T-CPDL: A Temporal Causal Probabilistic Description Logic for Developing Logic-RAG Agent

2025-06-23

AI Summary

Large language models (LLMs) exhibit limited capability in structured reasoning tasks involving temporal constraints, causal inference, and probabilistic reasoning. To address this, we propose Temporal Causal Probabilistic Description Logic (T-CPDL)—the first description logic framework unifying Allen’s interval algebra, explicit timestamped causal modeling, and probabilistic annotations. T-CPDL enables qualitative temporal reasoning, interpretable causal assertions, and confidence calibration through formal semantic extensions that ensure fine-grained expressivity and transparent inference. It is deeply integrated into the Logic-RAG architecture. Empirical evaluation on multiple temporal–causal joint reasoning benchmarks demonstrates significant improvements: +12.3% accuracy, enhanced interpretability, and superior probability calibration. T-CPDL thus establishes the first logically grounded foundation for knowledge graph–enhanced RAG systems that jointly supports temporal, causal, and probabilistic dimensions.

Technology Category

• Knowledge Representation and Reasoning: Description Logics
• Reasoning under Uncertainty: Relational Probabilistic Models
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Search and Retrieval-Augmented AI: Retrieval-Augmented Generation (RAG) and multi-modal RAG
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

Large language models excel at generating fluent text but frequently struggle with structured reasoning involving temporal constraints, causal relationships, and probabilistic reasoning. To address these limitations, we propose Temporal Causal Probabilistic Description Logic (T-CPDL), an integrated framework that extends traditional Description Logic with temporal interval operators, explicit causal relationships, and probabilistic annotations. We present two distinct variants of T-CPDL: one capturing qualitative temporal relationships through Allen's interval algebra, and another variant enriched with explicit timestamped causal assertions. Both variants share a unified logical structure, enabling complex reasoning tasks ranging from simple temporal ordering to nuanced probabilistic causation. Empirical evaluations on temporal reasoning and causal inference benchmarks confirm that T-CPDL substantially improves inference accuracy, interpretability, and confidence calibration of language model outputs. By delivering transparent reasoning paths and fine-grained temporal and causal semantics, T-CPDL significantly enhances the capability of language models to support robust, explainable, and trustworthy decision-making. This work also lays the groundwork for developing advanced Logic-Retrieval-Augmented Generation (Logic-RAG) frameworks, potentially boosting the reasoning capabilities and efficiency of knowledge graph-enhanced RAG systems.

Problem

• Addresses LLMs' struggles with temporal constraints and causal reasoning
• Integrates temporal, causal, and probabilistic logic for complex reasoning
• Enhances interpretability and accuracy in language model decision-making

Innovation

• Extends Description Logic with temporal operators
• Integrates causal relationships and probabilistic annotations
• Enhances reasoning with qualitative and timestamped variants