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

A Novel Approach to Multimedia Ontology Engineering for Automated Reasoning over Audiovisual LOD Datasets

Multimedia reasoning, which is suitable for, among others, multimedia content analysis and high-level video scene interpretation, relies on the formal and comprehensive conceptualization of the represented knowledge domain. However, most multimedia ontologies are not exhaustive in terms of role definitions, and do not incorporate complex role inclusions and role interdependencies. In fact, most multimedia ontologies do not have a role box at all, and implement only a basic subset of the available logical constructors. Consequently, their application in multimedia reasoning is limited. To address the above issues, VidOnt, the very first multimedia ontology with SROIQ(D) expressivity and a DL-safe ruleset has been introduced for next-generation multimedia reasoning. In contrast to the common practice, the formal grounding has been set in one of the most expressive description logics, and the ontology validated with industry-leading reasoners, namely HermiT and FaCT++. This paper also presents best practices for developing multimedia ontologies, based on my ontology engineering approach

Description Logics as Ontology Languages for the Semantic Web

The vision of a Semantic Web has recently drawn considerable attention, both from academia and industry. Description logics are often named as one of the tools that can support the Semantic Web and thus help to make this vision reality. In this paper, we describe what description logics are and what they can do for the Semantic Web. Descriptions logics are very useful for defining, integrating, and maintaining ontologies, which provide the Semantic Web with a common understanding of the basic semantic concepts used to annotate Web pages. We also argue that, without the last decade of basic research in this area, description logics could not play such an important rˆole in this domain

Synonymy and Polysemy in Legal Terminology and Their Applications to Bilingual and Bijural Translation

The paper focuses on synonymy and polysemy in the language of law in English-speaking countries. The introductory part briefly outlines the process of legal translation and tackle the specificity of bijural translation. Then, traditional understanding of what a term is and its application to legal terminology is considered; three different levels of vocabulary used in legal texts are outlined and their relevance to bijural translation explained. Next, synonyms in the language of law are considered with respect to their intension and distribution, and examples are given to show that most expressions or phrases which are interchangeable synonyms in the general language should be treated carefully in legal translation. Finally, polysemes in legal terminology are discussed and examples given to illustrate problems potentially encountered by translators

Terminological cycles and the ropositional μ-calculus

We investigate terminological cycles in the terminological standard logic mathcal{ALC} with the only restriction that recursively defined concepts must occur in their definition positively. This restriction, called syntactic monotonicity, ensures the existence of least and greatest fixpoint models. It turns out that as far as syntactically monotone terminologies of mathcal{ALC} are concerned, the descriptive semantics as well as the least and greatest fixpoint semantics do not differ in the computational complexity of the corresponding subsumption relation. In fact, we prove that in each case subsumption is complete for deterministic exponential time. We then show that the expressive power of finite sets of syntactically monotone terminologies of mathcal{ALC} is the very same for the least and the greatest fixpoint semantics and, moreover, in both cases they are strictly stronger in expressive power than mathcal{ALC} augmented by regular role expressions. These results are obtained by a direct correspondence to the so-called propositional mu-calculus which allows to express least and greatest fixpoints explicitly. We propose ALC augmented by the fixpoint operators of the mu-calculus as a unifying framework for all three kinds of semantics

Incorporating generalized quantifiers into description logic for representing data source contents

Title from cover. "January 1998."Includes bibliographical references (p. 19-21).Steven Yi-cheng Tu and Stuart E. Madnick

An empirical analysis of terminological representation systems

The family of terminological representation systems has its roots in the representation system KL-ONE. Since the development of this system more than a dozen similar representation systems have been developed by various research groups. These systems vary along a number of dimensions.In this paper, we present the results of an empirical analysis of six such systems. Surprisingly, the systems turned out to be quite diverse leading to problems when transporting knowledge bases from one system to another. Additionally, the runtime performance between different systems and knowledge bases varied more than we expected. Finally, our empirical runtime performance results give an idea of what runtime performance to expect from such representation systems. These findings complement previously reported analytical results about the computational complexity of reasoning in such systems