Non-monotone Dualization via Monotone Dualization

The non-monotone dualization (NMD) is one of the most essential tasks required for finding hypotheses in various ILP settings, like learning from entailment [1, 2] and learning from interpretations [3]. Its task is to generate an irredundant prime CNF formula ψ of the dual f where f is a general Boolean function represented by CNF [4]. The DNF formula φ of f is easily obtained by De Morgan’s laws interchanging the connectives of the CNF formula. Hence, the main task of NMD is to translate the DNF φ to an equivalent CNF ψ. This translation is used to find an alternative representation of the input form. For instance, given a set of models, it is desirable to seek underlying structure behind the models.