# Classification of Meronymy by Methods of Relational Concept Analysis

## Abstract

This paper introduces a method for classifying the meronymy relation based on quantificational tags. It is an example for an application of Relational Concept Analysis, which is an extension of Formal Concept Analysis, in the field of computational linguistics. Therefore this paper does not report the complete results of an investigation, but it tries to give ideas for further research using these methods. This paper cannot be viewed on all browsers. A full postscript version of this paper can be obtained.

## Introduction

Different authors have tried to classify the meronymy relation. Winston et al. (1987) distinguish six kinds of the meronymy relation which are separated by so-called relation elements'. Chaffin & Herrmann (1988) distinguish eight different kinds by using relation elements, but neither their kinds nor their relation elements coincide with the classification of Winston et al. A classification by Iris et al. (1988) which is based on four elementary models also only partly coincides with the other classifications. Cruse (1986) uses a different approach, he identifies four kinds of the meronymy relation based on quantificational differences. This approach is further developed by Woods (1991) who suggests that a semantic relation consists of a quantificational tag and a relational component. In this paper Woods' idea is embedded into the formal analysis of conceptual hierarchies. A theory for conceptual data structuring, called Formal Concept Analysis, has been developed for more than sixteen years at the Technische Hochschule Darmstadt (Ganter & Wille, 1996). It defines a concept based on its extent, which denotes the set of the formal objects of the concept, and on its intent, which denotes the set of the formal attributes of the concept. Concepts can either be represented in formal contexts which are cross-tables of the relation between objects and attributes or in the form of mathematical lattice diagrams. While Woods defines a relation r among instances' which leads to a relation R among classes', in the framework of Formal Concept Analysis, the relation r is defined among formal objects and inherited by concepts as relation R. This leads to Relational Concept Analysis, which is therefore the extension of Formal Concept Analysis to a more general theory that includes additional relations.

Formal and Relational Concept Analysis have already been used for applications in various subject areas. They are applicable to linguistics in several ways. First, they can facilitate the formalization of linguistic items by restricting lexical data to fixed contexts and specifying the role of each item in the context. While constructing formal contexts, the linguist has to determine if the formal objects are denotata of word forms, word forms or disambiguated word forms (Priss, in prep.2). The formal attributes can be attributes of denotata or connotational attributes. Depending on the selection of objects and attributes, the resulting formal concepts can represent denotative concepts, meta-concepts, word concepts or others.

Second, Woods' idea of inheritance of semantic relations (for example, from subconcepts to superconcepts) can be formalized, further investigated, and formally proved in the framework of Relational Concept Analysis (Priss, in prep.1). This can be applied to any semantic network that has hierarchical relations. Third, irregularities in the implementation of the semantic relations of a lexical database can be found and corrected. This is shown for the lexical database, WordNet, by Priss (in prep.3). Fourth, in this paper formal properties of semantic relations are used to obtain classificational attributes. This is demonstrated using the quantificational tags of the meronymy relation.

## Formal Concept Analysis

Formal Concept Analysis, as a theory of data structuring, starts with the notion of a formal context that is defined as a triple (G,M,I) where G is the set of formal objects (Gegenstaende), M is the set of formal attributes (Merkmale), and I is a binary relation between G and M for which gIm is interpreted as the object g has the attribute m' (Ganter & Wille, 1996).

Lattices are effectively visualized by line diagrams Each object g labels the concept \gamma g in the line diagram that is the smallest concept the object belongs to. Dually, an attribute m labels \mu m the largest concept it belongs to. The advantage of the lattice representation is that the similarity of the relation families' does not have to be calculated using statistical methods as in Chaffin & Herrmann's paper. But the similarities of the relation families to each other can be examined by investigating the lattice diagram. It becomes, for example, obvious that functional object' and functional location' are not properly discriminated. Maybe functional location' should also have the relation element locative'. It can be observed that group' is a subconcept of collection', because a group' has all the relation elements of a collection' but furthermore it has the relation element social'. These examples show that the lattice representation can serve as the basis for a scientific discussion on subjects whose structure would not be transparent otherwise.

## Quantificational tags for meronymy

The basic formal context for the investigation of semantic relations is a denotative context (Priss, in prep.3), which has denotata of words as formal objects and attributes of those denotata as formal attributes. The concepts can be denominated by disambiguated words in which case they are called denotative word concepts.

The table contains the attempt to classify the meronymy relation by using quantificational tags. The examples are not complete. Missing combinations do not suggest that those examples do not exist, but that the author has not found them yet.

The first rows of the table show that the quantificational tags depend on the level of abstraction of the objects (compare, for example, meat/sausage and sausage meat/sausage). Furthermore, although meronymy relations with different relational components can share the same tags, each class of relational components tends to prefer a special tag. Therefore the tags can be a basis of a classification. The resulting classes differ from the four meronymy models of Iris et al., which distinguish membership, segmented whole, subset, and functional components. Here membership and segmented whole are in some cases closer together (compare human/citizenship and chapter/book). For the object/object relations, which correspond to the functional components, this classification seems to be the most unsatisfactory. For example, Chaffin & Herrmann's component/integral object, topological part/object, time/time, and place/area are all subsumed under object/object. Hopefully there will be a combination of research on tags and relational components in the future.

## References

Chaffin, Roger; Herrmann, Douglas J. (1988). The nature of semantic relations: a comparison of two approaches. In: Evens, Martha W. (ed.). Relational Models of the Lexicon. Cambridge University Press.

Cruse, D. A. (1986). Lexical Semantics. Cambridge, New York.

Ganter, Bernhard; Wille, Rudolf (1996). Formale Begriffsanalyse: Mathematische Grundlagen. Springer-Verlag.

Iris, Madelyn; Litowitz, Bonnie; Evens, Martha (1988). Problems of Part-Whole Relations. In: Evens, Martha W. (ed.). Relational Models of the Lexicon. Cambridge University Press.

Priss, Uta E. (in preparation,1). Relationale Begriffsanalyse: Untersuchung semantischer Strukturen in Woerterbuechern und lexikalischen Datenbanken. Dissertation, TH-Darmstadt.

Priss, Uta E. (in preparation,2). Extracting Formal Contexts and Developing Conceptual Lattice Diagrams from Lexical Databases.

Priss, Uta E. (in preparation,3). The Formalization of WordNet by Methods of Relational Concept Analysis. In: Christiane Fellbaum (ed.). WordNet: An Electronic Lexical Database and some of its Applications. MIT Press.

Westerstahl, Dag (1989). Quantifiers in Formal and Natural Languages. In: Gabbay , D.; Guenther F. (ed.). Handbook of Philosophical Logic. Vol. 4, Kluwer, Dordrecht.

Winston, Morton E.; Chaffin, Roger; Herrmann, Douglas (1987). A Taxonomy of Part-Whole Relations. Cogn. Science. Vol. 11, pp. 417-444.

Woods, William A. (1991). Understanding Subsumption and Taxonomy: A Framework for Progress. In: Sowa, John (ed.). Principles of Semantic Networks: Explorations in the Representation of Knowledge, M. Kaufmann, San Mateo, California.