: An arithmetic approach, such as the Level-Finding method described in this paper for evaluating linear recursive queries in deductive database systems provides great potential for parallel processing. It has advantages over other approaches using state-of-the-art parallel processing technology to improve processing speed. In the arithmetic approach, we identify two kind of parallelism, namely bridge node parallelism and formula parallelism. In this paper, the arithmetic foundations and algorithm to exploit formula parallelism were given. The algorithm is fully parallel.