The Logic of Approximate Dependence

TL;DR

This paper introduces approximate dependence in dependence logic, extending the concept to include limited exceptions, and proves a completeness theorem, while discussing the need for multi-teams to address certain issues.

Contribution

It presents the first formal treatment of approximate dependence atoms and establishes a completeness theorem for them, advancing the theoretical framework of dependence logic.

Findings

Proves a completeness theorem for approximate dependence atoms

Identifies problematic features suggesting multi-teams are needed

Extends dependence logic to include limited exceptions

Abstract

We extend the treatment of functional dependence, the basic concept of dependence logic, to include the possibility of dependence with a limited number of exceptions. We call this approximate dependence. The main result of the paper is a Completeness Theorem for approximate dependence atoms. We point out some problematic features of this which suggests that we should consider multi-teams, not just teams.