The nature of conceptual thinking constitutes a central topic in a variety of scienti?c disciplines. Since 1993, the International Conference on Conceptual Structures (ICCS) has served as a platform that brings together researchersand practioners in information and computer sciences as well as social science to explore novel ways of representing and analyzing conceptual knowledge. Ori- nally centered around research on knowledge representation and reasoning with conceptual graphs, over the years ICCS has broadened its scope to include in- vations from a wider range of theories and related practices, among them other forms of graph-based formalisms like RDF or existential graphs, formal concept analysis, Semantic Web technologies, ontologies, concept mapping and more. Today, ICCS draws inspiration from areas as diverse as arti?cial intelligence, knowledge representation and reasoning, applied mathematics and lattice t- ory, computational linguistics, conceptual modeling and design, diagrammatic reasoning and logic, intelligent systems and knowledge management. In addition to vivid conferences, the vibrancy of the ?eld is documented by two recently published books (Hitzler, Scha ..rfe (Eds): Conceptual Structures in Practice and Chein, Mugnier: Graph-based Knowledge Representation: C- putational Foundations of Conceptual Graphs) as well as by an ISO standard ("Common Logic", ISO/ IEC 24707) which orginated in this community.

The 13th International Conference on Conceptual Structures (ICCS 2005) was held in Kassel, Germany, during July 17 22, 2005. Information about the c- ference can be found athttp: //www.kde.cs.uni-kassel.de/conf/iccs05. The title of this year s conference, Common Semantics for Sharing Kno- edge, waschosentoemphasizeontheonehandtheoverallaimofanyknowledge representationformalism, to support the sharing of knowledge, and on the other hand the importance of a common semantics to avoiddistortion of the meaning. We understand that both aspects are of equal importance for a successful future of the researcharea of conceptual structures. We are thus happy that the papers presentedatICCS2005addressedbothapplicationsandtheoreticalfoundations. Sharing knowledge can also be understood in a separate sense. Thanks to the German Research Foundation, DFG, we were able to invite nine inter- tionally renowned researchers from adjacent research areas. We had stimulating presentationsandlively discussions, with bidirectionalknowledgesharing.Ev- tually the ground can be laid for establishing common semantics between the respective theories. This year, 66 papers were submitted, from which 22 were selected to be included in this volume. In addition, the ?rst nine papers present the invited talks.Wewishtoexpressourappreciationtoalltheauthorsofsubmittedpapers, to the members of the Editorial Board and the Program Committee, and to the external reviewers for making ICCS 2005 a valuable contribution to the knowledge processing research ?eld."

The aim of contextual logic is to provide a formal theory of elementary logic, which is based on the doctrines of concepts, judgements, and conclusions. Concepts are mathematized using Formal Concept Analysis (FCA), while an approach to the formalization of judgements and conclusions is conceptual graphs, based on Peirce's existential graphs. Combining FCA and a mathematization of conceptual graphs yields so-called concept graphs, which offer a formal and diagrammatic theory of elementary logic.

Expressing negation in contextual logic is a difficult task. Based on the author's dissertation, this book shows how negation on the level of judgements can be implemented. To do so, cuts (syntactical devices used to express negation) are added to concept graphs. As we can express relations between objects, conjunction and negation in judgements, and existential quantification, the author demonstrates that concept graphs with cuts have the expressive power of first-order predicate logic. While doing so, the author distinguishes between syntax and semantics, and provides a sound and complete calculus for concept graphs with cuts. The author's treatment is mathematically thorough and consistent, and the book gives the necessary background on existential and conceptual graphs.