Ur, Shmuel; Paz, Azaria The representation power of probabilistic knowledge by undirected graphs and directed acyclic graphs: A comparison. (English) Zbl 0806.68101 Int. J. Gen. Syst. 22, No. 2, 219-231 (1994). Summary: Two modes of representation of probabilistic knowledge are considered: undirected graphs (UG’s) and directed acyclic graphs (DAG’s). It is shown that there is a UG such that the knowledge represented in it requires exponentially many (in the number of vertices of the UG) DAG’s for its representation and there is a DAG such that the knowledge represented in it requires exponentially many UG’s for its representation. It is thus shown that neither method can be preferred in all cases over the other. Cited in 1 Document MSC: 68T30 Knowledge representation 68R10 Graph theory (including graph drawing) in computer science Keywords:probabilistic knowledge; undirected graphs; directed acyclic graphs PDFBibTeX XMLCite \textit{S. Ur} and \textit{A. Paz}, Int. J. Gen. Syst. 22, No. 2, 219--231 (1994; Zbl 0806.68101) Full Text: DOI References: [1] Lauritzen S. L., Lectures on Contingency Tables (1982) [2] Lauritzen S. L., Independence Properties of Directed Markov Fields (1988) [3] Paz A., Closure Algorithms and Decision Problems for Graphoids Generated by Two Undirected Graphs–Abridged Version (1988) [4] Pearl J., In Proc. 6th Natl. Conf. pp 374– (1987) [5] Pearl J., GRAPHOIDS A Graph-Based Logic for Reasoning about Relevance Relations (1986) [6] Pearl J., Probabilistic Reasoning in Intelligent Systems Networks of Plausible Inference (1988) · Zbl 0746.68089 [7] Studený M. [ 1989 ], ”Attempts at Axiomatic Description of Conditional Independence.” Kybernetika , 25 ( 1989 ), No. 1–3 , pp. 72 – 79 . This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.