## Process-Algebraic Interpretations of Positive Linear and
Relevant Logics

**Mads Dam**
*Abstract:* 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
axiomatisations and shown to conservatively extend the positive
fragment of linear logic. Finally the induced interpretations of
formulas on process terms are characterised, 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.

*LFCS report ECS-LFCS-92-216*

To appear in the Journal of Logic and Computation.

Previous |

Index |

Next