The theory of graphoids: A survey

  • Azaria Paz
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 532)


A survey type presentation, introducing the theory of Graphoids and their representation in graphs. Graphoids are temary relations over a finite domain governed by a finite set of axioms. They are intended as models for the representation of irrelevance relations of the form I(X,Z,Y) where (X,Z,Y) in I has the following interpretation: given that the values of the variables in Z are known, the values of the variables in Y can add no further information about the values of the variables in X.


Axioms of Graph and Axioms of Graphoids Completeness Graphs Graph Grammar Decision Properties Irrelevance Relation Knowledge Representation Probabilistic Distribution Representation in Graphs Soundness 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Geiger, D., Towards the Formalization of Informal Dependencies, (M.Sc. Thesis), UCLA Cognitive Systems Lab., Technical Report No. R-102.Google Scholar
  2. [2]
    Geiger, D., Paz, A., and Pearl, J., "Axioms and algorithms for inferences involving probabilistic independence". To appear in Information and Computation, 1990.Google Scholar
  3. [3]
    Geiger, D., Graphoids: A Qualitative Framework for Probabilistic Inferences, (Ph.D. Thesis), Cognitive Systems Lab., Technical Report No. R-142.Google Scholar
  4. [4]
    Geva, R.Y. and Paz, A., Representation of Irrelevance Relations by Annotated Graphs, Technical Report #603, Computer Science Department, Technion-IIT, January 1990.Google Scholar
  5. [5]
    Or, S., Comparison of Graph-Representation Methods for Graphoids and the Membership Problem. (M.Sc. Thesis), Technion-IIT, 1990.Google Scholar
  6. [6]
    Paz, A., A Full Characterization of Pseudographoids in Terms of Families of Undirected Graphs, UCLA Cognitive Systems Laboratory, Technical Report 870055 (R-95), 1987.Google Scholar
  7. [7]
    Pearl, J., and Paz, A., GRAPHOIDS: A Graph-Based Logic for Reasoning about Relevance Relations, "Advances in Artificial Intelligence-II," edited by B. Du Boulay et al., Amsterdam: North-Holland.Google Scholar
  8. [8]
    Pearl, J., Probabilistic Reasoning in Intelligence Systems: Networks of Plausible Inference. Chapter 3, Morgan-Kaufmann, San Mateo, CA. (1988).Google Scholar
  9. [9]
    Pearl, J., and Verma, T.S., "The logic of representing dependencies by directed graphs". Proc. 6th Natl. Conf. on AI (AAAI-87), Seattle, 374–379, 1987.Google Scholar
  10. [10]
    Studeny, M., "Attempts at Axiomatic Description of Conditional Independence," Workshop on Uncertainty in Expert Systems, Alsovice, Chechoslovakia, June 20–23, 1988.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Azaria Paz
    • 1
  1. 1.Department of Computer ScienceTechnion — Israel Institute of TechnologyHaifaIsrael

Personalised recommendations