Finite Conjunctive Nondeterminism (Extended Abstract)

Abstract

In process description languages such as CCS, [M], processes correspond to terms over a given signature. Each operator of the signature, or combinator, corresponds to a method for constructing new processes from existing ones. In this paper we suggest that the choice of combinators should be governed by the logical properties they induce. Specifically they should be chosen so that the logical properties of the constructed process are easily inferred from those of its constituents. Of course we must ensure that these operators also have an acceptable operational and denotational semantics. In other words, we would like to develop an approach to the semantics of processes which reconciles the more usual denotational and operational semantics with logic. In such a framework we would expect the logic to determine the denotational semantics. More specifically, if ∥p∥ represents the denotation of p then we would expect ∥p∥ = ∥q∥ iff (for every φ, p ⊧ φ <=< q ⊧ φ) (*) where φ ranges over formulae from some suitable assertio n or property language.