Boolean Matrix Logic Programming on the GPU

TL;DR

This paper introduces Boolean Matrix Logic Programming (BMLP), a GPU-accelerated approach for efficient large-scale logic inference using Boolean matrix algebra, significantly outperforming existing systems.

Contribution

It presents novel GPU algorithms for BMLP, extending the framework to support general linear recursion, and demonstrates substantial performance improvements.

Findings

Achieves 1-4 orders of magnitude speedup on large graph queries

Extends BMLP to support general linear recursion

Demonstrates scalability and efficiency on real datasets

Abstract

Traditional logic programming relies on symbolic computation on the CPU, which can limit performance for large-scale inference tasks. Recent advances in GPU hardware enable high-throughput matrix operations, motivating a shift toward parallel logic inference. Boolean Matrix Logic Programming (BMLP) introduces a novel approach to datalog query evaluation using Boolean matrix algebra, well-suited to GPU acceleration. Building on this paradigm, we present two GPU-accelerated BMLP algorithms for bottom-up inference over linear dyadic recursive datalog programs. We further extend the BMLP theoretical framework to support general linear recursion with binary predicates. Empirical evaluations on reachability queries in large directed graphs and the Freebase 15K dataset show that our methods achieve 1-4 orders of magnitude speed up over state-of-the-art systems. These results demonstrate that Boolean matrix-based reasoning can significantly advance the scalability and efficiency of logic programming on modern hardware. Source code is available on https://github.com/lun-ai/BMLP.git.