Axiomatizing first-order consequences in independence logic

TL;DR

This paper provides a complete axiomatization for first-order consequences of independence logic sentences, extending previous results from dependence logic to independence logic.

Contribution

It introduces an explicit axiomatization for first-order consequences in independence logic and proves its completeness.

Findings

Established a complete axiomatization for first-order consequences

Generalized previous results from dependence logic

Proved the axiomatization's completeness

Abstract

Independence logic cannot be effectively axiomatized. However, first-order consequences of independence logic sentences can be axiomatized. In this article we give an explicit axiomatization and prove that it is complete in this sense. The proof is a generalization of the similar result for dependence logic.