Local Linear Logic for Locality Consciousness in Multiset Transformation

13 years 8 months ago

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We use Girard's linear logic (LL) to produce a semantics for Gamma, a multiset transformation language. The semantics improves on the existing structured operational semantics (SOS) of the language by highlighting Gamma's ine ciencies, which were hidden by the SOS. We propose a new logic called local linear logic (Local LL), which adds locality-consciousness to the resource-consciousness of linear logic. As a case study, we use this logic to propose a new semantics for Gamma. The new semantics suggests an annotation of Gamma which increases its e ciency without compromising its programming style. We show how the new semantics also gives us a better understanding of parallel Gamma and its implementation, and o ers insight into the nature of chemicalreaction based computational models in general.

Hugh McEvoy, Pieter H. Hartel

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