License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.FSTTCS.2018.15
URN: urn:nbn:de:0030-drops-99143
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/9914/
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Baelde, David ; Lick, Anthony ; Schmitz, Sylvain

A Hypersequent Calculus with Clusters for Tense Logic over Ordinals

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Abstract

Prior's tense logic forms the core of linear temporal logic, with both past- and future-looking modalities. We present a sound and complete proof system for tense logic over ordinals. Technically, this is a hypersequent system, enriched with an ordering, clusters, and annotations. The system is designed with proof search algorithms in mind, and yields an optimal coNP complexity for the validity problem. It entails a small model property for tense logic over ordinals: every satisfiable formula has a model of order type at most omega^2. It also allows to answer the validity problem for ordinals below or exactly equal to a given one.

BibTeX - Entry

@InProceedings{baelde_et_al:LIPIcs:2018:9914,
  author =	{David Baelde and Anthony Lick and Sylvain Schmitz},
  title =	{{A Hypersequent Calculus with Clusters for Tense Logic over Ordinals}},
  booktitle =	{38th IARCS Annual Conference on Foundations of Software  Technology and Theoretical Computer Science (FSTTCS 2018)},
  pages =	{15:1--15:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-093-4},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{122},
  editor =	{Sumit Ganguly and Paritosh Pandya},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/9914},
  URN =		{urn:nbn:de:0030-drops-99143},
  doi =		{10.4230/LIPIcs.FSTTCS.2018.15},
  annote =	{Keywords: modal logic, proof system, hypersequent}
}

Keywords: modal logic, proof system, hypersequent
Collection: 38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018)
Issue Date: 2018
Date of publication: 05.12.2018

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