Game Semantics for the Geiger-Paz-Pearl Axioms of Independence

Concurrency Semantics for the Geiger-Paz-Pearl Axioms of Independence

Independence between two sets of random variables is a well-known relation in probability theory. Its origins trace back to Abraham de Moivre’s work in the 18th century. The propositional theory of this relation was axiomatized by Geiger, Paz, and Pearl. Sutherland introduced a relation in information flow theory that later became known as “nondeducibility.” Subsequently, the first two authors ...

Axioms and Algorithms for Inferences Involving Probabilistic Independence

A Universal Algebraic Approach for Conditional Independence

In this paper we show that elementary properties of joint probability density functions naturally induce a universal algebraic structure suitable for studying probabilistic conditional independence (PCI) relations. We call this algebraic system the cain. In the cain algebra, PCI relations are represented in equational forms. In particular we show that the cain satisfies the axioms of the grapho...

A Graph-Based Inference Method for Conditional Independence

The graphoid axioms for conditional independence, originally described by Dawid [1979], are fundamental to probabilistic reasoning [Pearl, 1988]. Such axioms provide a mechanism for manipulating conditional independence assertions without resorting to their numerical definition. This paper explores a representation for independence statements using multiple undirected graphs and some simple gra...

Independence and Functional Dependence Relations on Secrets

We study logical principles connecting two relations: independence, which is known as nondeducibility in the study of information flow, and functional dependence. Two different epistemic interpretations for these relations are discussed: semantics of secrets and probabilistic semantics. A logical system sound and complete with respect to both of these semantics is introduced and is shown to be ...