Preference-Based Semantics for Nonmonotonic Logics

Abstract

A variant is proposed of the preference-based semantics for nonmonotonic
\nlogics that was originally considered by Shoham (1987,1988). In this variant it
\nis not assumed that preferences between standard models are aggregated into
\none preference order. This allows the capturing of all main nonmonotonic
\nformalisms, including Default Logic of Reiter (1980). The preferential models
\nintroduced in this paper are motivated from an epistemic point of view, and are
\ntherefore called epistemic preference models. The consequence operations
\ninduced by epistemic preference models are characterized. Further, the view is
\ndefended that the rationality of cumulative monotonicity does not imply that
\nnonmonotonic logics have to be cumulative, but only that a rational agent
\nshould not believe a set of default rules that induces a noncumulative consequence
\noperation.