Approximation and Dependence via Multiteam Semantics

TL;DR

This paper introduces multiteam semantics, a new framework based on multisets, and explores probabilistic inclusion and independence atoms along with approximation operators, advancing the understanding of dependence logic.

Contribution

It develops multiteam semantics and defines probabilistic dependence and independence atoms, extending the logic framework with approximation operators.

Findings

Multiteam semantics effectively models probabilistic dependence.

Probabilistic inclusion and independence atoms are formally defined.

Approximation operators provide new tools for dependence logic analysis.

Abstract

We define a variant of team semantics called multiteam semantics based on multisets and study the properties of various logics in this framework. In particular, we define natural probabilistic versions of inclusion and independence atoms and certain approximation operators motivated by approximate dependence atoms of V\"a\"an\"anen.