Preference-Based Semantics for Nonmonotonic Logics

A variant is proposed of the preference-based se­ mantics for nonmonotonic logics that was origi­ nally considered by Shoham [1987; 1988]. In this variant it is not assumed that preferences between standard models arc aggregated into one preference order. This allows the capturing of all main non­ monotonic formalisms, including Default Logic oi Reiter [1980]. The preferential models introduced in this paper are motivated from an cpistemic point of view, and are therefore called cpistemic preference models. The consequence operations induced by cpistemic preference models are characterized. Further, the view is defended that the rationality of cumulative monotonicity does not imply thai nonmonotonic logics have to be cumulative, but only that a rational agent should not believe a set of default rules that induces a noncumulative conse­ quence operation.