Weak Conditional Logics of Normality

Abstract

A default conditional a ---+ f3 has most often been informally interpreted as a defeasible version of a classical conditional, usually the material conditional. That is, the intuition is that a default should behave (implicitly or explicitly) as its (say) material counterpart "by default" or unless explicitly overridden. In this paper, we develop an alternative interpretation, in which a default is regarded more like a rule, leading from premises to conclusion. To this end, a general semantic framework under a "rule-based" interpretation is developed, and a family of weak conditional logics is specified, along with associated proof theories. Nonmonotonic inference is defined very easily in these logics. One obtains a rich set of nonmonotonic inferences concerning the incorporation of irrelevant properties and of property inheritance. Moreover, this interpretation resolves problems that have been associated with previous approaches.