A drawback which concept languages based on kl-one have is that all the terminological knowledge has to be defined on an abstract logical level. In many applications, one would like to be able to refer to concrete domains and predicates on these domains when defining concepts. Examples for such concrete domains are the integers, the real numbers, or also non-arithmetic domains, and predicates could be equality, inequality, or more complex predicates. In the present paper we shall propose a scheme for integrating such concrete domains into concept languages rather than describing a particular extension by some specific concrete domain. We shall define a terminological and an assertional language, and consider the important inference problems such as subsumption, instantiation, and consistency. The formal semantics as well as the reasoning algorithms are given on the scheme level. In contrast to existing kl-one based systems, these algorithms will be not only sound but also complete. The...

Abstract not found

Terminological Knowledge Representation Systems (TKRSs) are tools for designing and using knowledge bases that make use of terminological languages (or concept languages). The TKRS we consider in this paper is of practical interest since it goes beyond the capabilities of presently available TKRSs. First, our TKRS is equipped with a highly expressive concept, language, called ALCNR, including general complements of concepts, number restrictions and role conjunction. Second, it allows one to express inclusion statements between general concepts, in particular to express terminological cycles. We provide a sound, complete and terminating calculus for reasoning in ALCNR-knowledge bases based on the general technique of constraint systems.

Description logics are a family of knowledge representation formalisms that are descended from semantic networks and frames via the system Kl-one. During the last decade, it has been shown that the important reasoning problems (like subsumption and satisfiability) in a great variety of description logics can be decided using tableau-like algorithms. This is not very surprising since description logics have turned out to be closely related to propositional modal logics and logics of programs (such as propositional dynamic logic), for which tableau procedures have been quite successful. Nevertheless, due to different underlying intuitions and applications, most description logics differ significantly from run-of-the-mill modal and program logics. Consequently, the research on tableau algorithms in description logics led to new techniques and results, which are, however, also of interest for modal logicians. In this article, we will focus on three features that play an important role in description logics (number restrictions, terminological axioms, and role constructors), and show how they can be taken into account by tableau algorithms.

Abstract not found

It is natural to view concept and role definitions in Description Logics as expressing monadic and dyadic predicates in Predicate Calculus. We show that the descriptions built using the constructors usually considered in the DL literature are characterized exactly as the predicates definable by formulas in ¨L³, the subset of First Order Predicate Calculus with monadic and dyadic predicates which allows only three variable symbols. In order to handle “number bounds”, we allow numeric quantifiers, and for transitive closure of roles we use infinitary disjunction. Using previous results in the literature concerning languages with limited numbers of variables, we get as corollaries the existence of formulae of FOPC which cannot be expressed as descriptions. We also show that by omitting role composition, descriptions express exactly the formulae in ¨L², which is known to be decidable.

The article aims at establishing a logical approach to class-based data modeling. After a discussion on class-based formalisms for data modeling, we introduce a family of logics, called Description Logics, which stem from research on Knowledge Representation in Arti cial Intelligence. The logics of this family are particularly well suited for specifying data classes and relationships among classes, and are equipped with both formal semantics and inference mechanisms. We demonstrate that several popular data modeling formalisms, including the Entity-Relationship Model, and the most common variants of object-oriented data models, can be expressed in terms of speci c logics of the family. For this purpose we use a unifying Description Logic, which incorporates all the features needed for the logical reformulation of the data models used in the various contexts. We also discuss the problem of devising reasoning procedures for the unifying formalism, and show that they provide valuable supports for several important data modeling activities.

Abstract not found

The knowledge representation system kl-one rst appeared in 1977. Since then many systems based on the idea of kl-one have been built. The formal model-theoretic semantics which has been introduced for kl-one languages [BL84] provides means for investigating soundness and completeness of inference algorithms. It turned out that almost all implemented kl-one systems such as back, kl-two, loom, nikl, sb-one use sound but incomplete algorithms.

According to the logical model of Information Retrieval (IR), the task of IR can be described as the extraction, from a given document base, of those documents d that, given a query q, make the formula d → q valid, where d and q are formulae of the chosen logic and “→ ” denotes the brand of logical implication formalized by the logic in question. In this paper, although essentially subscribing to this view, we propose that the logic to be chosen for this endeavour be a Terminological Logic (TL): accordingly, the IR task becomes that of singling out those documents d such that d � q, where d and q are terms of the chosen TL and “�” denotes subsumption between terms. We call this the terminological model of IR. TLs are particularly suitable for modelling IR; in fact, they can be employed: 1) in representing documents under a variety of aspects (e.g. structural, layout, semantic content); 2) in representing queries; 3) in representing lexical, “thesaural ” knowledge. The fact that a single logical language can be used for all these representational endeavours ensures that all these sources of knowledge will participate in the retrieval process in a uniform and principled way. In this paper we introduce Mirtl, a TL for modelling IR according to the above guidelines; its syntax, formal semantics and inferential algorithm are described. 1