On the Advantage of a Non-Clausal Davis-Putnam Procedure

We propose a non-clausal decision procedure for classical propositional logic. It is a generalization of the Davis-Putnam procedure and deals with formulae which are not necessarily in clausal form. Since there is no need to translate the investigated formula into normal form, we avoid increasing its size but preserve its structure. This will in general lead to a much smaller search space and thus to a more efficient method. We introduce a short Prolog implementation of our procedure showing that it is possible to implement a non-clausal decision procedure in a compact and adaptable way. To demonstrate the good performance of the non-clausal approach some experimental results are provided. To this end we compare the non-clausal implementation with a clausalbased Davis-Putnam prover using the standard translation into clausal form as well as the definitional translation.