A Logical Approach to Context-Specific Independence
Bayesian networks constitute a qualitative representation for conditional independence (CI) properties of a probability distribution. It is known that every CI statement implied by the topology of a Bayesian network G is witnessed over G under a graph-theoretic criterion called d-separation. Alternatively, all such implied CI statements have been shown to be derivable using the so-called semi-graphoid axioms. In this article we consider Labeled Directed Acyclic Graphs (LDAG) the purpose of which is to graphically model situations exhibiting context-specific independence (CSI). We define an analogue of dependence logic suitable to express context-specific independence and study its basic properties. We also consider the problem of finding inference rules for deriving non-local CSI and CI statements that logically follow from the structure of a LDAG but are not explicitly encoded by it.
The third author was supported by grant 292767 of the Academy of Finland. The fourth author was supported by FDPSS via grant 141318 of the Academy of Finland.
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