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Embedding Defaults into Terminological Knowledge Representation Formalisms
 Journal of Automated Reasoning
, 1995
"... 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 firstorder logic. Semant ..."
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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 firstorder 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...
NonFirstOrder Features in Concept Languages
 In Proceedings of the Fourth Conference of the Italian Association for Artificial Intelligence (AI*IA95), Lecture Notes In Artificial Intelligence
, 1995
"... . 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 nonfirstorder aspects of framebased knowledge representation systems, by admitting ..."
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Cited by 10 (9 self)
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. 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 nonfirstorder aspects of framebased 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 framebased system. However, while the fragment of firstorder l...
@ 1995 Kluwer Academic Publishers. Printed in the Netherlands. Priorities on Defaults with Prerequisites, and Their Application in Treating Specificity in Terminological Default Logic*
, 1994
"... Abstract. In a recent paper we have proposed terminological default logic as a formalism that combines means both for structured representation of classes and objects and for default inheritance of properties. The major drawback that terminolo~cal default logic inherits from general default logic is ..."
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Abstract. In a recent paper we have proposed terminological default logic as a formalism that combines means both for structured representation of classes and objects and for default inheritance of properties. The major drawback that terminolo~cal default logic inherits from general default logic is that it does not take precedence of more specific defaults over more general ones into account. This behavior has already been criticized in the general context of default logic, but it is all the more problematic in the terminological case where the emphasis lies on the hierarchical organization of concepts. The present paper addresses the problem of modifying terminological default logic such that more specific defaults are preferred. We assume that the specificity ordering is induced by the hierarchical organization of concepts, which means that default information is not taken into account when computing priorities. It turns out that the existing approaches for expressing priorities between defaults do not seem to be appropriate for defaults with prerequisites. Therefore we shall consider an alternative approach for dealing with prioritization in the framework of Reiter's default logic. The formalism is presented in the general setting of default logic where priorities are given by an arbitrary partial ordering on the defaults. We shall exhibit some interesting properties of the new formalism, compare it with existing approaches, and describe an algorithm for computing extensions. In the terminological case, we thus obtain an automated default reasoning procedure that takes specificity into account. Key words: terminological default logic, default theories with priorities, knowledge representation.
Dipartimento di Informatica e Sistemistica, Universit`a di Roma "La Sapienza", Via Salaria 113, I00198 Roma, Italy,
"... 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 pop ..."
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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
Default Quantifier Logic
"... . In this paper we present a powerful uniform firstorder framework for representing and reasoning with complex forms of default knowledge. This is achieved by extending firstorder predicate logic with a new generalized quantifier, anchored in the quasiprobabilistic ranking measure paradigm [Weyde ..."
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. In this paper we present a powerful uniform firstorder framework for representing and reasoning with complex forms of default knowledge. This is achieved by extending firstorder predicate logic with a new generalized quantifier, anchored in the quasiprobabilistic 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 orderofmagnitude probability distributions have become an increasingly popular tool for encoding defeasible relationships. Conceptual adequacy, semantic transparency, probabilistic justifications, the existence of prooftheoretic 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...