Partial order and SOS semantics for linear constraint programs

Abstract

In this paper we consider linear constraint programming (Icp), a non-monotonic extension of concurrent constraint programming (ccp) which allows to remove information. The entailment relation of a linear constraint system, in terms of which linear constraint programs are defined, is based on the main underlying idea of linear logic: hypotheses in a logical derivation represent physical resources which are consumed, once used in the entailment relation.

We give a semantical analysis of this extension of ccp in terms of the causal relations among occurrences of basic actions (i.e. events). Using a partial order based history model, we define truly concurrent operational and partial order semantic models of lcp. They allow us to compare — and classify — various sublanguages of the proposed extension of ccp (including ccp itself) from the point of view of the degree of parallelism they generate. The two main results of the paper are consistency and completeness of the partial order model with respect to the operational semantics, and thus — as we will argue — its adequacy.

This work has been supported by the HCM Project EXPRESS and by the Esprit Research Project CALIBAN.