Extended Horn clauses: the framework and some semantics

Abstract

The purpose of this paper is twofold: to introduce a new extension of concurrent logic programming languages aiming at handling synchronicity and to present and compare several semantics for it. The extended framework essentially rests on an extension of Horn clauses, including multiple atoms in their heads and a guard construct, as well as a new operator between goals. The semantics discussed consist of four semantics. They range in the operational, declarative and denotational types and are issued both from the logic programming tradition and the imperative tradition. They are composed of an operational semantics, describing the (classical) success set and failure set, of two declarative semantics, extending the Herbrand interpretation and the immediate consequence operator to the extended framework, and of a denotational semantics, defined compositionally and on the basis of histories possibly involving hypothetical statements. The mathematical tools mainly used are complete lattices and complete metric spaces.