**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.