Abstract
We study the learnability of first order Horn expressions from equivalence and membership queries. We show that the class of range restricted Horn expressions, where every term in the consequent of every clause appears also in the antecedent of the clause, is learnable. The result holds both for the model where interpretations are examples (learning from interpretations) and the model where clauses are examples (learning from entailment).
The paper utilises a previous result on learning function free Horn expressions. This is done by using techniques for flattening and unflattening of examples and clauses, and a procedure for model finding for range restricted expressions. This procedure can also be used to solve the implication problem for this class.
This work was partly supported by EPSRC Grant GR/M21409.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
D. Angluin, M. Frazier, and L. Pitt. Learning conjunctions of Horn clauses. Machine Learning, 9:147–164, 1992.
D. Angluin and M. Kharitonov. When won’t membership queries help? Journal of Computer and System Sciences, 50:336–355, 1995.
D. Angluin. Queries and concept learning. Machine Learning, 2(4):319–342, 1988.
H. Arimura. Learning acyclic first-order Horn sentences from entailment. In Proceedings of the International Conference on Algorithmic Learning Theory. Springer-verlag, 1997. LNAI 1316.
C. Chang and J. Keisler. Model Theory. Elsevier, Amsterdam, Holland, 1990.
W. Cohen. PAC-learning recursive logic programs: Efficient algorithms. Journal of Artificial Intelligence Research, 2:501–539, 1995.
W. Cohen. PAC-learning recursive logic programs: Negative result. Journal of Artificial Intelligence Research, 2:541–573, 1995.
L. De Raedt. Logical settings for concept learning. Artificial Intelligence, 95(1):187–201, 1997. See also relevant Errata.
L. De Raedt and M. Bruynooghe. An overview of the interactive concept learner and theory revisor CLINT. In S. Muggleton, editor, Inductive Logic Programming. Academic Press, 1992.
L. De Raedt and S. Dzeroski. First order jk-clausal theories are PAC-learnable. Artificial Intelligence, 70:375–392, 1994.
M. Frazier and L. Pitt. Learning from entailment: An application to propositional Horn sentences. In Proceedings of the International Conference on Machine Learning, pages 120–127, Amherst, MA, 1993. Morgan Kaufmann.
D. Haussler. Learning conjunctive concepts in structural domains. Machine Learning, 4(1):7–40, 1989.
R. Khardon. Learning to take actions. In Proceedings of the National Conference on Artificial Intelligence, pages 787–792, Portland, Oregon, 1996. AAAI Press.
R. Khardon. Learning function free Horn expressions. Technical Report ECS-LFCS-98-394, Laboratory for Foundations of Computer Science, Edinburgh University, 1998. A preliminary version of this paper appeared in COLT 1998.
N. Littlestone. Learning quickly when irrelevant attributes abound: A new linear-threshold algorithm. Machine Learning, 2:285–318, 1988.
J.W. Lloyd. Foundations of Logic Programming. Springer Verlag, 1987. Second Edition.
S. Muggleton and W. Buntine. Machine invention of first order predicates by inverting resolution. In S. Muggleton, editor, Inductive Logic Programming. Academic Press, 1992.
S. Muggleton and L. De Raedt. Inductive logic programming: Theory andmethods. Journal of Logic Programming, 20:629–679, 1994.
S. Muggleton and C. Feng. Efficient induction of logic programs. In S. Muggleton, editor, Inductive Logic Programming. Academic Press, 1992.
J. Minker, editor. Foundations of Deductive Databases and Logic Programming. Morgan Kaufmann, 1988.
S. Nienhuys-Cheng and R. De Wolf. Foundations of Inductive Logic Programming. Springer-verlag, 1997. LNAI 1228.
G.D. Plotkin. A note on inductive generalization. In B. Meltzer and D. Michie, editors, Machine Intelligence 5, pages 153–163. American Elsevier, 1970.
C.H. Papadimitriou and M. Yannakakis. On the complexity of database queries. In Proceedings of the symposium on Principles of Database Systems, pages 12–19, Tucson, Arizona, 1997. ACM Press.
C. Rouveirol. Extensions of inversion of resolution applied to theory completion. In S. Muggleton, editor, Inductive Logic Programming. Academic Press, 1992.
K. Rao and A. Sattar. Learning from entailment of logic programs with local variables. In Proceedings of the International Conference on Algorithmic Learning Theory. Springer-verlag, 1998. LNAI 1501.
C. Reddy and P. Tadepalli. Learning Horn de_nitions with equivalence and membership queries. In International Workshop on Inductive Logic Programming, pages 243–255, Prague, Czech Republic, 1997. Springer. LNAI 1297.
C. Reddy and P. Tadepalli. Learning first order acyclic Horn programs from entailment. In International Conference on Inductive Logic Programming, pages 23–37, Madison, WI, 1998. Springer. LNAI 1446.
C. Reddy, P. Tadepalli, and S. Roncagliolo. Theory guided empirical speedup learning of goal decomposition rules. In International Conference on Machine Learning, pages 409–416, Bari, Italy, 1996. Morgan Kaufmann.
Y. Sagiv. Optimizing datalog programs. In J. Minker, editor, Foundations of Deductive Databases and Logic Programming. Morgan Kaufmann, 1988.
C. Sammut and R. Banerji. Learning concepts by asking questions. In R. Michalski, J. Carbonell, and T. Mitchell, editors, Machine Learning: An AI Approach, Volume II. Morgan Kaufman, 1986.
E.Y. Shapiro. Algorithmic Program Debugging. MIT Press, Cambridge, MA, 1983.
E. Shapiro. Inductive inference of theories from facts. In J. Lassez and G. Plotkin, editors, Computational Logic, pages 199–254. MIT Press, 1991.
L.G. Valiant. A theory of the learnable. Communications of the ACM, 27(11):1134–1142, 1984.
L.G. Valiant. Learning disjunctions of conjunctions. In Proceedings of the International Joint Conference of Artificial Intelligence, pages 560–566, Los Angeles, CA, 1985. Morgan Kaufmann.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Khardon, R. (1999). Learning Range Restricted Horn Expressions. In: Fischer, P., Simon, H.U. (eds) Computational Learning Theory. EuroCOLT 1999. Lecture Notes in Computer Science(), vol 1572. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-49097-3_10
Download citation
DOI: https://doi.org/10.1007/3-540-49097-3_10
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-65701-9
Online ISBN: 978-3-540-49097-5
eBook Packages: Springer Book Archive