Applications of Intuitionistic Temporal Logic to Temporal Answer Set Programming

2026-03-15

AI Summary

This work establishes a rigorous logical foundation for temporal answer set programming by extending Pearce’s equilibrium logic and Osorio’s notion of safe beliefs to the temporal setting. Integrating linear-time temporal operators, it introduces temporal equilibrium logic and presents the first formal correspondence between intuitionistic temporal logic and temporal logic programming. The study not only enhances the expressiveness of equilibrium logic and safe beliefs in temporal contexts but also incorporates intermediate logics and temporal fixed-point operators, thereby offering a novel theoretical framework for temporal non-monotonic reasoning and opening a new avenue for the formalization of temporal answer set programming.

Technology Category

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

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

The relationship between intuitionistic or intermediate logics and logic programming has been extensively studied, prominently featuring Pearce's equilibrium logic and Osorio's safe beliefs. Equilibrium logic admits a fixpoint characterization based on the logic of here-and-there, akin to theory completion in default and autoepistemic logics. Safe beliefs are similarly defined via a fixpoint operator, albeit under the semantics of intuitionistic or other intermediate logics. In this paper, we investigate the logical foundations of Temporal Answer Set Programming through the lens of Temporal Equilibrium Logic, a formalism combining equilibrium logic with linear-time temporal operators. We lift the seminal approaches of Pearce and Osorio to the temporal setting, establishing a formal correspondence between temporal intuitionistic logic and temporal logic programming. Our results deepen the theoretical underpinnings of Temporal Answer Set Programming and provide new avenues for research in temporal reasoning.

Problem

• Temporal Answer Set Programming
• Intuitionistic Temporal Logic
• Temporal Equilibrium Logic
• Logic Programming
• Temporal Reasoning

Innovation

• Temporal Equilibrium Logic
• Intuitionistic Temporal Logic
• Temporal Answer Set Programming
• Fixpoint Characterization
• Here-and-There Logic