Disjunctive closures for knowledge compilation

The knowledge compilation (KC) map [1] can be viewed as a multi-criteria evalu-ation of a number of target classes of representations for propositional KC. Usingthis map, the choice of a class for a given application can be made, consideringboth the space efficiency of it (i.e., its ability to represent information using lit-tle space), and its time efficiency, i.e., the queries and transformations which canbe achieved in polynomial time, among those of interest for the application un-der consideration. When no class of propositional representations offers all thetransformations one would expect, some of them can be left implicit. This is thekey idea underlying the concept of closure introduced here: instead of performingcomputationally expensive transformations, one just remembers that they have tobe done. In this paper, we investigate the disjunctive closure principles, i.e., dis-junction, existential quantification, and their combinations. We provide severalcharacterization results concerning the corresponding closures. We also extendthe KC map with new propositional languages obtained as disjunctive closures ofseveral incomplete propositional languages, including the well-known KROM (theCNF formulae containing only binary clauses), HORN (the CNF formulae contain-ing only Horn clauses), and AFF (the affine language, which is the set of conjunc-tions of XOR-clauses). Each introduced language is evaluated along the lines ofthe KC map.