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.