Characterising Normal Forms for Informational Independence

The concept of informational independence plays a key role in most knowledge-based systems. Although de ned di erently in di erent contexts, its basic properties have been axiomatised by J. Pearl and his co-researchers. Pearl's axiomatic system o ers a set of inference rules for deriving new independence statements from an initial set of statements and as such allows for a normal form for representing independences. Pearl's axioms, however, focus on mutually disjoint sets of variables only. We show that focusing on disjoint sets of variables can hide various interesting properties of independence. We extend Pearl's axiomatic system to capture these properties and thereby introduce a new normal form for informational independence.