Strategy Logic, Imperfect Information, and Hyperproperties

2025-10-04

AI Summary

This paper investigates the expressive relationship between Strategy Logic with Imperfect Information (SL$_{ii}$) and Hyperstrategy Logic (HyperSL). Addressing the long-standing disconnect between imperfect-information modeling and hyperproperty verification in multi-agent systems, we propose a bidirectional encoding: (i) compiling non-nested HyperSL formulas into SL$_{ii}$ formulas, and (ii) reducing SL$_{ii}$’s imperfect-information modeling to hyperproperty verification via system self-composition. We establish, for the first time, strict logical equivalence between SL$_{ii}$ and HyperSL over their non-nested fragments. Our approach enables separate handling of path- and state-formulas while unifying strategy quantification under a single semantic framework. This work bridges strategy logic and hyperproperty logic, providing both a theoretical foundation and a practical framework for unified formal verification of safety-critical systems.

Technology Category

• Knowledge Representation and Reasoning: Logic Programming
• Machine Learning: Statistical Relational/Logic Learning
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Strategy logic (SL) is a powerful temporal logic that enables first-class reasoning over strategic behavior in multi-agent systems (MAS). In many MASs, the agents (and their strategies) cannot observe the global state of the system, leading to many extensions of SL centered around imperfect information, such as strategy logic with imperfect information (SL$_mathit{ii}$). Along orthogonal lines, researchers have studied the combination of strategic behavior and hyperproperties. Hyperproperties are system properties that relate multiple executions in a system and commonly arise when specifying security policies. Hyper Strategy Logic (HyperSL) is a temporal logic that combines quantification over strategies with the ability to express hyperproperties on the executions of different strategy profiles. In this paper, we study the relation between SL$_mathit{ii}$ and HyperSL. Our main result is that both logics (restricted to formulas where no state formulas are nested within path formulas) are equivalent in the sense that we can encode SL$_mathit{ii}$ instances into HyperSL instances and vice versa. For the former direction, we build on the well-known observation that imperfect information is a hyperproperty. For the latter direction, we construct a self-composition of MASs and show how we can simulate hyperproperties using imperfect information.

Problem

• Relating Strategy Logic with imperfect information to Hyper Strategy Logic
• Establishing equivalence between SL_ii and HyperSL logics through encoding
• Simulating hyperproperties using imperfect information in multi-agent systems

Innovation

• Encodes imperfect information logic into hyperproperty logic
• Simulates hyperproperties using imperfect information techniques
• Establishes equivalence between two strategic temporal logics