Towards Constraint Temporal Answer Set Programming

2025-07-18

AI Summary

Answer Set Programming (ASP) lacks native support for nonmonotonic temporal reasoning and numerical constraint solving in fine-grained temporal and numeric dynamic systems. Method: This paper introduces the first framework integrating constraint logic into temporal ASP. It combines Linear Time Here-and-There logic with constraint logic to define Constraint Temporal ASP (CT-ASP), formalizing its nonmonotonic model semantics and solving principles. Contribution/Results: CT-ASP establishes the first formal foundation unifying expressive temporal logic with rigorous numerical constraint handling. It enables joint reasoning over discrete-time evolution and continuous/discrete numerical constraints—a novel paradigm for hybrid temporal-numerical inference. Moreover, it provides a compact, computationally tractable ASP-based modeling tool for high-resolution dynamic systems, including real-time control and cyber-physical systems. The framework preserves ASP’s declarative nature while extending its applicability to domains requiring tight integration of temporal dynamics and quantitative constraints.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Planning, Routing, and Scheduling: Temporal Planning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions

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.

Problem

• Extends ASP for fine-grained temporal and numeric reasoning
• Integrates nonmonotonic temporal logic with constraint handling
• Enables high-resolution modeling of dynamic systems in ASP

Innovation

• Extends Here-and-There logic with temporal constraints
• Integrates numeric constraints for dynamic systems
• First nonmonotonic temporal reasoning for ASP