On rules of abduction

We present a logical theory of abduction based on the idea of recognizing explanation, or abduction, as a separate reasoning activity. We describe a formalism for writing rules of abduction; furthermore, we define a validity criterion for such rules. The criterion is based on the concept of invariants. This idea allows us to link abduction with induction and deduction. We believe that the three types of inference rules can best be understood in terms of symmetry, i.e. types of relations they preserve, namely: explainability, falsifiability and truth. We also formulate a model theory of abduction and link it with a proof theory. We discuss a variety of rules of abduction and argue that logical forms of abduction do not have to be restricted to the reverse modus ponens. These rules are used to describe such tasks as word-sense disambiguation and anaphora resolution in natural language processing, as well as abduction-based diagnosis. © 1993 J.C. Baltzer AG, Science Publishers.