Protoconceptual contents and implications

  • Authors:

  • Joachim Hereth Correia;Julia Klinger

  • Affiliations:

  • Department of Mathematics, Institute for Algebra, Dresden University of Technology, Dresden, D;Department of Mathematics, Darmstadt University of Technology, Darmstadt, D

  • Venue:
  • ICFCA'05 Proceedings of the Third international conference on Formal Concept Analysis
  • Year:
  • 2005

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Abstract

The development of a mathematical model for judgments understood as compositions of concepts and relations has been an important branch of research in recent years. It led to the definitions of concept and protoconcept graphs which are based on information contained in a power context family, where incidence relations between objects (or tuples of objects) and attributes are stored. A theory of the information those graphs represent (called conceptual content) has been developed for concept graphs in [PW99] and [Wi03]. In [HK04], an extension of this theory to protoconcept graphs not considering object implications (as it is done for concept graphs) has been established. The first part of this paper concentrates on the investigation of the protoconceptual content of protoconcept graphs respecting both protoconceptual and object implications. The second part compares the different structures of conceptual and protoconceptual contents of a given power context family, showing how more background information (using object implications and concepts instead of protoconcepts) reduces the number of possible contents. The third and final part analyzes how the different approaches can be generalized. Here we will concentrate on the (generalized) conceptual content of a formal context. In each part an information context will be defined, which provides an accessible representation of the lattice of (proto-)conceptual closures.