Two-phase Exception Logic

In this paper we propose an exception logic { formalizing reasoning about exceptions. We use this logic to defend two claims. First, we argue that default logic { formalizing reasoning about default assumptions { is an extension of exception logic. A deconstruction argument shows that reasoning about exceptions is one of the rst principles of reasoning about default assumptions. Second, we argue that two phases have to be distinguished in reasoning about exceptions, and therefore also in reasoning about default assumptions. We identify two causes of the distinction between two phases, the disjunction rule or and right weakening rw. This sheds some new light on thesèstandard' (according to the Kraus-Lehmann-Magidor paradigm) properties of default inference. Introduction In this paper we analyze the conditional logic approach to default logic, the logic that formalizes reasoning about default assumptions. Conditional logic is a popular framework to formalize defeasible reasoning , see e.g. The conditional sentence \if (the antecedent or condition) then by default (the consequent or conclusion)" is represented in this framework by the formula >, wherè>' is some kind of implication of conditional logic. We distinguish between two approaches to formalize default reasoning in the conditional logic framework, which we call the strengthening and the weakening approach, respectively. The strengtening approach starts with a weak system (the so-called core) in which the conditionals do not have monotony, and adds defeasible reasoning schemes like System Z or Maximum Entropy to strengthen the system such that it has restricted monotony. The weakening approach starts with a strong system that has monotony, and adds constraints on monotony to incorporate defeasibility. In this paper we consider default logics of the weakening approach, which are extensions