Augmenting Negation Normal Form With Irrelevant Variables

Dangdang Niu,Shuai Lu,Lei Liu

doi:10.1109/access.2019.2927041

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 NNF PNI , NNF PI , and NNF NI are proposed based on different combinations of positive literals, negative literals, and irrelevant variables. Each sentence in NNF, NNF PI , NNF NI , or NNF PNI can be translated to an equivalent sentence in another language in polynomial time. We also define d-DNNF NI , d-DNNF PI , and d-DNNF PNI based on decomposability and determinism in NNF, which are subclasses of NNF PI , NNF NI , and NNF PNI , respectively. A number of querying and transforming methods for d-DNNF PNI , d-DNNF PI , and d-DNNF PI are designed to solve relevant reasoning problems in knowledge compilation map. Overall, d-DNNF PI and d-DNNF NI do not reduce the tractability of d-DNNF, so we propose a compressing method for d-DNNF based on d-DNNF PI and d-DNNF NI . The experimentally, the compiling results of the d-DNNF PI and d-DNNF NI are better with respect to d-DNNF for most instances, and our compressing method is significantly effective for all instances.

Highlights

Knowledge compilation has been emerging as a popular direction of research for improving the efficiency of computational tasks
Irrelevant variables are usually omitted in knowledge compilation languages, since they can be computed based on known positive literals and negative literals
We proposed three new knowledge compilation languages: NNFPNI, NNFPI and NNFNI, which are defined based on irrelevant variables in this paper

Summary

INTRODUCTION

Knowledge compilation has been emerging as a popular direction of research for improving the efficiency of computational tasks. This paper is primarily concerned with reducing the scale of compiling result of target compilation language, which can further improve the efficiency of on-line reasoning. D. Niu et al.: Augmenting Negation Normal Form With Irrelevant Variables compilation languages, since thy can be computed based on known positive literals and negative literals. We intend to augment NNF with irrelevant variables and to identify new knowledge compilation languages in this paper. In this way, we can further reduce the scale of compiling result of d-DNNF by replacing their positive literals or negative literals with irrelevant variables. In an NNFPNI sentence, each leaf node of each sentence is labeled by true, false, some positive literal, some negative literal, or some irrelevant variable. Experimental results show that our compressing method can sharply reduce the scale of sentences in d-DNNF for a number of benchmarks

BASIC DEFINITIONS

EXPERIMENTS

CONCLUSION