guarded logics as the modal μ-calculus plays within the modal domain. We provide a semantic characterization of μGF within an appropriate fragment of second-order logic, in terms of invariance under guarded bisimulation. The corresponding characterization of the modal μ-calculus, due to Janin and Walukiewicz, is lifted from the modal to the guarded domain by means of model theoretic translations. Guarded second-order logic, the fragment of second-order logic which is introduced in the context of our characterization theorem, captures a natural and robust level of expressiveness with several equivalent characterizations. For a wide range of issues in guarded logics it may take up a role similar to that of monadic second-order in relation to modal logics. At the more general methodological level, the translations between the guarded and modal domains make the intuitive analogy between guarded and modal logics available as a tool in the further analysis of the model theory of guarded logics.

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Cited By

Benedikt MKikot SOstropolski-Nalewaja PRomero M(2023)On Monotonic Determinacy and Rewritability for Recursive Queries and ViewsACM Transactions on Computational Logic10.1145/357283624:2(1-62)Online publication date: 17-Mar-2023
https://dl.acm.org/doi/10.1145/3572836
Gottlob GHernich AKupke CLukasiewicz T(2021)Stable Model Semantics for Guarded Existential Rules and Description Logics: Decidability and ComplexityJournal of the ACM10.1145/344750868:5(1-87)Online publication date: 22-Oct-2021
https://dl.acm.org/doi/10.1145/3447508
Abramsky SMarsden DGorla D(2021)Comonadic semantics for guarded fragmentsProceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science10.1109/LICS52264.2021.9470594(1-13)Online publication date: 29-Jun-2021
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Index Terms

Back and forth between guarded and modal logics
1. Theory of computation
  1. Logic
  2. Models of computation
    1. Computability

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cover image ACM Transactions on Computational Logic

ACM Transactions on Computational Logic Volume 3, Issue 3

July 2002

129 pages

ISSN:1529-3785

EISSN:1557-945X

DOI:10.1145/507382

Issue’s Table of Contents

Copyright © 2002 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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Publication History

Published: 01 July 2002

Published in TOCL Volume 3, Issue 3

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Cited By

Benedikt MKikot SOstropolski-Nalewaja PRomero M(2023)On Monotonic Determinacy and Rewritability for Recursive Queries and ViewsACM Transactions on Computational Logic10.1145/357283624:2(1-62)Online publication date: 17-Mar-2023
https://dl.acm.org/doi/10.1145/3572836
Gottlob GHernich AKupke CLukasiewicz T(2021)Stable Model Semantics for Guarded Existential Rules and Description Logics: Decidability and ComplexityJournal of the ACM10.1145/344750868:5(1-87)Online publication date: 22-Oct-2021
https://dl.acm.org/doi/10.1145/3447508
Abramsky SMarsden DGorla D(2021)Comonadic semantics for guarded fragmentsProceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science10.1109/LICS52264.2021.9470594(1-13)Online publication date: 29-Jun-2021
https://dl.acm.org/doi/10.1109/LICS52264.2021.9470594
Benedikt MKikot SOstropolski-Nalewaja PRomero MSuciu DTao YWei Z(2020)On Monotonic Determinacy and Rewritability for Recursive Queries and ViewsProceedings of the 39th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems10.1145/3375395.3387661(131-148)Online publication date: 14-Jun-2020
https://dl.acm.org/doi/10.1145/3375395.3387661
Blumensath AWolf F(2020)Bisimulation invariant monadic-second order logic in the finiteTheoretical Computer Science10.1016/j.tcs.2020.03.001823(26-43)Online publication date: Jul-2020
https://doi.org/10.1016/j.tcs.2020.03.001
Zhang XVan den Bussche JWang KWang ZMcIlraith SWeinberger K(2018)On the satisfiability problem of patterns in SPARQL 1.1Proceedings of the Thirty-Second AAAI Conference on Artificial Intelligence and Thirtieth Innovative Applications of Artificial Intelligence Conference and Eighth AAAI Symposium on Educational Advances in Artificial Intelligence10.5555/3504035.3504285(2054-2061)Online publication date: 2-Feb-2018
https://dl.acm.org/doi/10.5555/3504035.3504285
Benedikt MVan den Bussche JArenas M(2018)How Can Reasoners Simplify Database Querying (And Why Haven't They Done It Yet)?Proceedings of the 37th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems10.1145/3196959.3196989(1-15)Online publication date: 27-May-2018
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Bradfield JWalukiewicz I(2018)The mu-calculus and Model CheckingHandbook of Model Checking10.1007/978-3-319-10575-8_26(871-919)Online publication date: 19-May-2018
https://doi.org/10.1007/978-3-319-10575-8_26
Segoufin L(2017)A survey on guarded negationACM SIGLOG News10.1145/3129173.31291784:3(12-26)Online publication date: 28-Jul-2017
https://dl.acm.org/doi/10.1145/3129173.3129178
Elberfeld MGrohe MTantau T(2016)Where First-Order and Monadic Second-Order Logic CoincideACM Transactions on Computational Logic10.1145/294679917:4(1-18)Online publication date: 10-Sep-2016
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