A Cumulative-Model Semantics for Dynamic Preferences on Assumptions

Explicit preferences on assumptions as used in prioritized circumscription [McCarthy, 1986; Lifschitz, 1985; Grosof, 1991] and preferred subtheories [Brewka, 1989] provide a clear and declarative method for defining preferred models. In this paper, we show how to embed preferences in the logical theory itself. This gives a high freedom for expressing statements about preferences. Preferences can now depend on other assumptions and are thus dynamic. We elaborate a preferential semantics based on Lehmann's cumulative models, as well as a corresponding constructive characterization, which specifies how to correctly treat dynamic preferences in the default reasoning system E