# Facets of Distribution Identities in Probabilistic Team Semantics

## TL;DR

This paper explores the expressive power of probabilistic team semantics, focusing on logical and probabilistic dependencies, and addresses the complexity of the implication problem of conditional independence.

## Contribution

It classifies the expressive power of various probabilistic atoms and relates the framework to the first-order theory of the reals, advancing understanding of probabilistic dependencies.

## Key findings

- Classifies expressive power of probabilistic atoms
- Relates probabilistic team semantics to the first-order theory of reals
- Addresses complexity of the implication problem of conditional independence

## Abstract

We study probabilistic team semantics which is a semantical framework allowing the study of logical and probabilistic dependencies simultaneously. We examine and classify the expressive power of logical formalisms arising by different probabilistic atoms such as conditional independence and different variants of marginal distribution equivalences. We also relate the framework to the first-order theory of the reals and apply our methods to the open question on the complexity of the implication problem of conditional independence.