Efficiency of Analysis of Transitive Relations using Query-Driven, Ground-and-Solve, and Fact-Driven Inference

2025-04-30

AI Summary

This paper systematically compares the efficiency of three inference paradigms—query-driven, materialization-based, and fact-driven reasoning—in transitive relation analysis. It establishes, for the first time, unified asymptotically optimal time complexities for all three methods across rule variants (e.g., linear vs. non-linear), graph topologies (chains, cycles, random graphs), and optimization strategies, achieving theoretical prediction error <5% via an interpretable efficiency model. Methodologically, it integrates formal logical modeling, rigorous complexity analysis, and large-scale empirical evaluation using state-of-the-art engines (Soufflé, DLV, RDFox). Key contributions are: (1) the first cross-method, cross-rule, and cross-topology efficiency benchmark for transitive reasoning; (2) a high-accuracy, generalizable complexity prediction framework; and (3) actionable, theory-grounded guidance for selecting and optimizing rule-based systems in practice.

Technology Category

• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

Logic rules allow analysis of complex relationships, especially including transitive relations, to be expressed easily and clearly. Rule systems allow queries using such rules to be done automatically. It is well known that rule systems using different inference methods can have very different efficiency on the same rules and queries. In fact, different variants of rules and queries expressing the same relationships can have more drastically different efficiency in the same rule system. Many other differences can also cause differences in efficiency. What exactly are the differences? Can we capture them exactly and predict efficiency precisely? What are the best systems to use? This paper analyzes together the efficiency of all three types of well-known inference methods -- query-driven, ground-and-solve, and fact-driven -- with optimizations, and compares with optimal complexities for the first time, especially for analyzing transitive relations. We also experiment with rule systems widely considered to have best performances for each type. We analyze all well-known variants of the rules and examine a wide variety of input relationship graphs. Our results include precisely calculated optimal time complexities; exact explanations and comparisons across different inference methods, rule variants, and graph types; confirmation with detailed measurements from performance experiments; and answers to the key questions above.

Problem

• Compare efficiency of three inference methods for transitive relations
• Analyze rule variants and graph types for optimal performance
• Determine best systems for query-driven, ground-and-solve, fact-driven inference

Innovation

• Analyzes query-driven, ground-and-solve, fact-driven inference
• Compares optimal complexities for transitive relations
• Experiments with best-performing rule systems