### Abstract

Language | English |
---|---|

Pages | 367-380 |

Number of pages | 14 |

DOIs | |

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 |
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Country | Poland |

City | Gdansk, Poland |

Period | 17/08/15 → 19/08/15 |

### Fingerprint

### Keywords

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

### Cite this

*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

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

Research output: Contribution to conference › Paper

TY - CONF

T1 - Reasoning with global assumptions in arithmetic modal logics

AU - Kupke, Clemens

AU - Pattinson, Dirk

AU - Schröder, Lutz

PY - 2015/8/4

Y1 - 2015/8/4

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

UR - https://sites.google.com/site/fct2015gdansk/

U2 - 10.1007/978-3-319-22177-9_28

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

M3 - Paper

SP - 367

EP - 380

ER -