Relational exploration: combining description logics and formal concept analysis for knowledge specification

4 Danksagungen Contents Introduction 7 1 FCA and Attribute Exploration 11 1. Introduction In the Palace of the Vatican, on a wall of a room called stanza della segnatura, the visitor encounters the fresco The School of Athens created by the famous renaissance painter Raphael around 1509. It shows renowned representatives of the ancient artes liberales led by philosophy. Right in the center of this masterpiece, one finds the certainly most brilliant greek philosophers (besides Socrates): Plato and Aristotle. While Plato points up indicating his belief in the primacy of ideas situated in a higher world of forms, Aristotle holds his hand palm downwards suggesting a more grounded epistemic view, where real world facts (or in modern terms: the data) govern the way how concepts and classifications are formed. These two perspectives can be traced through the entire occidental philosophy occurring here and there in varying guises (cf. also the problem of universals or the bipolar setting rationalism vs. empirism brought up in the 19th century). These antagonistic approaches personified by the two philosophers seem also characteristic for the underlying ways of thinking in two fields of knowledge processing and representation, we want to deal with in our work: Formal Concept Analysis (FCA) and Description Logic (DL). The – more Aristotelian – mathematical theory of Formal Concept Analysis came into being some twenty years ago as the attempt to model (hierarchies of) concepts in terms of lattice theory. It is based on the dualistic understanding of concepts as consisting of concept extent (i.e., all entities belonging to that concept) and concept intent (i.e., all attributes characterizing it). FCA has proven solid in theory but also quite intuitive in representing conceptual knowledge, also for mathematically less skilled people. Thus, it has been successfully applied in various areas beyond mathematics. Besides this representational capabilities, algorithms assisting knowledge acquisition have been developed, implemented and used in practice. In recent years, FCA has been developed further and extended by the project 8 Introduction of contextual logic, widening the scope of interest from concepts to judgments. In the course of these developments, the relational aspect has been increasingly emphasized. Description Logics being a collective term for a family of knowledge representation formalisms are the result of a development starting in the 1970s with frame based systems and semantic networks. The common underlying idea is to characterize classes of entities (resp. objects) of a domain and …