# Metric Temporal Equilibrium Logic over Timed Traces

arXiv: https://arxiv.org/abs/2304.14778 · HTML: https://mlsanity.com/paper/2304.14778/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 37 references that are in the map.
- First posted on arXiv 28 Apr 2023.

## Builds on (most cited first, 2 of 2)

- [Temporal Answer Set Programming on Finite Traces](https://mlsanity.com/paper/1804.10227/) (2018)
- [Towards Metric Temporal Answer Set Programming](https://mlsanity.com/paper/2008.02038/) (2020)

## Built on by (most cited first, 4 of 4)

- [Metric Dynamic Equilibrium Logic](https://mlsanity.com/paper/2401.10781/) (2024)
- [Compiling Metric Temporal Answer Set Programming](https://mlsanity.com/paper/2506.08150/) (2025)
- [Meta-Programming for Linear-time Temporal Answer Set Programming](https://mlsanity.com/paper/2605.29965/) (2026)
- [Explainability Framework for Policy-Aware Autonomous Agents](https://mlsanity.com/paper/2607.21209/) (2026)

## Abstract (arXiv)

In temporal extensions of Answer Set Programming (ASP) based on linear-time, the behavior of dynamic systems is captured by sequences of states. While this representation reflects their relative order, it abstracts away the specific times associated with each state. However, timing constraints are important in many applications like, for instance, when planning and scheduling go hand in hand. We address this by developing a metric extension of linear-time temporal equilibrium logic, in which temporal operators are constrained by intervals over natural numbers. The resulting Metric Equilibrium Logic provides the foundation of an ASP-based approach for specifying qualitative and quantitative dynamic constraints. To this end, we define a translation of metric formulas into monadic first-order formulas and give a correspondence between their models in Metric Equilibrium Logic and Monadic Quantified Equilibrium Logic, respectively. Interestingly, our translation provides a blue print for implementation in terms of ASP modulo difference constraints.