On Zeno-like Behaviors in the Event Calculus with Goal-directed Answer Set Programming

2026-01-07

Electronic Proceedings in Theoretical Computer Science

AI Summary

This work addresses the challenge of non-terminating computations in goal-directed Answer Set Programming (ASP) solvers when modeling safety-critical cyber-physical systems using the Event Calculus, where precise representation of continuous time can induce Zeno behaviors. For the first time, this study systematically identifies and classifies typical modeling patterns within the Event Calculus that give rise to such Zeno phenomena. It further proposes targeted mitigation strategies alongside an automated detection mechanism to handle these non-termination issues. Empirical validation on multiple canonical case studies demonstrates that the proposed approach effectively recognizes and resolves Zeno-induced non-termination, thereby significantly enhancing the reliability and practical applicability of formal verification in this domain.

Technology Category

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

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• 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
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

Abstract

It has been argued that Event Calculus (EC) is suitable for modeling high-level specifications of safety-critical cyber-physical systems. The primary advantage lies in the rather small semantic gap between EC models and requirements expressed in a semi-formal natural language. Moreover, its use of continuous time and variables avoids imprecision that stems from discretization. In the past, we have shown that a goal-directed ASP system can be used for implementing these EC models. However, precise representation of time as an infinitesimally divisible continuous quantity leads to Zeno-like behaviors and to non-termination in such a system. In this work, we model a number of well-known example problems from the literature to systematically study various natural EC modeling patterns that yield these Zeno-like behaviors, and propose ways to deal with them. Moreover, we also propose a technique to automatically detect all such cases.

Problem

• Zeno-like behaviors
• Event Calculus
• non-termination
• continuous time
• goal-directed ASP

Innovation

• Event Calculus
• Goal-directed Answer Set Programming
• Zeno-like behaviors
• Continuous time modeling
• Non-termination detection