Introduction to higher order categorical logic
Introduction to higher order categorical logic
Theoretical Computer Science
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
Connection methods in linear logic and proof nets construction
Theoretical Computer Science - Special issue on proof-search in type-theoretic languages
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
Resource-distribution via Boolean constraints
ACM Transactions on Computational Logic (TOCL)
Separation Logic: A Logic for Shared Mutable Data Structures
LICS '02 Proceedings of the 17th Annual IEEE Symposium on Logic in Computer Science
Proof-Search and Countermodel Generation in Propositional BI Logic
TACS '01 Proceedings of the 4th International Symposium on Theoretical Aspects of Computer Software
CSL '02 Proceedings of the 16th International Workshop and 11th Annual Conference of the EACSL on Computer Science Logic
Connection-Based Proof Search in Propositional BI Logic
CADE-18 Proceedings of the 18th International Conference on Automated Deduction
LICS '99 Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science
Possible worlds and resources: the semantics of BI
Theoretical Computer Science - Mathematical foundations of programming semantics
Systems Modelling via Resources and Processes: Philosophy, Calculus, Semantics, and Logic
Electronic Notes in Theoretical Computer Science (ENTCS)
Classical BI: a logic for reasoning about dualising resources
Proceedings of the 36th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Exploring the relation between intuitionistic bi and boolean bi: An unexpected embedding
Mathematical Structures in Computer Science
A Unified Display Proof Theory for Bunched Logic
Electronic Notes in Theoretical Computer Science (ENTCS)
Electronic Notes in Theoretical Computer Science (ENTCS)
Expressivity properties of Boolean BI through relational models
FSTTCS'06 Proceedings of the 26th international conference on Foundations of Software Technology and Theoretical Computer Science
Nondeterministic Phase Semantics and the Undecidability of Boolean BI
ACM Transactions on Computational Logic (TOCL)
Studia Logica
A theorem prover for Boolean BI
POPL '13 Proceedings of the 40th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Inconsistency-Tolerant Bunched Implications
International Journal of Approximate Reasoning
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The logic of bunched implications, BI, provides a logical analysis of a basic notion of resource that is rich enough, for example, to form the logical basis for ‘pointer logic’ and ‘separation logic’ semantics for programs that 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, $\bot$, 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. Then, from these results, we can define a new resource semantics of BI, based on partially defined monoids, and prove that this semantics is complete. Such a semantics, based on partiality, is closely related to the semantics of BI's (intuitionistic) pointer and separation logics. Returning to the tableaux calculus, we propose a new version with liberalised rules for which the countermodels are closely related to the topological Kripke semantics of BI. As consequences of the relationships between semantics of BI and resource tableaux, we prove two new strong results for propositional BI: its decidability and the finite model property with respect to topological semantics.