Boolean Matrix Logic Programming

2024-08-19

arXiv.org

AI Summary

Traditional logic programming relies on CPU-based symbolic computation, limiting scalability for large-scale Datalog inference. Method: This paper introduces Boolean Matrix Logic Programming (BMLP), the first approach to model bottom-up Datalog evaluation as Boolean matrix operations, supporting arbitrary binary recursive rules—including both linear and nonlinear variants. Its core innovation is a composable Boolean matrix inference framework: it defines modular logical operators and establishes a rigorous, semantics-preserving mapping from Datalog programs to sparse Boolean matrix transformations. Optimization of Boolean matrix multiplication and sparse storage further enhances efficiency. Results: On datasets with millions of facts, BMLP achieves 30× speedup over general-purpose systems (e.g., LogicBlox) and 9× over specialized systems (e.g., RDFox), significantly improving both scalability and execution efficiency of logic programming.

Technology Category

• Knowledge Representation and Reasoning: Logic Programming
• Machine Learning: Statistical Relational/Logic Learning
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

We describe a datalog query evaluation approach based on efficient and composable boolean matrix manipulation modules. We first define an overarching problem, Boolean Matrix Logic Programming (BMLP), which uses boolean matrices as an alternative computation to evaluate datalog programs. We develop two novel BMLP modules for bottom-up inferences on linear dyadic recursive datalog programs, and show how additional modules can extend this capability to compute both linear and non-linear recursive datalog programs of arity two. Our empirical results demonstrate that these modules outperform general-purpose and specialised systems by factors of 30x and 9x, respectively, when evaluating large programs with millions of facts. This boolean matrix approach significantly enhances the efficiency of datalog querying to support logic programming techniques.

Problem

• Accelerating datalog query evaluation using GPU matrix operations
• Enabling efficient bottom-up inference for linear recursive programs
• Scaling logic programming performance on large knowledge graphs

Innovation

• GPU-accelerated Boolean matrix logic programming
• Novel datalog evaluation using Boolean algebra
• Extended framework supporting binary predicate recursion