Finitary S5-theories

Tran Cao Son; Enrico Pontelli; Chitta Baral; Gregory Gelfond

doi:10.1007/978-3-319-11558-0_17

Finitary S5-theories

Tran Cao Son, Enrico Pontelli, Chitta Baral, Gregory Gelfond

Research output: Contribution to journal › Article › peer-review

13 Scopus citations

Abstract

The objective of this paper is to identify a class of epistemic logic theories with group knowledge operators which have the fundamental property of being characterized by a finite number of finite models (up to equivalence). We specifically focus on S5-theories. We call this class of epistemic logic theories as finitary S5-theories. Models of finitary S5-theories can be shown to be canonical in that they do not contain two worlds with the same interpretation. When the theory is pure, these models are minimal and differ from each other only in the actual world. The paper presents an algorithm for computing all models of a finitary S5-theory. Finitary S5-theories find applications in several contexts—in particular, the paper discusses their use in epistemic multi-agent planning.

Original language	English (US)
Pages (from-to)	39-252
Number of pages	214
Journal	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	8761
DOIs	https://doi.org/10.1007/978-3-319-11558-0_17
State	Published - 2014

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

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10.1007/978-3-319-11558-0_17

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title = "Finitary S5-theories",

abstract = "The objective of this paper is to identify a class of epistemic logic theories with group knowledge operators which have the fundamental property of being characterized by a finite number of finite models (up to equivalence). We specifically focus on S5-theories. We call this class of epistemic logic theories as finitary S5-theories. Models of finitary S5-theories can be shown to be canonical in that they do not contain two worlds with the same interpretation. When the theory is pure, these models are minimal and differ from each other only in the actual world. The paper presents an algorithm for computing all models of a finitary S5-theory. Finitary S5-theories find applications in several contexts—in particular, the paper discusses their use in epistemic multi-agent planning.",

author = "Son, {Tran Cao} and Enrico Pontelli and Chitta Baral and Gregory Gelfond",

note = "Funding Information: Acknowledgments. The research has been partially supported by NSF grants HRD-1345232 and DGE-0947465. The authors would like to thank Guram Bezhanishvili and Nguyen L. A for the useful discussions and suggestions. Publisher Copyright: {\textcopyright} Springer International Publishing Switzerland 2014.",

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doi = "10.1007/978-3-319-11558-0_17",

language = "English (US)",

volume = "8761",

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T1 - Finitary S5-theories

AU - Son, Tran Cao

AU - Pontelli, Enrico

AU - Baral, Chitta

AU - Gelfond, Gregory

N1 - Funding Information: Acknowledgments. The research has been partially supported by NSF grants HRD-1345232 and DGE-0947465. The authors would like to thank Guram Bezhanishvili and Nguyen L. A for the useful discussions and suggestions. Publisher Copyright: © Springer International Publishing Switzerland 2014.

PY - 2014

Y1 - 2014

N2 - The objective of this paper is to identify a class of epistemic logic theories with group knowledge operators which have the fundamental property of being characterized by a finite number of finite models (up to equivalence). We specifically focus on S5-theories. We call this class of epistemic logic theories as finitary S5-theories. Models of finitary S5-theories can be shown to be canonical in that they do not contain two worlds with the same interpretation. When the theory is pure, these models are minimal and differ from each other only in the actual world. The paper presents an algorithm for computing all models of a finitary S5-theory. Finitary S5-theories find applications in several contexts—in particular, the paper discusses their use in epistemic multi-agent planning.

AB - The objective of this paper is to identify a class of epistemic logic theories with group knowledge operators which have the fundamental property of being characterized by a finite number of finite models (up to equivalence). We specifically focus on S5-theories. We call this class of epistemic logic theories as finitary S5-theories. Models of finitary S5-theories can be shown to be canonical in that they do not contain two worlds with the same interpretation. When the theory is pure, these models are minimal and differ from each other only in the actual world. The paper presents an algorithm for computing all models of a finitary S5-theory. Finitary S5-theories find applications in several contexts—in particular, the paper discusses their use in epistemic multi-agent planning.

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ER -

Finitary S5-theories

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