Approaches to abductive reasoning: an overview

Abstract

Abduction is a form of non-monotonic reasoning that has gained increasing interest in the last few years. The key idea behind it can be represented by the following inference rule $$O = \mathop C\limits_| - N = \mathop P\limits_|^| - O - \mathop C\limits_|^| - .$$ i.e., from an occurrence of ω and the rule “ϕ implies ω”, infer an occurrence of ϕ as aplausible hypothesis or explanation for ω. Thus, in contrast to deduction, abduction is as well as induction a form of “defeasible” inference, i.e., the formulae sanctioned are plausible and submitted to verification. In this paper, a formal description of current approaches is given. The underlying reasoning process is treated independently and divided into two parts. This includes a description ofmethods for hypotheses generation andmethods for finding the best explanations among a set of possible ones. Furthermore, the complexity of the abductive task is surveyed in connection with its relationship to default reasoning. We conclude with the presentation of applications of the discussed approaches focusing on plan recognition and plan generation.