Process-Algebraic Interpretations of Positive Linear and Relevant Logics

摘要

We investigate the use of positive linear and relevant logics to provide logical accounts of static process structure, and combinations of relevance and modality to account also for dynamic behaviour. A general notion of model is introduced, based on which, three examples are given using Milner's synchronous process calculus SCCS. The structure of models is enriched by prefixing operators to cover also dynamic behaviour. Logically dynamic behaviour is captured by adding past and future modal operators. The resulting logic is given sound and complete axiomatizations and shown to conservatively extend the positive fragment of linear logic. Finally the induced interpretations of formulas on process terms are characterized, and axiomatisations are given which are sound and complete with respect to validity in the process-based interpretations. The completeness proofs are based on rewriting and provide procedures for deciding validity and consistency of formulas with respect to the process-based interpretations.