Reducing Arbitrary Metric Temporal Formulas into Logic Programs under Answer Set Semantics

2026-05-28

AI Summary

This work addresses the challenge of modeling and verifying critical real-time properties—such as deadlines and durations—in embedded and cyber-physical systems by proposing an efficient reasoning approach based on Answer Set Programming (ASP). Leveraging a Tseitin-like transformation, the method reduces arbitrary metric temporal logic formulas to a restricted ASP fragment containing only past-time temporal operators. This reduction constitutes the first general-purpose, fully automated translation from full Metric Equilibrium Logic (MEL) into a form amenable to existing ASP solvers. The approach significantly enhances compatibility with state-of-the-art ASP solving technology and enables efficient multi-shot reasoning, thereby establishing a scalable foundation for verifying real-time system properties.

Abstract

Metric temporal equilibrium logic (\MEL) extends temporal equilibrium logic (\TEL) by incorporating quantitative timing constraints, enabling the specification and analysis of deadlines and durations. \MEL\ is particularly suited for domains where time-bound properties are crucial, such as embedded systems, cyber-physical systems, and real-time software. It facilitates the precise expression of timing behaviors, such as the requirement that an event must occur within 5 milliseconds of a trigger, which often elude traditional qualitative temporal logics. In this paper, we present a Tseitin-like translation that maps any metric temporal formula into a logic programming fragment restricted to past operators. This translation provides a formal bridge to leverage existing Answer Set Programming (ASP) solvers for reasoning about metric temporal constraints. By restricting the target fragment to past operators, we enable more effective evaluation and integration with current ASP-based toolchains for multi-shot solving.

Problem

• Metric Temporal Logic
• Answer Set Programming
• Temporal Reasoning
• Logic Programs
• Time Constraints

Innovation

• Metric Temporal Logic
• Answer Set Programming
• Tseitin Translation
• Past Operators
• Temporal Equilibrium Logic