Filter Models for Conjunctive-Disjunctive -calculi?

The distinction between the conjunctive nature of non-determinism as opposed to the disjunctive character of parallelism constitutes the motivation and the starting point of the present work. -calculus is extended with both a non-deterministic choice and a parallel operator; a notion of reduction is introduced, extending -reduction of the classical calculus. We study type assignment systems for this calculus, together with a denotational semantics which is initially de ned constructing a set semimodel via simple types. We enrich the type system with intersection and union types, dually re ecting the disjunctive and conjunctive behaviour of the operators, and we build a lter model. The theory of this model is compared both with a Morris-style operational semantics and with a semantics based on a notion of capabilities.