Basic independence axioms for the publication-citation system

On the Independence of the Axioms for Fork Algebras

We establish the independence of the fork axioms by examining their role and presenting expansions of (simple) algebras of relations that falsify each one of these fork equations while satisfying the other axioms. We aslo examine these algebras to obtain further information about the independence of these axioms.

Independence of axiom system of basic algebras

We prove that the axiom system of basic algebras as given in Chajda and Emanovský (Discuss Math Gen Algebra Appl 24:31–42, 2004) is not independent. The axiom (BA3) can be deleted and the remaining axioms are shown to be independent. The case when the axiom of double negation is deleted is also treated.

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 ...

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

The paper analyzes interdependencies between strategies of players in a Nash equilibrium using independence relation between two sets of players. A sound and complete axiomatization of this relation is given. It has been shown previously that the same axiomatic system describes independence in probability theory, information flow, and concurrency theory.

Axioms and Algorithms for Inferences Involving Probabilistic Independence