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 Σ. The notion of an explanation is defined by saying that a formula γ (consistent with Σ) is an explanation of α if Σ ∪ {γ } α. An explanatory relation is a binary relation among formulas where the intended meaning of α γ is "γ is a preferred explanation of α". To each explanatory relation is associated a consequence relation |∼ ab defined as follows: α |∼ ab β if Σ ∪ {γ } β for each γ such that α γ .
The study of the logical properties of explanatory reasoning is approached by a systematic analysis of |∼ ab . We show that there are rationality postulates for abduction (i.e., constraints on the explanatory relation ) 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 |∼ 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.