The Role of Abduction in Logic Programming

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Abstract

This paper extends and updates our earlier survey and analysis of work on the extension of logic programming to perform abductive reasoning [Kakas et al., 1993]. The purpose of the paper is to provide a critical overview of some of the main research results, in order to develop a common framework for evaluating these results, to identify the main unresolved problems, and to indicate directions for future work. The emphasis is not on technical details but on relationships and common features of different approaches. Some of the main issues we will consider are the contributions that abduction can make to the problems of reasoning with incomplete or negative information, the evolution of knowledge, and the semantics of logic programming and its extensions. We also discuss recent work on the argumentation-theoretic interpretation of abduction, which was introduced in the earlier version of this paper. The philosopher Peirce first introduced the notion of abduction. In [Peirce, 1931-58] he identified three distinguished forms of reasoning. Deduction, an analytic process based on the application of general rules to particular cases, with the inference of a result. Induction, synthetic reasoning which infers the rule from the case and the result. Abduction, another form of synthetic inference, but of the case from a rule and a result. Peirce further characterised abduction as the “probational adoption of a hypothesis” as explanation for observed facts (results), according to known laws. “It is however a weak kind of inference, because we cannot say that we believe in the truth of the explanation, but only that it may be true” [Peirce, 1931-58]. Abduction is widely used in common-sense reasoning, for instance in diagnosis, to reason from effect to cause [Charniak and McDermott, 1985; Pople, 1973]. We consider here an example drawn from [Pearl, 1987]. Abduction consists in computing such explanations for observations. It is a form of non-monotonic reasoning, because explanations which are consistent with one state of a knowledge base may become inconsistent with new information. In the example above the explanation rained-last-night may turn out to be false, and the alternative explanation sprinkler-was-on may be the true cause for the given observation.

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