On the connection between normal default reasoning and conditional logic

Conditional logic plays an important role in recent attempts to investigate default reasoning. Iii this paper we show that normal default reasoning ca n be captured in the conditional logic CL: Reiter extensions of a normal de fault theory Delta = (D, W) correspond to sets of sentences that are maxima lly CL-consistent with respect, to Cond-E(Delta) which is a set of conditio nal sentences constructed using defaults in D that are relevant to extensio ns. We also discuss Delgrande conditional approach to default reasoning and point out one of its weaknesses. In employing CL, we provide a semantic in terpretation of defaults that is weaker than that of normality/typicality p roposed by Delgrande and develop an approach that produces all the Reiter e xtensions of a normal default theory. We also show that there is a one-to-o ne correspondence between conditional proofs of sentences that belong to ex tensions and Reiter default proofs.