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.
Work partially supported by MICINN projects SESAAME-BAR (TIN2008-06582-C03-01) and FORMALISM (TIN2007-66523).
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Arias, M., Balcázar, J.L. (2009). Canonical Horn Representations and Query Learning. In: Gavaldà, R., Lugosi, G., Zeugmann, T., Zilles, S. (eds) Algorithmic Learning Theory. ALT 2009. Lecture Notes in Computer Science(), vol 5809. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04414-4_16
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DOI: https://doi.org/10.1007/978-3-642-04414-4_16
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