On a Framework for Logic Programming with Incomplete Information

Abstract

A framework for Logic Programming with Incomplete Information is proposed. Recently, an important problem has been much discussed in the field of knowledge bases, logic programming and AI, namely how effectively we use information which may have incompleteness, especially disjunctive information.

In order to express disjunctive information, we use the predicate symbol or ^m , where the superscript m implies its arity, and as arguments we put every disjunctive information in or ^m , which we call an or-type atom. Based on or-type atoms, we define a new language called or-type language. Logic Program with Incomplete Information(LPII) is a subset of the or-type language.

First, in a special case our framework is reduced to that of near-Horn prolog by Loveland and disjunctive logic programming by Minker.

Then, we consider a general case, which is seen as an advancement from Lipski’s incomplete information system. In this case, we show the model intersection property, fixpoint theorem, the soundness and the completeness of a resolution which we call Box-resolution.