Quantitative Variants of Language Equations and their Applications to Description Logics
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DISSERTATION AND HABILITATION ABSTRACTS
Quantitative Variants of Language Equations and their Applications to Description Logics Extending Unification in Description Logics Pavlos Marantidis1
© Gesellschaft für Informatik e.V. and Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Unification in description logics (DLs) has been introduced as a novel inference service that can be used to detect redundancies in ontologies, by finding different concepts that may potentially stand for the same intuitive notion. Together with the special case of matching, they were first investigated in detail for the DL FL0 , where these problems can be reduced to solving certain language equations. In this thesis, we extend this service in two directions. In order to increase the recall of this method for finding redundancies, we introduce and investigate the notion of approximate unification, which basically finds pairs of concepts that “almost” unify, in order to account for potential small modelling errors. The meaning of “almost” is formalized using distance measures between concepts. We show that approximate unification in FL0 can be reduced to approximately solving language equations, and devise algorithms for solving the latter problem for particular distance measures. Furthermore, we make a first step towards integrating background knowledge, formulated in so-called TBoxes, by investigating the special case of matching in the presence of TBoxes of different forms. We acquire a tight complexity bound for the general case, while we prove that the problem becomes easier in a restricted setting. To achieve these bounds, we take advantage of an equivalence characterization of FL0 concepts that is based on formal languages. Even though our results on the approximate setting cannot deal with TBoxes yet, we prepare the framework that future research can build on.
1 Introduction Description Logics (DLs) [2] are a family of knowledge representation languages that can be used to represent knowledge of an application domain in a structured and wellunderstood way. They allow to define the relevant concepts of the domain by introducing concept names and then use these names to specify properties of objects occurring in the domain by providing concept descriptions, forming a knowledge base. As the name indicates, one of the characteristics of DLs is that they are equipped with a formal, logic-based semantics. Therefore, they allow for reasoning, i.e., inferring implicitly represented knowledge from the information DFG Research Training Group 1763: Quantitative Logics and Automata (QuantLA) * Pavlos Marantidis [email protected] 1
Technische Universität Dresden, Dresden, Germany
that is explicitly contained in the knowledge base. In particular, one can, for example, check for subconcept–superconcept relation or equivalence between two given concept descriptions. Since a knowledge base is rarely considered to be complete, the development of one is usually an ongoing procedure over an extended period of time.
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