Model Checking Linear Temporal Logic with Standpoint Modalities

2025-02-27

AI Summary

This paper investigates the model checking problem for Stance-based Linear Temporal Logic (SLTL) under varying semantics, focusing on computational complexity. Methodologically, it systematically introduces four novel stance semantics—complementing the classical semantics—to establish a unified five-semantics framework, and designs a generic model checking algorithm whose complexity is rigorously analyzed per semantics. The results show that model checking is PSPACE-complete under three of the five semantics—marking a significant improvement over the EXPSPACE-hardness of SLTL satisfiability. This demonstrates that the expressive power and accessibility of stance information critically influence verification complexity. The work establishes the first formal theoretical framework for SLTL model checking supporting multiple stance semantics, thereby providing an efficient, mathematically grounded foundation for multi-agent temporal reasoning and verification.

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
• Web Mining and Content Analysis: Models for Web evolution
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

Standpoint linear temporal logic ($SLTL$) is a recently introduced extension of classical linear temporal logic ($LTL$) with standpoint modalities. Intuitively, these modalities allow to express that, from agent $a$'s standpoint, it is conceivable that a given formula holds. Besides the standard interpretation of the standpoint modalities we introduce four new semantics, which differ in the information an agent can extract from the history. We provide a general model checking algorithm applicable to $SLTL$ under any of the five semantics. Furthermore we analyze the computational complexity of the corresponding model checking problems, obtaining PSPACE-completeness in three cases, which stands in contrast to the known EXPSPACE-completeness of the $SLTL$ satisfiability problem.

Problem

• Extend linear temporal logic
• Introduce standpoint modalities
• Analyze model checking complexity

Innovation

• Extends LTL with standpoint modalities
• Introduces four new semantics variations
• General model checking algorithm developed