Safe Dependency Atoms and Possibility Operators in Team Semantics

TL;DR

This paper investigates which dependency atoms and operators in team semantics do not increase the expressive power of first-order logic, identifying safe dependencies and showing the possibility operator is safe to add.

Contribution

It characterizes safe dependency atoms and operators in team semantics, expanding understanding of their impact on the expressive power of FO(D).

Findings

Totality, non-constancy, non-emptiness are safe dependencies.

Constancy dependency is not safe for some FO(D) logics.

The possibility operator does not increase expressive power when added.

Abstract

I consider the question of which dependencies are safe for a Team Semantics-based logic FO(D), in the sense that they do not increase its expressive power over sentences when added to it. I show that some dependencies, like totality, non-constancy and non-emptiness, are safe for all logics FO(D), and that other dependencies, like constancy, are not safe for FO(D) for some choices of D despite being strongly first order. I furthermore show that the possibility operator, which holds in a team if and only if its argument holds in some nonempty subteam, can be added to any logic FO(D) without increasing its expressive power over sentences.