Formal Concept Analysis

Abstract

Formal concept analysis (FCA) [71] is a mathematical theory for concepts and concept hierarchies that reflects an understanding of “concept” which is first mentioned explicitly in the Logic of Port Royal [2] in 1668 and has been established in the German standard ‘DIN 2330 – Concepts and terms; general principles’ [19]. FCA explicitly formalises extension and intension of a concept, their mutual relationships, and the fact that increasing intent implies decreasing extent and vice versa. Based on lattice theory, it allows to derive a concept hierarchy from a given dataset. FCA complements thus the usual ontology engineering approach, where the concept hierarchy is modeled manually. FCA differs from other knowledge representation formalisms (like RDF (see chapter “Resource Description Framework”), description logics (see chapter “Description Logics”), OWL (see chapter “Web Ontology Language: OWL”), or conceptual graphs [53]). The standard DIN 2330 [19] helps us pointing out the difference. It distinguishes three levels: object level, concept level, and representation level (see Fig. 1). There is no immediate relationship between objects and names. This relationship is rather provided by concepts. On the concept level, the objects under discussion constitute the extension of the concept, while their shared properties constitute the intension of the