Ions and local definitions in logic programming

Abstract

In [1] Bowen and Kowalski suggest amalgamating language and metalanguage in logic programming in order to be able to explicitly refer to theories (i.e. collections of clauses), and discuss derivability from these theories. In particular, they use amalgamation in order to give a solution to the locality of definition problem. In this paper we reconsider this locality of definition problem, and present a new approach for solving it, whithout calling upon language and metalanguage amalgamation. To this end we introduce the notion of an ion, and extend to logic programming with ions various results from "classical" logic programming. We give a least fixpoint semantics, a set-theoretic characterization of successful derivations, and a skylight theorem characterizing approximations to the result computed by a given derivation.