Towards Constraint Temporal Answer Set Programming

TL;DR

This paper introduces a novel extension of Answer Set Programming that combines temporal reasoning with numeric constraints, enabling more effective modeling of complex dynamic systems with high resolution.

Contribution

It presents the first nonmonotonic temporal reasoning framework with constraints tailored for ASP, combining linear-time logic and constraint logic of Here-and-There.

Findings

Develops a new logical framework for dynamic systems with temporal and numeric constraints.

Integrates temporal and constraint-based reasoning within ASP.

Establishes foundational principles for high-resolution dynamic system modeling.

Abstract

Reasoning about dynamic systems with a fine-grained temporal and numeric resolution presents significant challenges for logic-based approaches like Answer Set Programming (ASP). To address this, we introduce and elaborate upon a novel temporal and constraint-based extension of the logic of Here-and-There and its nonmonotonic equilibrium extension, representing, to the best of our knowledge, the first approach to nonmonotonic temporal reasoning with constraints specifically tailored for ASP. This expressive system is achieved by a synergistic combination of two foundational ASP extensions: the linear-time logic of Here-and-There, providing robust nonmonotonic temporal reasoning capabilities, and the logic of Here-and-There with constraints, enabling the direct integration and manipulation of numeric constraints, among others. This work establishes the foundational logical framework for tackling complex dynamic systems with high resolution within the ASP paradigm.