Mathematics and Science Faculty, Darmstadt University of Applied Sciences, Schoefferstr. 3, D-64295 Darmstadt, Germany

摘要

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.