Models of abduction

The aim of this paper is to sketch a theory of abduction with its relations with deduction and induction in the sense of the second Peirce. The relation of abduction is seen as a relation which is in some sense reciprocal to deduction. Furthermore, this conception of abduction is directly compatible with the conception of induction underlying belief revision. The main result is a representation theorem which unifies the various meanings of abduction. This theorem has two faces, one axiomatic and the other geometric, which are equivalent. This meaning of abduction is expressed through models from the three main paradigms of cognition ; these models aim at establishing its adequation for the cognitive science