Augmenting Negation Normal Form With Irrelevant Variables

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.