The present work deals with Description Logics (DLs), a class of knowledge representation formalisms used to represent and reason about classes of individuals and relations between such classes in a formally well-defined way. We provide novel results in three main directions. (1) Tractable reasoning revisited: in the 1990s, DL research has largely answered the question for practically relevant yet tractable DL formalisms in the negative. Due to novel application domains, especially the Life Sciences, and a surprising tractability result by Baader, we have re-visited this question, this time looking in a new direction: general terminologies (TBoxes) and extensions thereof defined over the DL EL and extensions thereof. As main positive result, we devise EL++(D)-CBoxes as a tractable DL formalism with optimal expressivity in the sense that every additional standard DL constructor, every extension of the TBox formalism, or every more powerful concrete domain, makes reasoning intractable. (2) Non-standard inferences for knowledge maintenance: non-standard inferences, such as matching, can support domain experts in maintaining DL knowledge bases in a structured and well-defined way. In order to extend their availability and promote their use, the present work extends the state of the art of non-standard inferences both w.r.t. theory and implementation. Our main results are implementations and performance evaluations of known matching algorithms for the DLs ALE and ALN, optimal non-deterministic polynomial time algorithms for matching under acyclic side conditions in ALN and sublanguages, and optimal algorithms for matching w.r.t. cyclic (and hybrid) EL-TBoxes. (3) Non-standard inferences over general concept inclusion (GCI) axioms: the utility of GCIs in modern DL knowledge bases and the relevance of non-standard inferences to knowledge maintenance naturally motivate the question for tractable DL formalism in which both can be provided. As main result, we propose hybrid EL-TBoxes as a solution to this hitherto open question.

The concept of equivalence has for many years attracted attention of researchers in variousdisciplines: from mathematics to philosophy to translation theory to terminology. This thesisintends to survey the concept of equivalence in three subject fields all of which focus onlanguages and communication, namely: translation theory, lexicography and terminology. Thepurpose of the paper is twofold: to investigate the theoretical grounds of equivalence in thesethree disciplines and to survey the methods and practices of establishing equivalence inmultilingual terminology work. The results of the theoretical investigation are summed up onthe basis of the terminological concept analysis. Four concepts systems are structured andpresented in the form of concept diagrams (two for translation theory, one for lexicography andone for terminology). The concept systems give an overview of the current understanding ofequivalence in the three subject fields and expose the relations between equivalence and anumber of related concepts. The central theoretical question of the thesis whether equivalencecould be considered the same concept in all three disciplines is answered on the basis of theresults of the terminological concept analysis. The empirical investigation is carried out in theform of case studies in the frame of multilingual terminology work. It focuses on the problemsof establishing equivalence, of determining the degree of equivalence as well as on the methodsand practices of presenting equivalents in various terminological resources.

The present work deals with Description Logics (DLs), a class of knowledge representation formalisms used to represent and reason about classes of individuals and relations between such classes in a formally well-defined way. We provide novel results in three main directions. (1) Tractable reasoning revisited: in the 1990s, DL research has largely answered the question for practically relevant yet tractable DL formalisms in the negative. Due to novel application domains, especially the Life Sciences, and a surprising tractability result by Baader, we have re-visited this question, this time looking in a new direction: general terminologies (TBoxes) and extensions thereof defined over the DL EL and extensions thereof. As main positive result, we devise EL++(D)-CBoxes as a tractable DL formalism with optimal expressivity in the sense that every additional standard DL constructor, every extension of the TBox formalism, or every more powerful concrete domain, makes reasoning intractable. (2) Non-standard inferences for knowledge maintenance: non-standard inferences, such as matching, can support domain experts in maintaining DL knowledge bases in a structured and well-defined way. In order to extend their availability and promote their use, the present work extends the state of the art of non-standard inferences both w.r.t. theory and implementation. Our main results are implementations and performance evaluations of known matching algorithms for the DLs ALE and ALN, optimal non-deterministic polynomial time algorithms for matching under acyclic side conditions in ALN and sublanguages, and optimal algorithms for matching w.r.t. cyclic (and hybrid) EL-TBoxes. (3) Non-standard inferences over general concept inclusion (GCI) axioms: the utility of GCIs in modern DL knowledge bases and the relevance of non-standard inferences to knowledge maintenance naturally motivate the question for tractable DL formalism in which both can be provided. As main result, we propose hybrid EL-TBoxes as a solution to this hitherto open question.

Facing the growing amount of information in today's society, the task of specifying human knowledge in a way that can be unambiguously processed by computers becomes more and more important. Two acknowledged fields in this evolving scientific area of Knowledge Representation are Description Logics (DL) and Formal Concept Analysis (FCA). While DL concentrates on characterizing domains via logical statements and inferring knowledge from these characterizations, FCA builds conceptual hierarchies on the basis of present data. This work introduces Relational Exploration, a method for acquiring complete relational knowledge about a domain of interest by successively consulting a domain expert without ever asking redundant questions. This is achieved by combining DL and FCA: DL formalisms are used for defining FCA attributes while FCA exploration techniques are deployed to obtain or refine DL knowledge specifications.