On elementary logics for quantitative dependencies

TL;DR

This paper introduces new probabilistic logics within team semantics and metafinite structures, providing axiomatizable, tractable systems with polynomial data complexity, advancing the theoretical understanding of quantitative dependencies.

Contribution

It develops novel probabilistic logics in team semantics and metafinite structures, with translations into fixed point logic ensuring computational efficiency.

Findings

Logics are axiomatizable and tractable.

All logics can be translated into fixed point logic.

Data complexity is polynomial in BSS model.

Abstract

We define and study logics in the framework of probabilistic team semantics and over metafinite structures. Our work is paralleled by the recent development of novel axiomatizable and tractable logics in team semantics that are closed under the Boolean negation. Our logics employ new probabilistic atoms that resemble so-called extended atoms from the team semantics literature. We also define counterparts of our logics over metafinite structures and show that all of our logics can be translated into functional fixed point logic implying a polynomial time upper bound for data complexity with respect to BSS-computations.