The least fixpoint transformation for disjunctive logic programs

Abstract

The paradigm of disjunctive logic programming (DLP) enhances greatly the expressive power of normal logic programming (NLP) and many (declarative) semantics have been defined for DLP to cope with various problems of knowledge representation in artificial intelligence. However, the expressive ability of the semantics and the soundness of program transformations for DLP have been rarely explored. This paper defines an immediate consequence operatorT P G for each disjunctive program and shows thatT P G has the least and computable fixpointLft(P). Lft is, in fact, a program transformation for DLP, which transforms all disjunctive programs into negative programs. It is shown thatLft preserves many key semantics, including the disjunctive stable models, well-founded model, disjunctive argument semantics DAS, three-valued models, etc. This means that every disjunctive programP has a unique canonical formLft(P) with respect to these semantics. As a result, the work in this paper provides a unifying framework for studying the expressive ability of various semantics for DLP. On the other hand, the computing of the above semantics for negative programs is just a trivial task, therefore,Lft(P) is also an optimization method for DLP. Another application ofLft is to derive some interesting semantic results for DLP.