13th International Conference on Conceptual Structures
Conceptual Structures: Common Semantics for Sharing Knowledge

Tutorial "Mathematical Foundations of Conceptual Graphs"

July 17, 10:00-13:00

The system of conceptual graphs is a comprehensive logic system which is designed to be used in fields like software specification and modeling, knowledge representation, natural language generation and information extraction. These fields have to cope with various problems of implementational, mathematical or linguistic nature. This lead to different modifications and extensions of conceptual graphs, which in turn lead to several difficulties and fallacies, ranging from lacks of preciseness and ambiguities over minor gaps to major mistakes and contradictions, in and between different notations or implementations of conceptual graphs.

Since the invention of conceptual graphs, several authors discussed them from the viewpoint of mathematical logic. Due to its complexity, there exists no mathematical elaboration of the overall system of conceptual graphs. Instead, different fragments of the system have been mathematically defined and investigated. This tutorial aims to provide an overview over these different formalizations.
This includes the different underlying graph formalizations (labeled bipartite graphs, labeled directed multi-hypergraphs), the different semantics (translations to FO, relational structures, contextual structures), the different forms of calculi (projections, simple transformation rules, complex transformation rules based of Peirce's calculus for existential graphs), and an overview over the different levels of expressiveness among the different formalizations.

The tutorial will mainly focus on the works of Chein/Mugnier et al, as well as on the different forms of so-called concept graphs by Wille et al. the different underlying graph formalizations (labeled bipartite graphs, labeled directed multi-hypergraphs), the different semantics (translations to FO, relational structures, contextual structures), the different forms of calculi (projections, simple transformation rules, complex transformation rules based of Peirce's calculus for existential graphs), and an overview over the different levels of expressiveness among the different formalizations.

The tutorial will mainly focus on the works of Chein/Mugnier et al, as well as on the different forms of so-called concept graphs by Wille et al.

Lecturer

Dr. Frithjof Dau earned a Diploma degree in Mathematics from the University of Hannover, Germany, in 1994. After working 2 1/2 years in industry as a C++-developper and IT-consultant, he joined the Department of Mathematics of the Darmstadt University of Technology (Technische Universität Darmstadt) as a research assistant, where he wrote his PhD-thesis "The Logic System of Concept Graphs (And its Relationship to Predicate Logic)" under the supervision of Prof. Dr. Wille. The thesis was defended In 2002 with distinction. The thesis has subsequentely been published by Springer in the series "Lecture Notes in Artificial Intelligence", vol. LNCS 2892, in november 2003, which attest the signifcance of the work. Since then, Dau has broadened his research to different forms of diagrammatic reasoning, e.g. Peirce's existential graphs, further elaborations of Sowa's conceptual graphs, and RDF. In 2005, Dau is co-chair of the International Conference on Conceptual Structures. Dau has been more or less continously employed as a teaching assistant at the Darmstadt University of Technology since 1997 - except for two periods of 6 months where he was appointed a lecturer at the Applied University of Darmstadt. Dau is currently working towards his habilitation on the subject of diagrammatic reasoning.