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International Workshop on Computer Science Logic

CSL 2009: Computer Science Logic pp 287–301Cite as

Craig Interpolation for Linear Temporal Languages

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5771))

Abstract

We study Craig interpolation for fragments and extensions of propositional linear temporal logic (PLTL). We consider various fragments of PLTLobtained by restricting the set of temporal connectives and, for each of these fragments, we identify its smallest extension that has Craig interpolation. Depending on the underlying set of temporal operators, this extension turns out to be one of the following three logics: the fragment of PLTLhaving only the Next operator; the extension of PLTLwith a fixpoint operator μ (known as linear time μ-calculus); the fixpoint extension of the “Until-only” fragment of PLTL.

We are grateful to Alexandru Baltag for helpful comments and to Frank Wolter for first raising the question. The first author was supported by a GLoRiClass fellowship of the European Commission (Research Training Fellowship MEST-CT-2005-020841) and the second author by the Netherlands Organization for Scientific Research (NWO) grant 639.021.508 and by ERC Advanced Grant Webdam on Foundation of Web data management.

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Author information

Authors and Affiliations

  1. ILLC, Universiteit van Amsterdam, Netherlands

    Amélie Gheerbrant

  2. INRIA and ENS Cachan, France

    Balder ten Cate

Authors
  1. Amélie Gheerbrant
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  2. Balder ten Cate
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Editor information

Editors and Affiliations

  1. Mathematische Grundlagen der Informatik, RWTH Aachen, 52056, Aachen, Germany

    Erich Grädel

  2. CENTRIA and Departamento de Matemática, Universidade Nova de Lisboa, 2829-516, Caparica, Portugal

    Reinhard Kahle

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Gheerbrant, A., ten Cate, B. (2009). Craig Interpolation for Linear Temporal Languages. In: Grädel, E., Kahle, R. (eds) Computer Science Logic. CSL 2009. Lecture Notes in Computer Science, vol 5771. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04027-6_22

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  • DOI: https://doi.org/10.1007/978-3-642-04027-6_22

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-04026-9

  • Online ISBN: 978-3-642-04027-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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