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Formal concept analysis as mathematical theory of concepts and concept hierarchies
 Formal Concept Analysis, Foundations and Applications
, 2005
"... Abstract. Formal Concept Analysis has been originally developed as a subfield of Applied Mathematics based on the mathematization of concept and concept hierarchy. Only after more than a decade of development, the connections to the philosophical logic of human thought became clearer and even later ..."
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Abstract. Formal Concept Analysis has been originally developed as a subfield of Applied Mathematics based on the mathematization of concept and concept hierarchy. Only after more than a decade of development, the connections to the philosophical logic of human thought became clearer and even later the connections to Piaget’s cognitive structuralism which Thomas Bernhard Seiler convincingly elaborated to a comprehensive theory of concepts in his recent book [Se01]. It is the main concern of this paper to show the surprisingly rich correspondences between Seiler’s multifarious aspects of concepts in the human mind and the structural properties and relationships of formal concepts in Formal Concept Analysis. These correspondences make understandable, what has been experienced in a great multitude of applications, that Formal Concept Analysis may function in the sense of transdisciplinary mathematics, i.e., it allows mathematical thought to aggregate with other ways of thinking and thereby to support human thought and action. 1 Formal Concept Analysis, Mathematics, and Logic Formal Concept Analysis had its origin in activities of restructuring mathematics, in particular mathematical order and lattice theory. In the initial paper [Wi82], restructuring lattice theory is explained as “an attempt to reinvigorate connections with our general culture by interpreting the theory as concretely as possible, and in this way to promote better communication between lattice theorists and potential users of lattice theory. ” Since then, Formal Concept Analysis has been developed as a subfield of Applied Mathematics based on the mathematization of concepts and concept hierarchies. Only after more than a decade of development, the connections to Philosophical Logics of human thought became clearer, mainly through Charles Sanders Peirce’s late philosophy. Even our general understanding of mathematics did improve as pointed out in the recent paper “Kommunikative Rationalität, Logik und Mathematik ” (“Communicative Rationality, Logic, and Mathematics”) [Wi02b]. The concern of that paper is to explain and to substantiate the following thesis:
An application of relation algebra to lexical databases
, 2006
"... 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 settheoretic semantics or via an algebraic structure. With respect to formalisms based on nary relations (such as rela ..."
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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 settheoretic semantics or via an algebraic structure. With respect to formalisms based on nary 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.
An FCA interpretation of Relation Algebra
, 2006
"... This paper discusses an interpretation of relation algebra and fork algebra with respect to FCA contexts. In this case, "relation algebra" refers to the DeMorganPeirceSchroederTarski algebra and not to the "relational algebra" as described by Codd. The goal of this interpre ..."
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This paper discusses an interpretation of relation algebra and fork algebra with respect to FCA contexts. In this case, "relation algebra" refers to the DeMorganPeirceSchroederTarski algebra and not to the "relational algebra" as described by Codd. The goal of this interpretation is to provide an algebraic formalisation of objectrelational 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 partwhole relations for building relational databases.
Conceptual Exploration of Semantic Mirrors
 Formal Concept Analysis: Third International Conference, ICFCA 2005
, 2005
"... The "Semantic Mirrors Method" (Dyvik, 1998) is a means for automatic derivation of thesaurus entries from a wordaligned parallel corpus. The method is based on the construction of lattices of linguistic features. This paper models the Semantic Mirrors Method with Formal Concept Analysi ..."
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The "Semantic Mirrors Method" (Dyvik, 1998) is a means for automatic derivation of thesaurus entries from a wordaligned parallel corpus. The method is based on the construction of lattices of linguistic features. This paper models the Semantic Mirrors Method with Formal Concept Analysis. It is argued that the method becomes simpler to understand with the help of FCA. This paper then investigates to what extent the Semantic Mirrors Method is applicable if the linguistic resource is not a high quality parallel corpus but, instead, a medium quality bilingual dictionary. This is a relevant question because medium quality bilingual dictionaries are freely available whereas high quality parallel corpora are expensive and difficult to obtain. The analysis shows that by themselves, bilingual dictionaries are not as suitable for the Semantic Mirrors Method but that this can be improved by applying conceptual exploration. The combined method of conceptual exploration and Semantic Mirrors provides a useful toolkit specifically for smaller size bilingual resources, such as ontologies and classification systems. The last section of this paper suggests that such applications are of interest in the area of ontology engineering.
Data Weeding Techniques Applied to Roget’s Thesaurus. Knowledge Processing in Practice
, 2008
"... Abstract. It can be difficult to automatically generate “nice ” graphical representations for concept lattices from lexical databases, such as Roget’s Thesaurus, because the data sources tend to be large and complex. This paper discusses a variety of “data weeding ” techniques that can be applied in ..."
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Abstract. It can be difficult to automatically generate “nice ” graphical representations for concept lattices from lexical databases, such as Roget’s Thesaurus, because the data sources tend to be large and complex. This paper discusses a variety of “data weeding ” techniques that can be applied in order to reduce the size of a concept lattice, first in general, and then with respect to Roget’s Thesaurus. The aim is that resulting lattices should display neither too much, nor too little information, independently of which search terms have been entered by a user. 1
Concept Neighbourhoods in Lexical Databases
"... Abstract. This paper discusses results from an experimental study of concept neighbourhoods in WordNet and Roget’s Thesaurus. The general aim of this research is to determine ways in which neighbourhood lattices can be derived in real time from a lexical database and displayed on the web. In order t ..."
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Abstract. This paper discusses results from an experimental study of concept neighbourhoods in WordNet and Roget’s Thesaurus. The general aim of this research is to determine ways in which neighbourhood lattices can be derived in real time from a lexical database and displayed on the web. In order to be readable the lattices must not be too large, not contain overlapping concepts or labels and must be calculated within seconds. Lattices should, furthermore, not be too small and they should contain sufficient complexity to be interesting for the viewer. For these purposes the sizes of the lattices of different types of concept neighbourhoods have been calculated. Using the size information should help with the task of online generation of the lattices. 1
Revisiting the Potentialities of a Mechanical Thesaurus
"... Abstract. This paper revisits the latticebased thesaurus models which Margaret Masterman used for machine translation in the 1950’s and 60’s. Masterman’s notions are mapped onto modern, Formal Concept Analysis (FCA) terminology and three of her thesaurus algorithms are formalised with FCA methods. ..."
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Abstract. This paper revisits the latticebased thesaurus models which Margaret Masterman used for machine translation in the 1950’s and 60’s. Masterman’s notions are mapped onto modern, Formal Concept Analysis (FCA) terminology and three of her thesaurus algorithms are formalised with FCA methods. The impact of the historical and social situatedness of Roget’s Thesaurus on such algorithms is considered. The paper concludes by discussing connections between Masterman’s research and modern research. 1
Homograph Disambiguation Using Formal Concept Analysis
"... Abstract. Homographs are words with identical spellings but different origins and meanings. Natural language processing must deal with the disambiguation of homographs and the attribution of senses to them. Advances have been made using context to discriminate homographs, but the problem is still op ..."
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Abstract. Homographs are words with identical spellings but different origins and meanings. Natural language processing must deal with the disambiguation of homographs and the attribution of senses to them. Advances have been made using context to discriminate homographs, but the problem is still open. Disambiguating homographs is possible using formal concept analysis. This paper discusses the issues, illustrated by examples, using data from Roget’s Thesaurus. Keywords: Type10 chains, partitions, components, Roget’s Thesaurus, plus operator, word fields, neighbourhood lattices.
Establishing connections between Formal Concept Analysis and Relational Databases
 Common Semantics for Sharing Knowledge: Contributions to ICCS 2005
, 2005
"... 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 databas ..."
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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 objectrelational algebra is suggested in this paper as a possible future replacement of relational algebra.
Bilingual Word Association Networks
, 2007
"... Bilingual word association networks can be beneficial as a tool in foreign language education because they show relationships among cognate words of different languages and correspond to structures in the mental lexicon. This paper discusses possible technologies that can be used to generate and re ..."
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Bilingual word association networks can be beneficial as a tool in foreign language education because they show relationships among cognate words of different languages and correspond to structures in the mental lexicon. This paper discusses possible technologies that can be used to generate and represent word association networks.