Implementing Metric Temporal Answer Set Programming

Abstract

We develop a computational approach to Metric Answer Set Programming (ASP) to express quantitative temporal constrains, such as durations and deadlines. We investigate two specific fragments: plain metric logic programs, restricted to local temporal constraints, and general metric logic programs, which allow for arbitrary metric formulas. A central challenge in this context is maintaining scalability when dealing with fine-grained timing constraints, which can significantly exacerbate grounding bottleneck of ASP. To address this issue, we propose translations of both fragments into standard ASP and ASP extended with difference constraints, a simplified form of linear constraints, and prove their correctness and completeness. Our implementation, realized via meta-encodings, effectively decouples metric ASP from the granularity of time, resulting in a solution that is independent of time precision.