Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
The logic of representing dependencies by directed graphs
AAAI'87 Proceedings of the sixth National conference on Artificial intelligence - Volume 1
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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.