Resource tableaux - (extended abstract)

Didier Galmiche, Daniel Mery, David Pym

Research output: Chapter or section in a book/report/conference proceedingChapter or section

13 Citations (SciVal)


The logic of bunched implications, BI, provides a logical analysis of a basic notion of resource rich enough to provide a "pointer logic" semantics for programs which manipulate mutable data structures. We develop a theory of semantic tableaux for BI, so providing an elegant basis for efficient theorem proving tools for BI. It is based on the use of an algebra of labels for BI's tableaux to solve the resource-distribution problem, the labels being the elements of resource models. For BI with inconsistency, perpendicular to, the challenge consists in dealing with BI's Grothendieck topological models within such a proof-search method, based on labels. We prove soundness and completeness theorems for a resource tableaux method TBI with respect to this semantics and provide a way to build countermodels from so-called dependency graphs. As consequences, we have two strong new results for BI: the decidability of propositional BI and the finite model property with respect to Grothendieck topological semantics. In addition, we propose, by considering partially defined monoids, a new semantics which generalizes the semantics of BI's pointer logic and for which BI is complete.
Original languageEnglish
Title of host publicationComputer Science Logic
Subtitle of host publication16th International Workshop, CSL 2002 11th Annual Conference of the EACSL Edinburgh, Scotland, UK, September 22–25 Proceedings
EditorsJ. Bradfield
Place of PublicationBerlin, Germany
Number of pages17
ISBN (Print)9783540442400
Publication statusPublished - 2002
Event16th International Workshop, CSL 2002 11th Annual Conference of the EACSL - Edinburgh, UK United Kingdom
Duration: 22 Sept 200225 Sept 2002

Publication series

NameLecture Notes in Computer Science


Conference16th International Workshop, CSL 2002 11th Annual Conference of the EACSL
Country/TerritoryUK United Kingdom

Bibliographical note

ID number: ISI:000187294300013


  • tableaux
  • resources
  • decidability
  • semantics
  • finite model property
  • bi
  • logic


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