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.

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

One of the main characteristics of knowledge representation systems based on the description of concepts is the clear distinction between terminological and assertional knowledge. Although this characteristic leads to several computational and representational advantages, it usually limits the expressive power of the system. For this reason, some attempts have been done, allowing for a limited form of amalgamation between the two components and a more complex interaction between them. In particular, one of these attempts is based on letting the individuals to be referenced in the concept expressions. This is generally performed by admitting a constructor for building a concept from a set of enumerated individuals. In this paper we investigate on the consequences of introducing constructors of this type in the concept description language. We also provide a complete reasoning procedure to deal with these constructors and we obtain some complexity results on it. 1 Introduction The ide...

Description Logics (DLs, for short) provide a logical reconstruction of the so-called frame-based knowledge representation languages. Originally, four-valued DLs have been proposed in order to develop expressively powerful DLs with tractable subsumption algorithms. Recently, four-valued DLs have been proposed as a model for (multimedia) document retrieval. In this context, the main reasoning task is instance checking. Unfortunately, the known subsumption algorithms for four-valued DLs, based on "structural" subsumption, do not work with respect to the semantics proposed in the DL-based approach to document retrieval. Moreover, they are unsuitable for solving the instance checking problem, as this latter problem is more general than the subsumption problem. We present an alternative decision procedure for four-valued DLs with the aim to solve these problems. The decision procedure is a sequent calculus for instance checking. Since in general the four-valued subsumption problem can be ...

In recent years a number of positive (i.e. tractability and decidability) results have been found concerning the computational complexity of Description Logics (DLs) [Buchheit et al.,1993; Donini et al.,1991;

Concept languages have been studied in order to give a formal account of the basic features of frame-based languages. The focus of research in concept languages was initially on the semantical reconstruction of frame-based systems and the computational complexity of reasoning. More recently, attention has been paid to the formalization of other aspects of frame-based languages, such as non-monotonic reasoning and procedural rules, which are necessary in order to bring concept languages closer to implemented systems. In this paper we discuss the above issues in the framework of concept languages enriched with an epistemic operator. In particular, we show that the epistemic operator both introduces novel features in the language, such as sophisticated query formulation and closed world reasoning, and makes it possible to provide a formal account for some aspects of the existing systems, such as rules and definitions, that cannot be characterized in a standard first-order framework. Dip...

This report presents the status of the research the author is conducting on the development of a complete Description Logics knowledge representation system. Description Logics knowledge representation systems are based of a family of formal languages for describing complex structured classes. These languages comprise boolean operators and quantification over class attributes, as well as the declaration of elements of the classes and their properties. DL knowledge bases are partitioned in an intensional part which describes the general organisation of the classes, and an extensional part for describing class elements. Reasoning with DL knowledge bases involves both the terminological reasoning, which considers the intensional part only, and hybrid reasoning which consider the whole knowledge base. Although for terminological reasoning different promising techniques have been successfully applied, on the hybrid reasoning side there is still a lack of results. The aim of this research ...