Reasoning with global assumptions in arithmetic modal logics

Clemens Kupke, Dirk Pattinson, Lutz Schröder

Research output: Contribution to conferencePaper

1 Citation (Scopus)

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.

Conference

Conference20th International Symposium on Fundamentals of Computation Theory
CountryPoland
CityGdansk, Poland
Period17/08/1519/08/15

Fingerprint

Modal Logic
Reasoning
Polynomials
Logic
Upper bound
Probabilistic Logic
Tableau
Caching
Elimination
Linear Inequalities
Polynomial

Keywords

  • coalgebraic modal logic
  • elimination algorithm
  • a global caching algorithm

Cite this

Kupke, C., Pattinson, D., & Schröder, L. (2015). Reasoning with global assumptions in arithmetic modal logics. 367-380. Paper presented at 20th International Symposium on Fundamentals of Computation Theory, Gdansk, Poland, Poland. https://doi.org/10.1007/978-3-319-22177-9_28
Kupke, Clemens ; Pattinson, Dirk ; Schröder, Lutz. / Reasoning with global assumptions in arithmetic modal logics. Paper presented at 20th International Symposium on Fundamentals of Computation Theory, Gdansk, Poland, Poland.14 p.
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Kupke, C, Pattinson, D & Schröder, L 2015, 'Reasoning with global assumptions in arithmetic modal logics' Paper presented at 20th International Symposium on Fundamentals of Computation Theory, Gdansk, Poland, Poland, 17/08/15 - 19/08/15, pp. 367-380. https://doi.org/10.1007/978-3-319-22177-9_28

Reasoning with global assumptions in arithmetic modal logics. / Kupke, Clemens; Pattinson, Dirk; Schröder, Lutz.

2015. 367-380 Paper presented at 20th International Symposium on Fundamentals of Computation Theory, Gdansk, Poland, Poland.

Research output: Contribution to conferencePaper

TY - CONF

T1 - Reasoning with global assumptions in arithmetic modal logics

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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.

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Kupke C, Pattinson D, Schröder L. Reasoning with global assumptions in arithmetic modal logics. 2015. Paper presented at 20th International Symposium on Fundamentals of Computation Theory, Gdansk, Poland, Poland. https://doi.org/10.1007/978-3-319-22177-9_28