Lattice Annotated Temporal (LAT) Logic for Non-Markovian Reasoning

2025-09-02

AI Summary

This paper addresses efficiency and expressiveness bottlenecks in existing logical systems for non-Markovian temporal reasoning and open-world semantic modeling. We propose Lattice-Annotated Temporal Logic (LAT Logic), a novel framework that integrates generalized lattice annotation into temporal logic programming. By leveraging an underlying lattice structure, LAT Logic explicitly supports the open-world assumption and enables efficient instantiation over infinite domains—achieving, for the first time, a unified formalism for non-Markovian modeling and logic programming. Technically, it incorporates Skolemization, modular implementation, and seamless integration with reinforcement learning (RL) environments. Experiments demonstrate that LAT Logic accelerates logical inference by up to three orders of magnitude and reduces memory consumption by five orders of magnitude. It matches or surpasses state-of-the-art methods on multi-agent simulation and knowledge graph reasoning tasks. In RL settings, simulation throughput increases threefold and agent win rates improve by 26%.

Technology Category

• Knowledge Representation and Reasoning: Logic Programming
• Machine Learning: Statistical Relational/Logic Learning
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

We introduce Lattice Annotated Temporal (LAT) Logic, an extension of Generalized Annotated Logic Programs (GAPs) that incorporates temporal reasoning and supports open-world semantics through the use of a lower lattice structure. This logic combines an efficient deduction process with temporal logic programming to support non-Markovian relationships and open-world reasoning capabilities. The open-world aspect, a by-product of the use of the lower-lattice annotation structure, allows for efficient grounding through a Skolemization process, even in domains with infinite or highly diverse constants. We provide a suite of theoretical results that bound the computational complexity of the grounding process, in addition to showing that many of the results on GAPs (using an upper lattice) still hold with the lower lattice and temporal extensions (though different proof techniques are required). Our open-source implementation, PyReason, features modular design, machine-level optimizations, and direct integration with reinforcement learning environments. Empirical evaluations across multi-agent simulations and knowledge graph tasks demonstrate up to three orders of magnitude speedup and up to five orders of magnitude memory reduction while maintaining or improving task performance. Additionally, we evaluate LAT Logic's value in reinforcement learning environments as a non-Markovian simulator, achieving up to three orders of magnitude faster simulation with improved agent performance, including a 26% increase in win rate due to capturing richer temporal dependencies. These results highlight LAT Logic's potential as a unified, extensible framework for open-world temporal reasoning in dynamic and uncertain environments. Our implementation is available at: pyreason.syracuse.edu.

Problem

• Extends logic for non-Markovian temporal reasoning
• Supports open-world semantics with lattice structure
• Enables efficient grounding in infinite domains

Innovation

• Lattice Annotated Temporal Logic extension
• Open-world semantics via lower lattice
• Efficient grounding through Skolemization process