Explanations and Proof Trees

Introduction This paper proposes a model for explanations in a set theoretical framework using the notions of closure or fixpoint. In this approach, sets of rules associated with monotonic operators allow to define proof trees (Aczel 1977). The proof trees may be considered as a declarative view of the trace of a computation. We claim they are explanations of the result of a computation. First, the general scheme is given. This general scheme is applied to Constraint Logic Programming, two notions of explanations are given: positive explanations and negative explanations. A use for declarative error diagnosis is proposed. Next, the general scheme is applied to Constraint Programming. In this framework, two definitions of explanations are described as well as an application to constraint retraction.