Relational Concept Analysis is an extension of Formal Concept Analysis. It combines mathematical lattices with relational structures and provides a formal language for the modeling of semantic relations in lexical databases and thesauri. The first chapter of this dissertation presents a short introduction to Formal Concept Analysis, an overview of the linguistic terminology and linguistic or philosophical theories on the subject of `word', `concept', `meaning', and `denotation'. This leads to the definition of `disambiguated words' which have `particular meanings', are contained or stored in a lexical structure, and present the basic units for most of the modelings in this dissertation. The concepts that correspond to a disambiguated word are differentiated into denotative and connotative word concepts. This terminology allows the formalization of several `linguistic contexts' and `linguistic lattices' which can be applied to a variety of linguistic datasets for a variety of purposes. The chapter terminates with formalizations of a traditional dictionary, a natural language thesaurus, and a lexical database.
The second chapter introduces Relational Concept Analysis and discusses the mathematical formalizations and theorems that apply, such as the development of bases for concept relations which allow optimal implementations of relations in lexical databases; the inheritance structures and other formal properties (such as transitivity) of concept relations; auto- and polyrelations; graphical representations; and applications to linguistic contexts and lattices.
The third chapter concentrates on linguistic aspects of semantic relations. A broad classification of semantic relations is developed based on formal characteristics. The semantic relations, synonymy, hyponymy, hypernymy, cohyponymy, disjointness, meronymy, contrast (antonymy), sequence, cause, backward presupposition, and entailment are formally defined. The major example for this chapter is the meronymy relation which is distinguished from Lesniewski's mereology. Transitivity of meronymy is discussed. A classification of meronymy based on quantifications is developed and compared to the classifications based on content by other authors. Examples from the lexical database WordNet demonstrate how Relational Concept Analysis can be utilized to discover irregularities in the implementations of semantic relations in lexical databases.
Finally, the last chapter provides further applications and extensions of Relational Concept Analysis. It is argued that the lexical and conceptual structures of a natural language both form separate systems that interrelate. A graphical representation technique for semantic and lexical relations in a denotative lattice is developed. Formal composition rules for lexical and conceptual items are defined and related to each other. Unary relations are introduced and used to assign additional attributes to a concept lattice. Such additional attributes can be prototypical or default attributes that are not shared by all objects in the extent of a concept. The connections of Relational Concept Analysis to Relational Algebra, many-valued contexts, the Entity-Relationship model, terminological logic, and semantic networks are discussed.