Abstract
Generalization is a fundamental operation of inductive inference. While first order syntactic generalization (anti-unification) is well understood, its various extensions are needed in applications. This paper discusses syntactic higher order generalization in a higher order language λ2[1]. Based on the application ordering, we proved the least general generalization exists and is unique up to renaming. An algorithm to compute the least general generalization is presented.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
H. Barendregt, Introduction to generalized type systems, Journal of functional programming, Vol. 1, N0. 2, 1991. 124–154.
Coquand, T., Huet, G., The calculus of constructions, Information and Computation, Vol.76, No.3/4 (1988), 95–120.
C. Feng, S. Muggleton, Towards inductive generalization in higher order logic, In D. Sleeman et al (eds.), Proceedings of the Ninth International Workshop on Machine Learning, San Mateo, California, 1992. Morgan Kaufman.
M. Hagiya, Generalization from partial parametrization in higher order type theory, Theoretical Computer Science, Vol.63 (1989), pp.113–139.
R. Hasker, The replay of program derivations, Ph.D. thesis, Department of Computer Science, University of Illinois at Urbana-Champaign, 1995.
G.P. Huet, A unification algorithm for typed lambda calculus, Theoretical Computer Science, 1 (1975), 27–57.
G. Huet, Bernard Lang, Proving and applying program transformations expressed with second order patterns, Acta Informatica 11, 31–55 (1978)
Peter Idestam-Almquist, Generalization of Horn clauses, Ph.D. dissertation, Department of Computer Science and Systems Science, Stockholm University and the Royal Institute of Technology, 1993.
Jianguo Lu, Jiafu Xu, Analogical Program Derivation based on Type Theory, Theoretical Computer Science, Vol.113, North Holland 1993, pp.259–272.
Stephen Muggleton, Inductive logic programming, New generation computing, 8(4):295–318, 1991
Charles David Page jr., Anti-unification in constraint logic: foundations and applications to learnability in first order logic, to speed-up learning, and to deduction, Ph.D. Dissertation, University of Illinois at Urbana-Champaign, 1993.
Frank Pfenning, Unification and anti-unification in the calculus of constructions, Proceedings of the 6th symposium on logic in computer science, 1991. pp.74–85.
Plotkin, G. D., A note on inductive generalization, Machine Intelligence 5, Edinburgh University Press 1970, pp. 153–163.
Plotkin, G.D., A further note on inductive generalization, Machine Intelligence 6, Edinburgh University Press 1971, pp. 101–124.
John C. Reynolds, Transformational systems and the algebraic structure of atomic formulas, Machine Intelligence 5, Edinburgh University Press 1970, 135–151.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1998 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Lu, J., Harao, M., Hagiya, M. (1998). Higher Order Generalization. In: Dix, J., del Cerro, L.F., Furbach, U. (eds) Logics in Artificial Intelligence. JELIA 1998. Lecture Notes in Computer Science(), vol 1489. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-49545-2_25
Download citation
DOI: https://doi.org/10.1007/3-540-49545-2_25
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-65141-3
Online ISBN: 978-3-540-49545-1
eBook Packages: Springer Book Archive