Augmenting Negation Normal Form with Irrelevant Variables

Abstract

Irrelevant variables are always omitted in knowledge compilation languages since their assignments do not change the satisfiability of sentences. In order to identify new knowledge compilation languages and reduce the scale of compiling result of d-DNNF, we augment NNF with irrelevant variables in this paper. The NNFPNI, NNFPI, and NNFNI are proposed based on different combinations of positive literals, negative literals, and irrelevant variables. Each sentence in NNF, NNFPI, NNFNI, or NNFPNI can be translated to an equivalent sentence in another language in polynomial time. We also define d-DNNFNI, d-DNNFPI, and d-DNNFPNI based on decomposability and determinism in NNF, which are subclasses of NNFPI, NNFNI, and NNFPNI, respectively. A number of querying and transforming methods for d-DNNFPNI, d-DNNFPI, and d-DNNFNI are designed to solve relevant reasoning problems in knowledge compilation map. Overall, d-DNNFPI and d-DNNFNI do not reduce the tractability of d-DNNF, so we propose a compressing method for d-DNNF based on d-DNNFPI and d-DNNFNI. The experimentally, the compiling results of the d-DNNFPI and d-DNNFNI are better with respect to d-DNNF for most instances, and our compressing method is significantly effective for all instances.