Conditional logics of normality: A modal approach

Abstract

Several conditional theories of default reasoning have recently been proposed for the representation of statements about normal states of affairs or prototypical properties. The natural semantics of these systems and their ability to reason about default rules make these approaches quite appealing. We present a family of modal logics in which we define a conditional connective for statements of normality and examine its properties. We also demonstrate that two of the most important conditional approaches are equivalent to fragments of our conditional logics of normality (and to standard modal logics). The approach we take is general enough to allow the expression of a number of different forms of defeasible reasoning, and can be used to illustrate the relationship between these types of reasoning (e.g., belief revision, subjunctive and autoepistemic reasoning) and our default logics. This relationship is explored in a companion paper.