Metric Temporal Equilibrium Logic over Timed Traces

TL;DR

This paper introduces Metric Equilibrium Logic, extending temporal logic with quantitative timing constraints, enabling more precise modeling of dynamic systems in answer set programming.

Contribution

It develops a metric extension of linear-time temporal equilibrium logic with interval-constrained operators, bridging it with monadic first-order logic for implementation.

Findings

Provides a translation of metric formulas into monadic first-order formulas.

Establishes correspondence between models of Metric Equilibrium Logic and Monadic Quantified Equilibrium Logic.

Offers a blueprint for implementing the logic using ASP with difference constraints.

Abstract

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.