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Chain graphs: Semantics and expressiveness

  • Remco R. Bouckaert
  • Milan Studený
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 946)

Abstract

A chain graph (CG) is a graph admitting both directed and undirected edges with forbidden directed cycles. It generalizes both the concept of undirected graph (UG) and the concept of directed acyclic graph (DAG). CGs can be used efficiently to store graphoids, that is, independency knowledge of the form “X is independent of Y given Z” obeying a set of five properties (axioms).

Two equivalent criteria for reading independencies from a CG are formulated, namely the moralization criterion and the separation criterion. These criteria give exactly the graphoid closure of the input list for the CG. Moreover, a construction of a CG from a graphoid (through an input list), which produces a minimal I-map of that graphoid, is given.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Remco R. Bouckaert
    • 1
  • Milan Studený
    • 2
  1. 1.Department of Computer ScienceUtrecht UniversityTB UtrechtThe Netherlands
  2. 2.Inst. of Inform. Theory & Autom.Czech Academy of SciencesPragueCzech Republic

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