Abstract not found

The aim of this paper is to contribute to Data Analysis by clarifying how concept graphs may be derived from data tables. First it is shown how, by the method of relational scaling, a many-valued data context can be transformed into a power context family. Then it is proved that the concept graphs of a power context family form a lattice which can be described as a subdirect product of specific intervals of the concept lattices of the power context family (each extended by a new top-element). How this may become practical is demonstrated using a data table about the domestic flights in Austria. Finally, the lattice of syntactic concept graphs over an alphabet of object, concept, and relation names is determined and related to the lattices of concept graphs of the power context families which are semantic models of the given contextual syntax.

The aim of this paper is to indicate how TOSCANA may be extended to allow graphical representations not only of concept lattices but also of concept graphs in the sense of Contextual Logic. The contextual-logic extension of TOSCANA requires the logical scaling of conceptual and relational scales for which we propose the Peircean Algebraic Logic as reconstructed by R. W. Burch. As graphical representations we recommend, besides labelled line diagrams of concept lattices and Sowa's diagrams of conceptual graphs, particular information maps for utilizing background knowledge as much as possible. Our considerations are illustrated by a small information system about the domestic ights in Austria.

Conceptual Graphs and Formal Concept Analysis have in common basic concerns: the focus on conceptual structures, the use of diagrams for supporting communication, the orientation by Peirce`s Pragmatism, and the aim of representing and processing knowledge. These concerns open rich possibilities of interplay and integration. We discuss the philosophical foundations of both disciplines, and analyze their specific qualities. Based on this analysis, we discuss some possible approaches of interplay and integration.

. Triadic concept graphs have been introduced as a mathematization of conceptual graphs with subdivision. In this paper it is shown that triadic concept graphs of a triadic power context family always form a complete lattice with respect to the generalization order. For stating this result, a clarification of the notion of generalization is needed. It turns out that the generalization order may be differently defined, depending on the assumed background knowledge, respectively. Contents 1. Triadic Concept Graphs 2. The Generalization Order 3. Lattices of Triadic Concept Graphs 1 Triadic Concept Graphs The aim of this paper is to show that the triadic concept graphs of a triadic power concept family (see [Wi98]) always form a complete lattice with respect to the generalization order (cf. [PW99]). For this we have to clarify the notion of generalization for triadic concept graphs which, of course, presupposes a basic understanding of triadic power context families and their c...

A main goal of Formal Concept Analysis from its very beginning has been the support of rational communication. The source of this goal lies in our understanding of mathematics as a science which should encompass both its philosophical basis and its social consequences. This can be achieved by a process named 'restructuring'. This approach shall be extended to logic, which is based on the doctrines of concepts, judgments and conclusions. The program of restructuring logic is named Contextual Logic (CL). A main idea of CL is to combine Formal Concept Analysis and Concept Graphs (which are mathematical structures based on conceptual graphs). Concept graphs formulate judgments on the contained concepts, and conclusions can be drawn by inferring one concept graph from another. So we see that concept graphs can be understood as a crucial part of the mathematical implementation of CL, based on Formal Concept Analysis as the mathematization of the doctrine of concepts.

In the last years, the main orientation of Formal Concept Analysis (FCA) has turned from mathematics towards computer science.

Conceptual Information Systems are based on a formalization of the concept of `concept' as it is discussed in traditional philosophical logic. This formalization supports a human-centered approach to the development of Information Systems. We discuss this approach by means of an implemented Conceptual Information System for supporting IT security management in companies and organizations.

Query graphs with cuts are inspired by Sowa’s conceptual graphs, which are in turn based on Peirce’s existential graphs. In my thesis ‘The Logic System of Concept Graphs with Negations’, conceptual graphs are elaborated mathematically, and the cuts of existential graphs are added to them. This yields the system of concept graphs with cuts. These graphs correspond to the closed formulas of first order predicate logic. Particularly, concept graphs are propositions which are evaluated to truth-values. In this paper, concept graphs are extended to so-called query graphs, which are evaluated to relations instead. As the truth-values TRUE and FALSE can be understood as the two 0-ary relations, query graphs extend the expressiveness of concept graphs. Query graphs can be used to elaborate the logic of relations. In this sense, they bridge the gap between concept graphs and the Peircean Algebraic Logic, as it is described in Burch’s book ’A Peircean Reduction Thesis’. But in this paper, we focus on deduction procedures on query graphs, instead of operations on relations, which is the focus in PAL. Particularly, it is investigated how the adequate calculus of concept graphs can be transferred to query graphs.

In this article, we provide di#erent possibilities for doing reasoning on simple concept(ual) graphs without negations or nestings. First of all, we have on the graphs the usual semantical entailment relation |=, and we consider the restriction of the calculus for concept graph with cuts, which has been introduced in [Da02], to the system of concept graphs without cuts. Secondly, we introduce a semantical entailment relation as well as syntactical transformation rules between models. Finally, we provide definitions for standard graphs and standard models so that we translate graphs to models and vice versa. Together with the relations on the graphs and on the models, we show that both calculi are adequate and that reasoning can be carried over from graphs to models and vice versa. 1