Reasoning with global assumptions in arithmetic modal logics

Clemens Kupke; Dirk Pattinson; Lutz Schröder

doi:10.1007/978-3-319-22177-9_28

Reasoning with global assumptions in arithmetic modal logics

Clemens Kupke, Dirk Pattinson, Lutz Schröder

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Abstract

We establish a generic upper bound ExpTime for reasoning with global assumptions in coalgebraic modal logics. Unlike earlier results of this kind, we do not require a tractable set of tableau rules for the in- stance logics, so that the result applies to wider classes of logics. Examples are Presburger modal logic, which extends graded modal logic with linear inequalities over numbers of successors, and probabilistic modal logic with polynomial inequalities over probabilities. We establish the theoretical upper bound using a type elimination algorithm. We also provide a global caching algorithm that offers potential for practical reasoning.

Original language	English
Pages	367-380
Number of pages	14
DOIs	https://doi.org/10.1007/978-3-319-22177-9_28
Publication status	Published - 4 Aug 2015
Event	20th International Symposium on Fundamentals of Computation Theory - Gdansk, Poland, Poland Duration: 17 Aug 2015 → 19 Aug 2015

Conference

Conference	20th International Symposium on Fundamentals of Computation Theory
Country	Poland
City	Gdansk, Poland
Period	17/08/15 → 19/08/15

Keywords

coalgebraic modal logic
elimination algorithm
a global caching algorithm

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10.1007/978-3-319-22177-9_28

Kupke-etal-CT2015-reasoning-global-assumptions-arithmetic-modal-logicsAccepted author manuscript, 329 KB

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AU - Pattinson, Dirk

AU - Schröder, Lutz

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N2 - We establish a generic upper bound ExpTime for reasoning with global assumptions in coalgebraic modal logics. Unlike earlier results of this kind, we do not require a tractable set of tableau rules for the in- stance logics, so that the result applies to wider classes of logics. Examples are Presburger modal logic, which extends graded modal logic with linear inequalities over numbers of successors, and probabilistic modal logic with polynomial inequalities over probabilities. We establish the theoretical upper bound using a type elimination algorithm. We also provide a global caching algorithm that offers potential for practical reasoning.

AB - We establish a generic upper bound ExpTime for reasoning with global assumptions in coalgebraic modal logics. Unlike earlier results of this kind, we do not require a tractable set of tableau rules for the in- stance logics, so that the result applies to wider classes of logics. Examples are Presburger modal logic, which extends graded modal logic with linear inequalities over numbers of successors, and probabilistic modal logic with polynomial inequalities over probabilities. We establish the theoretical upper bound using a type elimination algorithm. We also provide a global caching algorithm that offers potential for practical reasoning.

KW - coalgebraic modal logic

KW - elimination algorithm

KW - a global caching algorithm

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ER -

Reasoning with global assumptions in arithmetic modal logics

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Keywords

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