Exploiting stability for compact representation of independency models

The notion of stability in semi-graphoid independency models was introduced to describe the dynamics of (probabilistic) independency upon inference. We revisit the notion in view of establishing compact representations of semi-graphoid models in general. Algorithms for this purpose typically build upon dedicated operators for constructing new independency statements from a starting set of statements. In this paper, we formulate a generalised strong-contraction operator to supplement existing operators, and prove its soundness. We then embed the operator in a state-of-the-art algorithm and illustrate that the thus enhanced algorithm may establish more compact model representations