Complexity Results in Team Semantics: Nonemptiness Is Not So Complex

2025-10-09

AI Summary

This paper investigates the computational complexity of convex logic under team semantics—i.e., classical propositional logic extended with a non-emptiness atom (NE). It systematically analyzes the three fundamental decision problems: satisfiability, validity, and model checking. Using polynomial-time reductions and algorithmic constructions, the authors establish tight complexity bounds. They show that while NE enhances expressive power, it does not increase the complexity of satisfiability, which remains NP-complete; validity is coNP-complete; and model checking is solvable in polynomial time. These results precisely locate convex logic within the computational complexity landscape under team semantics, filling a foundational gap in the complexity theory of convex logics. Moreover, the work provides a critical benchmark for subsequent complexity analyses of modal and dependence logics.

Technology Category

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

Application Category

• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

Abstract

We initiate the study of the complexity-theoretic properties of convex logics in team semantics. We focus on the extension of classical propositional logic with the nonemptiness atom NE, a logic known to be both convex and union closed. We show that the satisfiability problem for this logic is NP-complete, that its validity problem is coNP-complete, and that its model-checking problem is in P.

Problem

• Analyzes complexity of convex logics in team semantics
• Studies satisfiability and validity of propositional logic with NE atom
• Determines computational complexity for model-checking in this logic

Innovation

• Complexity analysis of convex logics in team semantics
• Extension of propositional logic with nonemptiness atom NE
• Established NP-complete satisfiability and P model-checking