The logic of bunched implications

@article{OHearn1999TheLO,
  title={The logic of bunched implications},
  author={P. O'Hearn and D. Pym},
  journal={Bull. Symb. Log.},
  year={1999},
  volume={5},
  pages={215-244}
}
We introduce a logic BI in which a multiplicative (or linear) and an additive (or intuitionistic) implication live side-by-side. The propositional version of BI arises from an analysis of the proof-theoretic relationship between conjunction and implication; it can be viewed as a merging of intuitionistic logic and multiplicative intuitionistic linear logic. The naturality of BI can be seen categorically: models of propositional BI' s proofs are given by bicartesian doubly closed categories, i.e… Expand
On bunched predicate logic
  • D. Pym
  • Mathematics, Computer Science
  • Proceedings. 14th Symposium on Logic in Computer Science (Cat. No. PR00158)
  • 1999
Logic Programming with Bunched Implications
  • D. Pym
  • Computer Science
  • Electron. Notes Theor. Comput. Sci.
  • 1998
Towards a Cut-free Sequent Calculus for Boolean BI
Possible worlds and resources: the semantics of BI
Provability in BI's Sequent Calculus is Decidable
Sub-classical Boolean Bunched Logics and the Meaning of Par
Classical BI: a logic for reasoning about dualising resources
Proof-Search and Countermodel Generation in Propositional BI Logic
Classical Logic of Bunched Implications
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