Exact Learning: On the Boundary between Horn and CNF

Abstract

A major problem in computational learning theory is whether the class of formulas in conjunctive normal form (CNF) is efficiently learnable. Although it is known that this class cannot be polynomially learned using either membership or equivalence queries alone, it is open whether the CNF class can be polynomially learned using both types of queries. One of the most important results concerning a restriction of the CNF class is that propositional Horn formulas are polynomial time learnable in Angluin’s exact learning model with membership and equivalence queries. In this work, we push this boundary and show that the class of multivalued dependency formulas (MVDF), which non-trivially extends propositional Horn, is polynomially learnable from interpretations. We then provide a notion of reduction between learning problems in Angluin’s model, showing that a transformation of the algorithm suffices to efficiently learn multivalued database dependencies from data relations. We also show via reductions that our main result extends well known previous results and allows us to find alternative solutions for them.