An argument-based approach to reasoning with specificity

• Authors: Phan Minh Dung;Tran Cao Son
• Venue: Artificial Intelligence
• Year: 2001

We present a new priority-based approach to reasoning with specificity which subsumes inheritance reasoning. The new approach differs from other priority-based approaches in the literature in the way priority between defaults is handled. Here, it is conditional rather than unconditional as in other approaches. We show that any unconditional handling of priorities between defaults as advocated in the literature until now is not sufficient to capture general defeasible inheritance reasoning. We propose a simple and novel argumentation semantics for reasoning with specificity taking the conditionality of the priorities between defaults into account. Since the proposed argumentation semantics is a form of stable semantics of nonmonotonic reasoning, it inherits a common problem of the latter where it is not always defined for every default theory. We propose a class of stratified default theories for which the argumentation semantics is always defined. We also show that acyclic and consistent inheritance networks are stratified. We prove that the argumentation semantics satisfies the basic properties of a nonmonotonic consequence relation such as deduction, reduction, conditioning, and cumulativity for well-defined and stratified default theories. We give a modular and polynomial transformation of default theories with specificity into semantically equivalent Reiter default theories.