Labelled Sequent Calculi for Propositional Team Logics

2026-06-30

AI Summary

This study addresses the lack of systematic and computationally effective proof systems for team-semantic propositional logics by introducing, for the first time, labeled sequent calculi for four representative logics—including basic inquisitive logic with tensor disjunction and its intuitionistic dependence variant. By simplifying the labeling structure and devising efficient proof-search strategies, the proposed calculi achieve terminating derivations within languages featuring finitely many propositional atoms. The calculi are proven to be sound and complete, and they admit the structural rules of weakening, contraction, and cut. These results establish both a theoretical foundation and a practical framework for automated reasoning in team-based logics.

Abstract

Team semantics is a general framework where formulas are not interpreted with respect to a single point of evaluation, but with respect to sets of such points. Team semantics is used in dependence logic, to reason about dependencies between variables, and in inquisitive logic, to formalize the meaning of questions. We provide sound and complete labelled sequent calculi for four logics based on team semantics: basic inquisitive logic, propositional intuitionistic dependence logic, and their respective extensions with tensor disjunction. For technical reasons, we restrict ourselves to languages with finitely many propositional atoms. The rules of weakening, contraction and cut are shown to be admissible in each of our calculi. In the last part of the paper, we present terminating proof search procedures for variants of our proof systems, in which labels have a simplified structure.

Problem

• team semantics
• labelled sequent calculi
• propositional logic
• inquisitive logic
• dependence logic

Innovation

• labelled sequent calculus
• team semantics
• inquisitive logic
• dependence logic
• proof search