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DOI: 10.4230/LIPIcs.TYPES.2013.150

A Hybrid Linear Logic for Constrained Transition Systems

Authors: Joëlle Despeyroux and Kaustuv Chaudhuri

Published in: LIPIcs, Volume 26, 19th International Conference on Types for Proofs and Programs (TYPES 2013)

Abstract

Linear implication can represent state transitions, but real transition systems operate under temporal, stochastic or probabilistic constraints that are not directly representable in ordinary linear logic. We propose a general modal extension of intuitionistic linear logic where logical truth is indexed by constraints and hybrid connectives combine constraint reasoning with logical reasoning. The logic has a focused cut-free sequent calculus that can be used to internalize the rules of particular constrained transition systems; we illustrate this with an adequate encoding of the synchronous stochastic pi-calculus.

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Joëlle Despeyroux and Kaustuv Chaudhuri. A Hybrid Linear Logic for Constrained Transition Systems. In 19th International Conference on Types for Proofs and Programs (TYPES 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 26, pp. 150-168, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@InProceedings{despeyroux_et_al:LIPIcs.TYPES.2013.150,
  author =	{Despeyroux, Jo\"{e}lle and Chaudhuri, Kaustuv},
  title =	{{A Hybrid Linear Logic for Constrained Transition Systems}},
  booktitle =	{19th International Conference on Types for Proofs and Programs (TYPES 2013)},
  pages =	{150--168},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-72-9},
  ISSN =	{1868-8969},
  year =	{2014},
  volume =	{26},
  editor =	{Matthes, Ralph and Schubert, Aleksy},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TYPES.2013.150},
  URN =		{urn:nbn:de:0030-drops-46302},
  doi =		{10.4230/LIPIcs.TYPES.2013.150},
  annote =	{Keywords: Linear logic, hybrid logic, stochastic pi-calculus, focusing, adequacy}
}

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A Hybrid Linear Logic for Constrained Transition Systems

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