S. Ishtiaq and D. Pym. Kripke resources models of a dependently-typed bunched -calculus. In 13th Int. Workshop on Computer Science Logic, CSL'99, LNCS 1683, pages 235249, Madrid, Spain, 1999. September.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....(or intuitionistic) connectives cohabit [29] This resource aware logic can be viewed as a merging of intuitionistic logic (IL) and multiplicative intuitionistic linear logic (MILL) that allows to capture interferences between resources. It can be well understood through its Kripke resource models [21] but also proof theoretically through its bunched sequent calculus [34] and the corresponding calculus [27] With its so called sharing interpretation, the BI logic appears as an appropriate logical foundation for logic programming [2] for reasoning about mutable data structures [20] and for ....

....connectives which occur during the proof search process. We know that the tableau method directly provides countermodel generation for a wide range of logics, including IL, but not for substructural logics like linear logic [25, 26] In this work, we focus on the Kripke resource semantics of BI [21] in which the possible worlds are justi ed in terms of pieces of information [37] It is important to mention that the unit of the additive disjunction internalizes inconsistency in BI and that the Kripke resource semantics does not account for inconsistency ( is nowhere forced) Accordingly, ....

S. Ishtiaq and D. Pym. Kripke resources models of a dependently-typed bunched -calculus. In 13th Int. Workshop on Computer Science Logic, CSL'99, LNCS 1683, pages 235249, Madrid, Spain, 1999. September.

.... cohabit [27] The propositional fragment of BI can be viewed as a merging of intuitionistic logic (IL) and multiplicative intuitionistic linear logic (MILL) This new logic has been studied from proof theoretic and semantic point of views [33] with main focuses on Kripke resources models [18] and on the corresponding calculus [25] With its sharing interpretation, BI is an appropriate foundation for some computer science applications as for instance logic programming [2] or for reasoning about mutable data structures [17] In this context, our aim is to provide useful and e cient ....

.... logics like linear logic [23, 24] Our aim is to provide such a calculus for BI and thus we de ne a labelled tableau calculus for propositional BI by a speci c application of the methodology of Labelled Deductive Systems (LDS) 9] A key point is to consider the Kripke resource semantics of BI [18] where the possible worlds are justi ed in terms of pieces of information [36] But it is important to note that the unit of the additive disjunction internalizes inconsistency in BI and the Kripke resource semantics does not account for inconsistency ( is nowhere forced) Accordingly, the ....

S. Ishtiaq and D. Pym. Kripke resources models of a dependently-typed bunched -calculus. In Computer Science Logic, CSL'99, LNCS, Madrid, Spain, 1999.

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