Two-level Default Theories
نویسندگان
چکیده
Default Logic employs assumption-based default rules to draw plausible consequences in face of incomplete information. In ontology representation, there are two kinds of relations between concepts: subsumption relation and default subsumption relation. Subsumption relation is transitive, whereas default subsumption relation is transitive by default. Both default transitivity of default subsumption and default inheritance of default property should be represented as defaults about defaults, i.e. two-level defaults. None of existing default logics can represent two-level defaults. In this paper, we propose two-level default theories which augment default theories with two-level defaults. A twolevel default theory can be divided into two levels and its extensions can be generated by two steps. We prove that normal two-level default theories cannot reduce to normal default theories. Specifically, there is a normal two-level default theory such that there exists no normal default theory such that they share the same set of extensions.
منابع مشابه
Default theories that always have extensions * Christos
Default logic is an important and influential formalization of commonsense reasoning. Determining whether a given default theory has an extension is the main computational problem pertinent to default logic, the analog of testing for validity and finding deductions in more classical logics. Substantially generalizing a result by Etherington [5] we show that all default theories that have no odd...
متن کاملOn Relating Causal Theories to Other Formalisms
This paper explores mathematical relationships between the \causal theories" formalism recently introduced by the authors and several other (well-known) formalisms. More specii-cally, it relates causal theories to default logic and autoepistemic logic, and describes translations back and forth between causal theories and classical propositional logic. It also relates action representations in c...
متن کاملMore on modal aspects of default logic
Investigations of default logic have been so far mostly concerned with the notion of an extension of a default theory. It turns out, however, that default logic is much richer. Namely, there are other natural classes of objects that might be associated with default reasoning. We study two such classes of objects with emphasis on their relations with modal nonmonotonic formalisms. First, we intr...
متن کاملModel-Preference Default Theories
Most formal theories of default inference have very poor computational properties, and are easily shown to be intractable, or worse, undecidable. We are therefore investigating limited but efficiently computable theories of default reasoning. This paper defines systems of Propositional Model-Preference Defaults, which provide a true modeltheoretic account of default inference with exceptions. T...
متن کاملPrioritizing Default Logic: Abridged Report
A number of prioritized variants of Reiter’s default logic have been described in the literature. In this paper, we introduce two natural principles for preference handling and show that all existing approaches fail to satisfy them. We develop a new approach which does not suffer from these shortcomings. We start with the simplest case, supernormal default theories, where preferences are handle...
متن کامل