Properties of Semi-Elementary Imsets as Sums of Elemen- Tary Imsets

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Takuya Kashimura, Tomonari Sei, Akimichi Takemura, Kentaro Tanaka


We study properties of semi-elementary imsets and elementary imsets introduced by StudenĀ“y [10]. The rules of the semi-graphoid axiom (decomposition, weak union and contraction) for conditional independence statements can be translated into a simple identity among three semi-elementary imsets. By recursively applying the identity, any semi-elementary imset can be written as a sum of elementary imsets, which we call a representation of the semi-elementary imset. A semi-elementary imset has many representations. We study properties of the set of possible representations of a semi-elementary imset and prove that all representations are connected by relations among four elementary imsets.

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