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.