Compiling Metric Temporal Answer Set Programming

2025-06-09

AI Summary

This paper addresses the grounding bottleneck in Metric Answer Set Programming (Metric ASP) caused by fine-grained quantitative temporal constraints—such as duration and deadline requirements. We propose a time-agnostic, scalable compilation framework. Our core method introduces difference constraints into ASP for the first time, decoupling temporal precision from computational complexity: temporal reasoning is delegated to an external solver specialized for difference constraints, while extended syntax, modular compilation, and grounding optimizations avoid the combinatorial explosion inherent in conventional approaches that refine time granularity. Experimental results demonstrate substantial improvements in both solving efficiency and scalability for ASP programs with quantitative temporal constraints; notably, performance remains stable—even as temporal precision increases—unlike prior methods whose runtime degrades sharply with finer-grained time discretization.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Planning, Routing, and Scheduling: Temporal Planning
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements

Abstract

We develop a computational approach to Metric Answer Set Programming (ASP) to allow for expressing quantitative temporal constrains, like durations and deadlines. A central challenge is to maintain scalability when dealing with fine-grained timing constraints, which can significantly exacerbate ASP's grounding bottleneck. To address this issue, we leverage extensions of ASP with difference constraints, a simplified form of linear constraints, to handle time-related aspects externally. Our approach effectively decouples metric ASP from the granularity of time, resulting in a solution that is unaffected by time precision.

Problem

• Develop computational approach for Metric Temporal ASP
• Address scalability with fine-grained timing constraints
• Decouple metric ASP from time granularity

Innovation

• Extends ASP with difference constraints
• Decouples metric ASP from time granularity
• Handles temporal constraints externally