Approximate reasoning

Abstract

In this paper, we investigate approximate forms of deductive and nonmonotonic reasoning. In the case of approximate deductive reasoning, we propose a logic programming approach that combines features of the ‘limited inference’ approach of Schaerf and Cadoli [21] with a notion of ‘relevance’ as introduced by Brüning and Schaub [1]. It is argued that approximate reasoning is more appropriate if nonmonotonic logics are considered. For this case, we present the guided inference strategy. It relies on distinguishing preconditions from default conditions in antecedents of default rules (Elkan [8], Ginsberg [10,12]). While preconditions are treated as ordinary subgoals in a logic program clause, default conditions of format not A can be left partly unproved. The Fire-and-Remember mechanism that is part of the strategy may take advantage of incomplete proofs and speed up subsequent computations of similar queries. The main contribution of our paper is twofold. First, we show that approximate deductive reasoning can be seen as a form of relevant reasoning. Second, we describe a strategy for approximate nonmonotonic reasoning that is robust for dynamically changing knowledge bases.