Abstract
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 inefficiencies, 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 efficiency without compromising its programming style. We show how the new semantics also gives us a better understanding of parallel Gamma and its implementation, and offers insight into the nature of chemicalreaction based computational models in general.KeywordsCellular AutomatonSequential CompositionLinear LogicAbstract SyntaxSequent CalculusThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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