Canonical Horn Representations and Query Learning

Abstract. We describe an alternative construction of an existing canonical representation for definite Horn theories, the Guigues-Duquenne basis (or GD basis), which minimizes a natural notion of implicational size. We extend the canonical representation to general Horn, by providing a reduction from definite to general Horn CNF. We show how this representation relates to two topics in query learning theory: first, we show that a well-known algorithm by Angluin, Frazier and Pitt that learns Horn CNF always outputs the GD basis independently of the counterexamples it receives; second, we build strong polynomial certificates for Horn CNF directly from the GD basis.

• Type: Conference
• Year: 2009
• Where: ALT
• Authors: Marta Arias, José L. Balcázar
• Keywords: ALT 2009, GD Basis, General Horn, Horn Theories, Machine Learning