First-order logic and automated theorem proving
First-order logic and automated theorem proving
Anytime, anywhere: modal logics for mobile ambients
Proceedings of the 27th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
BI as an assertion language for mutable data structures
POPL '01 Proceedings of the 28th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
T-String Unification: Unifying Prefixes in Non-classical Proof Methods
TABLEAUX '96 Proceedings of the 5th International Workshop on Theorem Proving with Analytic Tableaux and Related Methods
LICS '99 Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science
Deciding validity in a spatial logic for trees
Journal of Functional Programming
The semantics of BI and resource tableaux
Mathematical Structures in Computer Science
Elimination of quantifiers and undecidability in spatial logics for concurrency
Theoretical Computer Science - Concurrency theory (CONCUR 2004)
A Calculus and logic of resources and processes
Formal Aspects of Computing
Context logic as modal logic: completeness and parametric inexpressivity
Proceedings of the 34th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Systems Modelling via Resources and Processes: Philosophy, Calculus, Semantics, and Logic
Electronic Notes in Theoretical Computer Science (ENTCS)
Models and Separation Logics for Resource Trees
Journal of Logic and Computation
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
Adjunct elimination through games in static ambient logic
FSTTCS'04 Proceedings of the 24th international conference on Foundations of Software Technology and Theoretical Computer Science
A Unified Display Proof Theory for Bunched Logic
Electronic Notes in Theoretical Computer Science (ENTCS)
Electronic Notes in Theoretical Computer Science (ENTCS)
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
Parametric completeness for separation theories
Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages
Proof search for propositional abstract separation logics via labelled sequents
Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages
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The logic of Bunched Implications, through both its intuitionistic version (BI) and one of its classical versions, called Boolean BI (BBI), serves as a logical basis to spatial or separation logic frameworks. In BI, the logical implication is interpreted intuitionistically whereas it is generally interpreted classically in spatial or separation logics, as in BBI. In this paper, we aim to give some new insights into the semantic relations between BI and BBI. Then we propose a sound and complete syntactic constraints based framework for the Kripke semantics of both BI and BBI, a sound labelled tableau proof system for BBI, and a representation theorem relating the syntactic models of BI to those of BBI. Finally, we deduce as our main, and unexpected, result, a sound and faithful embedding of BI into BBI.