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Abstract: This paper provides guidelines and examples for visualising lexical relations using Formal Concept Analysis. Relations in lexical databases often form trees, imperfect trees or poly-hierarchies which can be embedded into concept lattices. Manyto-many relations can be represented as concept lattices where the values from one domain are used as the formal objects and the values of the other domain as formal attributes. This paper further discusses algorithms for selecting meaningful subsets of lexical databases, the representation of complex relational structures in lexical databases and the use of lattices as basemaps for other lexical relations.

this paper was partially supported by the Zentrum fur Interdisziplinare Technikforschung, Darmstadt be described by their hypernyms, attributes, and other relations, but are not denominated by words. Two formal contexts are needed for the study of semantic relations, a denotative context, which contains the denotational meanings of word forms (denotata) and their conceptual ordering, and a lexical context, which has the words as constitutive elements. The words are always assumed to be disambiguated (for example by WordNet sense numbers) to avoid problems of polysemy and homonymy. A denotative context is usually incomplete because it is not possible to write a list of all denotata of a language. But, as semantic relations refer to relations among denotata, they cannot be defined on words without studying the denotata in a denotative context. Examples for lexical contexts are lexical fields (Kipke & Wille, 1987). Furthermore, every dictionary or thesaurus can be interpreted as a lexical context. Words are names for concepts in a denotative context and formal objects in a lexical context. Therefore it has to be investigated whether semantic relations have the same properties in both contexts. WordNet is formalized as such a lexical context, but only the noun synsets are investigated in this chapter (Section 7.3). The other parts of speech and more details can be found elsewhere (Priss, 1996). In Section 7.7, three examples of the meronymy relation in WordNet show how this theoretical framework can be used to find irregularities among the semantic relations in WordNet1.5

The research presented in this paper is part of a larger project of building a graphical interface for document retrieval which is based on a conceptual analysis of explicit and implicit structures among document data. Mathematical lattices, which are formalized according to Formal Concept Analysis, serve as an internal model. The lattice model is opposed to the more traditional vector space-based information retrieval models. Besides the document database a thesaurus is included in the system and also formalized as a lattice. The system obtains a high degree of flexibility, i.e. adaptability to different document databases or knowledge bases and to changing users preferences, from its modular design and from a set of lattice combination options. 1

Abstract. This paper presents an application of relation algebra to lexical databases. The semantics of knowledge representation formalisms and query languages can be provided either via a set-theoretic semantics or via an algebraic structure. With respect to formalisms based on n-ary relations (such as relational databases or power context families), a variety of algebras is applicable. In standard relational databases and in formal concept analysis (FCA) research, the algebra of choice is usually some form of Cylindric Set Algebra (CSA) or Peircean Algebraic Logic (PAL). A completely different choice of algebra is a binary Relation Algebra (RA). In this paper, it is shown how RA can be used for modelling FCA applications with respect to lexical databases. 1

The science of linguistics tells us that Ontology is the specification of meaning for the elements of a language, and the relationships between those elements. Within the world of data modeling, as different models must interact with each other, the ability to describe the ontology of a data model becomes increasingly more important. This is especially true in the realm of simulation interoperability, where each different simulation system has it’s own data model, and therefore, it’s own ontology. One of the most crucial paths of research currently being explored by a number of different parties is the use of the Command and Control Information Exchange Data Model (C2IEDM) as a referential tool enabling the interchange of data between two (or more) distinct systems. The C2IEDM necessarily has it’s own ontology, but is it sufficiently complete to serve as a referential ontology for simulation interoperability? This paper will first describe what defines an ontology, and what is a sufficiently complete ontology to serve as a reference for simulation interoperability. A review of the functional areas of the C2IEDM will follow, and finally based on this review, an evaluation will be made as to whether the C2IEDM is a sufficiently complete ontology.

This paper discusses an interpretation of relation algebra and fork algebra with respect to FCA contexts. In this case, "relation algebra" refers to the DeMorgan-Peirce-Schroeder-Tarski algebra and not to the "relational algebra" as described by Codd. The goal of this interpretation is to provide an algebraic formalisation of object-relational databases that is based on binary relations and thus closer to FCA and formal contexts than the traditional formalisation based on Codd. The formalisation provides insights into certain symmetries (among quantifiers) and the use of ternary relations and part-whole relations for building relational databases.

The relationship between relational databases and formal concept analysis (FCA) has been the topic of several papers in the past. This paper intends to extend some of the ideas presented in the previous papers by analysing the relationship between FCA and two central notions of relational databases: database schemata and normalforms. An object-relational algebra is suggested in this paper as a possible future replacement of relational algebra.

General objects are classes of individual objects that are considered to be extents of concepts of a formal context. In this paper, different contexts with general objects are defined and their conceptual structure and relation to other contexts is analyzed with methods of Formal Concept Analysis.

In a manually built-up semantic net in which not the concept definitions automatically determine the position of the concepts in the net, but rather the links coded by the lexicographers, the formal properties of the encoded attributes and relations provide necessary but not sufficient conditions to support maintenance of internal consistency and avoidance of redundancy. According to our experience the potential of this methodology has not yet been fully expIoited due to lack of understanding of applicable formal rules, or due to inflexibility of available software tools. Based on a more comprehensive in- quiry performed on the lexical database Word- Net TM 1.5, this paper presents a selection of pertinent checking rules and the results of their application to WordNet 1,5. Transferable insights are: 1. Semantic relations which are closely related but differing in a checkable property, should be differentiated. 2. Inferable relations - such as the transitive closure of a hierarchical relation or semantic relations induced by lexical ones - need to be taken into account when checking real relations, i.e. directly stored relations. 3. A semantic net needs proper repre- sentation of lexical gaps. A disjunctive hypernym, implemented as a set of hypernyms, is considered harmful.