Default Reasoning with Specificity

We present a new approach to reasoning with specificity which subsumes inheritance reasoning. The new approach differs from other approaches in the literature in the way priority between defaults is handled. Here, it is context sensitive rather than context independent as in other approaches. We show that any context independent 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 context-dependency 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 identify the class of stratified default theories which is large enough to accommodate acyclic and consistent inheritance networks and for which the argumentation semantics is always defined. We also prove that the argumentation semantics satisfies the basic properties of a nonmonotonic consequence relation such as deduction, reduction, conditioning, and cumulativity for stratified default theories.

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