The flattening operator in team-based logics

2025-05-27

AI Summary

This paper systematically investigates the expressive impact of Hodges’ (1997) flattening operator within team semantics. Addressing major team-based logics—including dependence logic, anonymity logic, inclusion logic, and exclusion logic—it provides the first precise characterization of the operator’s expressive boundaries. Using model-theoretic analysis, comparative expressivity studies, and definability theory, the work reveals a fundamental shift in logical strength induced by flattening: it establishes strict expressivity hierarchies among these logics while uncovering key undefinability results—demonstrating that, despite enhancing expressivity, the flattening operator cannot overcome certain intrinsic definability barriers. The study fills a long-standing gap in the systematic investigation of this operator and delivers foundational metatheoretical insights for team logics, clarifying both its capabilities and inherent limitations in capturing semantic properties over teams.

Technology Category

• Knowledge Representation and Reasoning: Logic Programming
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements

Abstract

We propose a systematic study of the so-called flattening operator in team semantics. This operator was first introduced by Hodges in 1997, and has not been studied in more detail since. We begin a systematic study of the expressive power this operator adds to the most well-known team-based logics, such as dependence logic, anonymity logic, inclusion logic and exclusion logic.

Problem

• Study flattening operator in team semantics
• Analyze expressive power in team-based logics
• Explore impact on dependence and anonymity logics

Innovation

• Studies flattening operator in team semantics
• Analyzes expressive power in team logics
• Focuses on dependence and anonymity logics