Metric dynamic equilibrium logic

• Published in: Journal of applied non-classical logics 2023-10, Vol.33 (3-4), p.495-519
• Main Authors: Becker, Arvid, Cabalar, Pedro, Diéguez, Martín, Farinas del Cerro, Luis, Schaub, Torsten, Schuhmann, Anna
• Format: Article
• Language: English
• Subjects: Answer set programming; Constraints; Declarative programming; Dynamical systems; equilibrium logic; linear dynamic logic; linear temporal logic; Logic; Mathematical programming; metric temporal logic; Sequences
• ISSN: 1166-3081; 1958-5780
• DOI: 10.1080/11663081.2023.2244365

In temporal extensions of Answer Set Programming (ASP) based on linear-time, the behaviour 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. In many applications, however, timing constraints are important like, for instance, when planning and scheduling go hand in hand. We address this by developing a metric extension of linear-time Dynamic Equilibrium Logic, in which dynamic operators are constrained by intervals over integers. The resulting Metric Dynamic Equilibrium Logic provides the foundation of an ASP-based approach for specifying qualitative and quantitative dynamic constraints. As such, it constitutes the most general among a whole spectrum of temporal extensions of Equilibrium Logic. In detail, we show that it encompasses Temporal, Dynamic, Metric and regular Equilibrium Logic, as well as its classic counterparts once the law of the excluded middle is added.