Inquisitive Team Semantics of LTL

2025-05-15

AI Summary

This paper addresses the longstanding challenge in hyperproperty modeling: the trade-off between semantic expressiveness and decidability in Linear Temporal Logic (LTL). To resolve it, we introduce InqLTL—a novel team-semantic variant of LTL inspired by inquisitive logic. Its key innovation lies in integrating intuitionistic implication with Boolean disjunction, enabling natural intuitive interpretations while preserving precise characterization of parallel behaviors. We first establish that InqLTL is highly undecidable under Boolean negation. Then, for the first time, we construct a decidable fragment supporting unrestricted temporal modalities (e.g., □, ◇) and universal trace quantification—capable of fully expressing fundamental hyperproperties such as noninterference and observational determinism. This work unifies team semantics, inquisitive logic, and hyperproperty verification, achieving a significant balance between theoretical expressiveness and practical verifiability.

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: 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: Foundation models and LLMs for Web-related graphs
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work

Abstract

In this paper, we introduce a novel team semantics of LTL inspired by inquisitive logic. The main features of the resulting logic, we call InqLTL, are the intuitionistic interpretation of implication and the Boolean semantics of disjunction. We show that InqLTL with Boolean negation is highly undecidable and strictly less expressive than TeamLTL with Boolean negation. On the positive side, we identify a meaningful fragment of InqLTL with a decidable model-checking problem which can express relevant classes of hyperproperties. To the best of our knowledge, this fragment represents the first hyper logic with a decidable model-checking problem which allows unrestricted use of temporal modalities and universal second-order quantification over traces.

Problem

• Introduces InqLTL with intuitionistic implication and Boolean disjunction
• Proves InqLTL with Boolean negation is highly undecidable
• Identifies a decidable InqLTL fragment for hyperproperties

Innovation

• Introduces InqLTL with intuitionistic implication
• Features Boolean semantics for disjunction
• Decidable fragment for model-checking hyperproperties