Resource-distribution via Boolean constraints
ACM Transactions on Computational Logic (TOCL)
Proof-Search and Countermodel Generation in Propositional BI Logic
TACS '01 Proceedings of the 4th International Symposium on Theoretical Aspects of Computer Software
Kripke Resource Models of a Dependently-Typed, Bunched lambda-Calculus
CSL '99 Proceedings of the 13th International Workshop and 8th Annual Conference of the EACSL on Computer Science Logic
CSL '02 Proceedings of the 16th International Workshop and 11th Annual Conference of the EACSL on Computer Science Logic
IJCAR '01 Proceedings of the First International Joint Conference on Automated Reasoning
A formalization of an Ordered Logical Framework in Hybrid with applications to continuation machines
MERLIN '03 Proceedings of the 2003 ACM SIGPLAN workshop on Mechanized reasoning about languages with variable binding
Agents via Mixed-Mode Computation in Linear Logic
Annals of Mathematics and Artificial Intelligence
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
Systems Modelling via Resources and Processes: Philosophy, Calculus, Semantics, and Logic
Electronic Notes in Theoretical Computer Science (ENTCS)
Exploring the relation between intuitionistic bi and boolean bi: An unexpected embedding
Mathematical Structures in Computer Science
Algebra and logic for resource-based systems modelling
Mathematical Structures in Computer Science
| Hi-index | 0.00 |
We present the logic of bunched implications, 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, and may be viewed as a merging of intuitionistic logic and multiplicative, intuitionistic linear logic. The predicate version of BI includes, in addition to usual additive quantifiers, multiplicative (or intensional) quantifiers 8new and 9new ,which arise from observing restrictions on structural rules on the level of terms as well as propositions. Moreover, these restrictions naturally allow the distinction between additive predication and multiplicative predication for each propositional connective. We provide a natural deduction system, a sequent calculus, a Kripke semantics and a BHK semantics for BI. We mention computational interpretations, based on locality and sharing, at both the propositional and predicate levels. We explain BI's relationship with intuitionistic logic, linear logic and other relevant logics.