On a rule-based interpretation of default conditionals

In nonmonotonic reasoning, a default conditional α→β has most often been informally interpreted as a defeasible version of a classical conditional, usually the material conditional. There is however an alternative interpretation, in which a default is regarded essentially as a rule, leading from premises to conclusion. In this paper, we present a family of logics, based on this alternative interpretation. A general semantic framework under this rule-based interpretation is developed, and associated proof theories for a family of weak conditional logics is specified. Nonmonotonic inference is easily defined in these logics. Interestingly, the logics presented here are weaker than the commonly-accepted base conditional approach for defeasible reasoning. However, this approach resolves problems that have been associated with previous approaches.