Local Linear Logic for Locality Consciousness in Multiset Transformation

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.

• Type: Conference
• Year: 1995
• Where: PLILP
• Authors: Hugh McEvoy, Pieter H. Hartel
• Keywords: Automated Reasoning, Linear Logic, PLILP 1995, Semantics, Structured Operational Semantics