The axioms and algebra of ambiguity

This paper continues a study of event ambiguity as a primitive concept. Axioms are described for a comparative ambiguity relation on an arbitrary event set that are necessary and sufficient for a representation of the relation by a functional that is nonnegative, vanishes at the empty event, and satisfies complementary equality and submodularity. Uniqueness characteristics of representing functionals are discussed. The theory is extended to multifactor events, where marginal ambiguity and additive representations arise.

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