Affiliations: Computer Science Department, Technion - Israel Institute of Technology, Haifa 32000, Israel. paz@cs.technion.ac.il | Intel Corporation, Santa Clara, California, U.S.A. robert.geva@intel.com | Institute of Information Theory and Automation, Academy of Sciences of the Czech Republic, Prague, Czech Republic. studeny@utia.cas.cz
Note: [] Address for correspondence: Computer Science Department, Technion - Israel Institute of Technology, Haifa 32000, Israel
Note: [] Address for correspondence: Intel Corporation, Santa Clara, California, U.S.A.
Note: [] The second affiliation: Laboratory of Intelligent Systems, University of Economics Prague, Czech Republic. Address for correspondence: Institute of Information Theory and Automation, Academy of Sciences of the Czech Republic, Prague, Czech Republic
Abstract: Irrelevance relations are sets of statements of the form: given that the ‘value’ of Z is known, the ‘values’ of Y can add no further information about the ‘values’ of X. Undirected Graphs (UGs), Directed Acyclic Graphs (DAGs) and Chain Graphs (CGs) were used and investigated as schemes for the purpose of representing irrelevance relations. It is known that, although all three schemes can approximate irrelevance, they are inadequate in the sense that there are relations which cannot be fully represented by anyone of them. In this paper annotated graphs are defined and suggested as a new model for graphical representation. It is shown that this new model is a proper generalization of the former models: any irrelevance relation that can be represented by either one of the previous models can also be represented by an annotated graph, and there are relations that can be represented by an annotated graph but cannot be represented by either one of the former models. The question of whether this new model is powerful enough to represent all the irrelevance relations, as well as some other related questions, is still open.
