First-order logic and automated theorem proving
First-order logic and automated theorem proving
Deciding provability of linear logic formulas
Proceedings of the workshop on Advances in linear logic
Labelled proof systems for intuitionistic provability
Labelled deduction
BI as an assertion language for mutable data structures
POPL '01 Proceedings of the 28th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Proof-Search and Countermodel Generation in Propositional BI Logic
TACS '01 Proceedings of the 4th International Symposium on Theoretical Aspects of Computer Software
Local Reasoning about Programs that Alter Data Structures
CSL '01 Proceedings of the 15th International Workshop on Computer Science Logic
Resource-Distribution via Boolean Constraint (Extended Abstract)
CADE-14 Proceedings of the 14th International Conference on Automated Deduction
LICS '99 Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science
Resource-distribution via Boolean constraints
ACM Transactions on Computational Logic (TOCL)
Possible worlds and resources: the semantics of BI
Theoretical Computer Science - Mathematical foundations of programming semantics
The semantics of BI and resource tableaux
Mathematical Structures in Computer Science
Systems Modelling via Resources and Processes: Philosophy, Calculus, Semantics, and Logic
Electronic Notes in Theoretical Computer Science (ENTCS)
Resource Graphs and Countermodels in Resource Logics
Electronic Notes in Theoretical Computer Science (ENTCS)
CSL'09/EACSL'09 Proceedings of the 23rd CSL international conference and 18th EACSL Annual conference on Computer science logic
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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 developa 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, 驴, 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.