Towards a Rule-Based Interpretation of Conditional Defaults

For 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. One obtains a rich set of nonmonotonic inferences concerning the incorporation of irrelevant properties and of property inheritance. Interestingly, the logics presented here are weaker than the commonlyaccepted base conditional approach for defeasible reasoning. However, this interpretation resolves problems that have been associated with previous approaches.