Theoretical Computer Science
From multiple sequent for additive linear logic to decision procedures for free lattices
Theoretical Computer Science
Logic of Information Structures
Logic of Information Structures
Resource-distribution via Boolean constraints
ACM Transactions on Computational Logic (TOCL)
Journal of Functional Programming
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
Linear and affine logics with temporal, spatial and epistemic operators
Theoretical Computer Science
Measures of inconsistency and defaults
International Journal of Approximate Reasoning
A framework for reasoning under uncertainty based on non-deterministic distance semantics
International Journal of Approximate Reasoning
A Syntax-based approach to measuring the degree of inconsistency for belief bases
International Journal of Approximate Reasoning
Proof theory of Nelson's paraconsistent logic: A uniform perspective
Theoretical Computer Science
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It is known that logical systems with the property of paraconsistency can deal with inconsistency-tolerant and uncertainty reasoning more appropriately than systems which are non-paraconsistent. It is also known that the logic BI of bunched implications is useful for formalizing resource-sensitive reasoning. In this paper, a paraconsistent extension PBI of BI is studied. The logic PBI is thus intended to formalize an appropriate combination of inconsistency-tolerant reasoning and resource-sensitive reasoning. A Gentzen-type sequent calculus SPBI for PBI is introduced, and the cut-elimination and decidability theorems for SPBI are proved. An extension of the Grothendieck topological semantics for BI is introduced for PBI, and the completeness theorem with respect to this semantics is proved.