First-order logic and automated theorem proving
First-order logic and automated theorem proving
Linear logic: its syntax and semantics
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
BI as an assertion language for mutable data structures
POPL '01 Proceedings of the 28th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Separation Logic: A Logic for Shared Mutable Data Structures
LICS '02 Proceedings of the 17th Annual IEEE Symposium on Logic in Computer Science
A Spatial Logic for Concurrency
TACS '01 Proceedings of the 4th International Symposium on Theoretical Aspects of Computer Software
A Spatial Logic for Querying Graphs
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
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
A connection-based characterization of bi-intuitionistic validity
CADE'11 Proceedings of the 23rd international conference on Automated deduction
Characterizing provability in BI's pointer logic through resource graphs
LPAR'05 Proceedings of the 12th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
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In this abstract we emphasize the role of a semantic structure called resource graph in order to study the provability in some resource-sensitive logics, like the Bunched Implications Logic (BI) or the Non-commutative Logic (NL). Such a semantic structure is appropriate for capturing the particular interactions between different kinds of connectives (additives and multiplicatives in BI, commutatives and non-commutatives in NL) that occur during proof-search and is also well-suited for providing countermodels in case of non-provability. We illustrate the key points with a tableau method with labels and constraints for BI and then present tools, namely BILL and CheckBI, which are respectively dedicated to countermodel generation and verification in this logic.