Correctness Proof and Complexity Analysis of the Hybrid Reasoning Algorithm of Beta-PSML

We have studied the theoretical problems of logic of ß-PSML (problem solver markup language) constructed by combining description logic and Horn clauses. In the nonrecursive case, we show that a single step of applying a Horn clause needs to be replaced by a more sophisticated reasoning step in ß-PSML. We call it as the hybrid reasoning algorithm. We described the hybrid reasoning algorithm in former paper. In this paper, we will prove the correctness of the hybrid reasoning algorithm. Hybrid reasoning algorithm provides a sound and complete inference procedure for nonrecursive ß-PSML knowledge bases in which the description logic component is decidable.