Possible and impossible conditionals for team logics

TL;DR

This paper investigates the existence of well-behaved conditionals in team logics with team semantics, showing they exist for some closure properties but not others, and explores weaker conditions.

Contribution

It characterizes when conditionals satisfying key logical properties can be added to team logics based on their closure properties.

Findings

Well-behaved conditionals exist for downward or upward closed logics.

Such conditionals generally do not exist for union closed, convex, or intersection closed logics.

The paper also explores conditionals with weaker logical requirements.

Abstract

We study whether a logic based on team semantics can be enriched with a conditional satisfying minimal requirements--namely, preservation of the closure property of the logic, Modus Ponens, and the Deduction Theorem. We show that such well-behaved conditionals exist for downward or upward closed logics, but do not typically exist for union closed, convex or intersection closed logics. We also briefly investigate conditionals satisfying weaker requirements.