Conceptual Structures for Knowledge Creation and Communication

In Contextual Judgment Logic, Sowa’s conceptual graphs (understood as graphically structured judgments) are made mathematically explicit as concept graphs which represent information formally based on a power context family and rhetorically structured by relational graphs. The conceptual content of a concept graph is viewed as the information directly represented by the graph together with the information deducible from the direct information by object and concept implications coded in the power context family. The main result of this paper is that the conceptual contents can be derived as extents of the so-called conceptual information context of the corresponding power context family. In short, the conceptual contents of judgments are formally derivable as concept extents. 1 Information in Contextual Judgment Logic In this paper, information in the scope of Conceptual Knowledge Processing shall be understood in the same way as in Devlin’s book “Infosense Turning Information into Knowledge” [De99]. Devlin briefly summarizes his understanding of information and knowledge by the formulas: Information = Data + Meaning Knowledge = Internalized information + Ability to utilize the information Through Devlin’s understanding it becomes clear that Formal Concept Analysis [GW99] enables to support the representation and processing of information and knowledge as outlined in [Wi02a]. Since Contextual Logic [Wi00] with its semantics is based on Formal Concept Analysis, it is desirable to make also explicit why and how Contextual Logic may support the representation and processing of information and knowledge. In this paper, we concentrate on approaching this aim for Contextual Judgment Logic [DK03]. In Contextual Judgment Logic, judgments understood as asserting propositions are formally mathematized by so-called concept graphs which have been semantically introduced in [Wi97] as mathematizations of Sowa’s conceptual graphs [So84]. Since judgments are philosophically conceived as assertional combinations of concepts, their mathematizatzion is based on formal concepts of formal contexts (introduced in [Wi82]): The semantical base is given by a power A. de Moor, W. Lex, and B. Ganter (Eds.): ICCS 2003, LNAI 2746, pp. 1–15, 2003. c © Springer-Verlag Berlin Heidelberg 2003