Reasoning about exceptions (extended abstract)

Abstract

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. The conditional sentence “if β (the antecedent or condition) then by default α (the consequent or conclusion)” is represented in this framework by the formula β > α, where ‘>’ is some kind of implication of conditional logic. In this paper different usages of preference orderings for defeasible conditional logics are discussed. The different usages, so-called minimizing and ordering, are represented by different modal operators. Each operator validates different inference rules. Hence, the combination of different modal operators imposes restrictions on the proof theory of the logic. The restriction discussed in this paper is that a proof rule can be blocked in a derivation due to the fact that another proof rule has already been used earlier in the derivation. We call this the two-phase approach in the proof theory.