A Logical Notion of Conditional Independence Properties and Applications

We propose a notion of conditional independence with respect to propositional logic and study some of its key properties We present several equivalent formulations of the proposed notion each oriented towards a speci c application of logical reasoning such as abduction and diagnosis We suggest a frame work for utilizing logical independence computationally by structuring a propositional logic database around a directed acyclic graph This structuring explicates many of the independences satis ed by the underlying database Based on these structural independences we develop an algorithm for a class of structured databases that is not necessarily Horn The algorithm is linear in the size of a database structure and can be used for deciding entailment computing abductions and diagnoses The presented results are motivated by similar results in the literature on probabilistic and constraint based reasoning