On the connection between normal default reasoning and conditional logic

Conditional logic plays an important role in recent attempts to investigate default reasoning. In this paper we show that normal default reasoning can be captured in the conditional logic CL: Reiter extensions of a normal def ault theory Delta = (D, W) correspond to sets of sentences that are maximal ly CL-consistent with respect to Cond-E(Delta) which is a set of conditiona l sentences constructed using defaults in D that are relevant to extensions . We also discuss Delgrande conditional approach to default reasoning: and point out one of its weaknesses. In employing CL, we provide a semantic int erpretation of defaults that is weaker than that of normality/typicality pr oposed by Delgrande and develop an approach that produces all the Reiter ex tensions of a normal default theory. We also show that there is a one-to-on e correspondence between conditional proofs of sentences that belong to ext ensions and Reiter default proofs.