Probabilistic team semantics

TL;DR

This paper explores a variant of probabilistic team semantics, relating it to a two-sorted logic and demonstrating that simple formulas can lead to NP-hard model checking problems.

Contribution

It introduces a new variant of probabilistic team semantics and connects it to Tarskian two-sorted logic, highlighting computational complexity implications.

Findings

Probabilistic team semantics can be related to Tarskian two-sorted logic.

Simple quantifier-free formulas in this framework lead to NP-hard model checking.

The framework extends previous semantics to accommodate probabilistic dependencies.

Abstract

Team semantics is a semantical framework for the study of dependence and independence concepts ubiquitous in many areas such as databases and statistics. In recent works team semantics has been generalised to accommodate also multisets and probabilistic dependencies. In this article we study a variant of probabilistic team semantics and relate this framework to a Tarskian two-sorted logic. We also show that very simple quantifier-free formulae of our logic give rise to NP-hard model checking problems.