Abstract
Formal Concept Analysis (FCA) is a field of applied mathematics with its roots in order theory, in particular the theory of complete lattices. Over the past 20 years, FCA has been widely studied. Description Logics (DLs) are a family of knowledge representation languages which can be used to represent the terminological knowledge of an application domain in a structured and formally well-understood way. Nowadays, properties and semantics of ontology constructs mainly are determined by DLs. The current research progress and the existing problems of FCA are analyzed. In this paper, we semantify FCA with DLs, in other words, we present an extended FCA (i.e., semantic FCA) by using the concepts of DLs to act as the attributes of formal contexts. Furthermore, we semantify the three components (i.e., formal concepts, attribute implications, and concept lattices) of traditional FCA. In addition, we also study the attribute reduction of formal contexts, formal concepts, and concept lattices from a semantics point of view.
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