Terminological representation, natural language & relation algebra

In this paper I establish a link between {\sc kl-one}-based knowledge representation concerned with {\em terminological representation} and the work of P. Suppes (1976,1979,1981) and M. B\"ottner (1985,1989) in computational linguistics. I show how this link can be utilised for the problem of finding adequate terminological representations for given information formulated in ordinary English

Decidable Reasoning in Terminological Knowledge Representation Systems

Terminological knowledge representation systems (TKRSs) are tools for designing and using knowledge bases that make use of terminological languages (or concept languages). We analyze from a theoretical point of view a TKRS whose capabilities go beyond the ones of presently available TKRSs. The new features studied, often required in practical applications, can be summarized in three main points. First, we consider a highly expressive terminological language, called ALCNR, including general complements of concepts, number restrictions and role conjunction. Second, we allow to express inclusion statements between general concepts, and terminological cycles as a particular case. Third, we prove the decidability of a number of desirable TKRS-deduction services (like satisfiability, subsumption and instance checking) through a sound, complete and terminating calculus for reasoning in ALCNR-knowledge bases. Our calculus extends the general technique of constraint systems. As a byproduct of the proof, we get also the result that inclusion statements in ALCNR can be simulated by terminological cycles, if descriptive semantics is adopted.Comment: See http://www.jair.org/ for any accompanying file

Attributive Concept Descriptions with Unions and Complements

This paper investigates the consequences of adding unions and complements to the attributive concept descriptions employed in KL-ONE-like knowledge representation languages. It is shown that deciding consistency and subsumption of such descriptions are PSPACE-complete problems that can be decided with linear space

The complexity of existential quantification in concept languages

Much of the research on concept languages, also called terminological languages, has focused on the computational complexity of subsumption. The intractability results can be divided into two groups. First, it has been shown that extending the basic language FL- with constructs containing some form of logical disjunction leads to co-NP-hard subsumption problems. Second, adding negation to FL- makes subsumption PSPACE-complete. The main result of this paper is that extending FL- with unrestricted existential quantification makes subsumption NP-complete. This is the first proof of intractability for a concept language containing no construct expressing disjunction--whether explicitly or implicitly. Unrestricted existential quantification is therefore, alongside disjunction, a source of computational complexity in concept languages

Subsumption algorithms for concept languages

We investigate the subsumption problem in logic-based knowledge representation languages of the KL-ONE family and give decision procedures. All our languages contain as a kernel the logical connectives conjunction, disjunction, and negation for concepts, as well as role quantification. The algorithms are rule-based and can be understood as variants of tableaux calculus with a special control strategy. In the first part of the paper, we add number restrictions and conjunction of roles to the kernel language. We show that subsumption in this language is decidable, and we investigate sublanguages for which the problem of deciding subsumption is PSPACE-complete. In the second part, we amalgamate the kernel language with feature descriptions as used in computational linguistics. We show that feature descriptions do not increase the complexity of the subsumption problem

A formal definition for the expressive power of knowledge representation languages

The notions "expressive power" or "expressiveness" of knowledge representation languages (KR-languages) can be found in most papers on knowledge representation; but these terms are usually just used in an intuitive sense. The papers contain only informal descriptions of what is meant by expressiveness. There are several reasons which speak in favour of a formal definition of expressiveness: For example, if we want to show that certain expressions in one language cannot be expressed in another language, we need a strict formalism which can be used in mathematical proofs. Though we shall only consider KL-ONE-based KR-language in our motivation and in the examples, the definition of expressive power which will be given in this paper can be used for all KR-languages with model-theoretic semantics. This definition will shed a new light on the tradeoff between expressiveness of a representation language and its computational tractability. There are KR-languages with identical expressive power, but different complexity results for reasoning. Sometimes, the tradeoff lies between convenience and computational tractability. The paper contains several examples which demonstrate how the definition of expressive power can be used in positive proofs -- that is, proofs where it is shown that one language can be expressed by another language -- as well as for negative proofs -- which show that a given language cannot be expressed by the other language

An empirical analysis of optimization techniques for terminological representation systems : or: \u27Making KRIS get a move on\u27

We consider different methods of optimizing the classification process of terminological representation systems, and evaluate their effect on three different types of test data. Though these techniques can probably be found in many existing systems, until now there has been no coherent description of these techniques and their impact on the performance of a system. One goal of this paper is to make such a description available for future implementors of terminological systems. Building the optimizations that came off best into the KRIS system greatly enhanced its efficiency