Learning Orthogonal F-Horn Formulas

Abstract

In the PAC-learning, or the query learning model, it has been an important open problem to decide whether the class of DNF and CNF formulas is learnable. Recently, it was pointed out that the problem of PAC-learning for these classes with membership queries can be reduced to that of query learning for the class of k -quasi Horn formulas with membership and equivalence queries. A k -quasi Horn formula is a CNF formula with each clause containing at most k unnegated literals. In this paper, notions of F -Horn formulas and l-F -Horn formulas, which are extensions of k -quasi formulas, are introduced, and it is shown that the problem of PAC-learning for DNF and CNF formulas with membership queries can be reduced to that of query learning for l-F -Horn formulas with membership and equivalence queries for an appropriate choice of F . It is shown that under some condition, the class of orthogonal F -Horn formulas is learnable with membership, equivalence and subset queries. Moreover, it is shown that under some condition the class of orthogonal l-F -Horn formulas is learnable with membership and equivalence queries.