Jumping to explanations versus jumping to conclusions
Abduction is usually defined as the process of inferring the best explanation of an observation. There are many information processing operations that can be viewed as a search for an explanation. For instance, diagnosis, natural language interpretation and plan recognition. This paper is concerned about the following aspects of abduction: (i) what are the logical properties of abduction when it is regarded as a form of inference? and (ii) how close is abduction to reversed deduction? In the logic-based approach to abduction, the background theory is given by a consistent set of formulas Sigma. The notion of an explanation is defined by saying that a formula gamma (consistent with Sigma) is an explanation of alpha if Sigma boolean OR {gamma} proves alpha. An explanatory relation is a binary relation /similar to among formulas where the intended meaning of alpha /similar to gamma is "gamma is a preferred explanation of alpha". To each explanatory relation is associated a consequence relation \similar to(ab) defined as follows: or \similar to(ab) beta if Sigma boolean OR {gamma} proves beta for each gamma such that alpha /similar to gamma. The study of the logical properties of explanatory reasoning is approached by a systematic analysis of \similar to(ab). We show that there are rationality postulates for abduction (i.e., constraints on the explanatory relation /similar to) that are, in a very precise sense, equivalent to rationality postulates (in the Krauss-Lehmann-Magidor tradition) for nonmonotonic reasoning (i.e., for the relation \similar to(ab)) This tight correspondence between postulates for explanatory reasoning and nonmonotonic reasoning will make apparent a strong duality between these two forms of inference. Isolating the postulates and showing this duality are the main contributions of the paper. We introduce the notion of a causal explanatory relation and show its close connection with reversed nonmonotonic reasoning. (C) 1999 Elsevier Science B.V. All rights reserved.
abduction explanatory and nonmonotonic reasoning nonmonotonic consequence relations