We consider the problem of integrating Reiter's default logic into terminological representation systems. It turns out that such an integration is less straightforward than we expected, considering the fact that the terminological language is a decidable sublanguage of first-order logic. Semantically, one has the unpleasant effect that the consequences of a terminological default theory may be rather unintuitive, and may even vary with the syntactic structure of equivalent concept expressions. This is due to the unsatisfactory treatment of open defaults via Skolemization in Reiter's semantics. On the algorithmic side, we show that this treatment may lead to an undecidable default consequence relation, even though our base language is decidable, and we have only finitely many (open) defaults. Because of these problems, we then consider a restricted semantics for open defaults in our terminological default theories: default rules are only applied to individuals that are explicitly presen...

. In this paper we propose an epistemic concept language, where the epistemic operator is interpreted in terms of minimal knowledge. We show that the proposed formalism provides an adequate characterization of many non-first-order aspects of frame-based knowledge representation systems, by admitting in the knowledge base various forms of epistemic sentences. In particular, we address the formalization of defaults and role closure. We argue that the minimization of knowledge captures intuitive and natural forms of reasoning that arise by restricting the attention to the individuals that are known to the knowledge base. Many of these forms of reasoning are actually provided by several knowledge representation systems, whose implementation is object centered. 1 Introduction Concept languages (also called terminological logics, description languages) have been studied in the past years to provide a formal characterization of frame-based system. However, while the fragment of first-order l...

this paper we propose a concept language with an epistemic operator interpreted in terms of minimal knowledge [8, 6, 11], and we show that it provides an adequate treatment of the following features: defaults, procedural rules, weak definitions and role closures, as they are provided in the most popular systems based on concept languages. The intuitive reason that makes our approach suitable for a precise characterization of the behaviour of implemented systems is that the minimization of knowledge on possible world structures carries

. In this paper we present a powerful uniform first-order framework for representing and reasoning with complex forms of default knowledge. This is achieved by extending first-order predicate logic with a new generalized quantifier, anchored in the quasi-probabilistic ranking measure paradigm [Weydert 94], which subsumes and refines the original, propositional notion of a default conditional [Delgrande 88, Weydert 91, Boutilier 94]. 1. INTRODUCTION In recent times, default conditionals interpreted by ranking measures or order-of-magnitude probability distributions have become an increasingly popular tool for encoding defeasible relationships. Conceptual adequacy, semantic transparency, probabilistic justifications, the existence of proof-theoretic characterizations, the correct, natural handling of specificity and the availability of promising nonmonotonic inference relations [Weydert 96] are strong arguments in favour of this approach. However, like most formalisms for plausible reaso...