Abstract
This paper presents an algorithmic learning theory for analogical synthesis of logic programs from their examples. An analogical synthesizer is defined as a kind of inductive inference machine that uses analogy. More precisely speaking, it synthesizes target programs from their examples, given a source program to which the target programs should be similar. One of the difficulties in realizing an efficient analogical synthesizer is to distinguish useless and inappropriate similarities from the other. A similarity is inappropriate if every similar program with respect to the similarity is not correct. If our synthesizer cannot refute such similarities then it would waste computational resources without succeeding to find a desired program.
To cope with this hard problem on analogical synthesis, this paper first applies the notion of refutably inferable class of linear programs, and obtains a basic synthesizer. It has a function of refuting inappropriate similarities. Secondly this paper investigates another method of refuting inappropriate similarities, using an analogous technique that has been employed for theorem proving with abstraction. Incorporating this method into the basic synthesizer, we obtain a more efficient one. All the synthesizers presented in this paper are proved to identify a similar correct program in the limit, given a source program.
This is a preview of subscription content, log in via an institution.
Preview
Unable to display preview. Download preview PDF.
References
Bipin Indurkhya. On the role of interpretive analogy in learning. In Proc. 1st Internat. Workshop on Algorithmic Learning Theory, pages 174–189, 1990.
Hiroki Ishizaka. Model inference incorporating generalization. Journal of Information Processing, 11(3):206–211, 1988.
J.W. Lloyd. Foundations of Logic Programming. Springer-Verlag, second edition, 1987.
Stephen Muggleton. Inductive logic programming. In Inductive Logic Programming, pages 3–27. ACADEMIC PRESS, 1992.
Yasuhito Mukouchi and Setsuo Arikawa. Towards a mathematical theory of machine discovery from facts. Theoretical Computer Science, 137:53–84, 1995.
David A. Plaisted. Theorem proving with abstraction. Artificial Intelligence, 16:47–108, 1981.
G.D. Plotkin. A note on inductive generalization. In Machine Intelligence 5, pages 153–163. Edinburgh University Press, 1970.
Luc De Raedt and Maurice Bruynooghe. Interactive concept-learning and constructive induction by analogy. Machine Learning, 8:107–150, 1992.
J.C. Reynolds. Transformational systems and the algebraic structure of atomic formulas. In Machine Intelligence 5, pages 135–153. Edinburgh University Press, 1970.
J. A. Robinson. A machine-oriented logic based on the resolution principle. Journal of the Association for Computing Machinery, 12:13–41, Mach. 1965.
Céline Rouveirol. Extension of inversion of resolution applied to theory completion. In Inductive Logic Programming, pages 64–92. ACADEMIC PRESS, 1992.
Ken Sadohara and Makoto Haraguchi. Analogical logic program synthesis from examples. In Proc. 8th European Conference on Machine Learning, Lecture Notes in Artificial Intelligence Vol. 914, pages 232–244. Springer-Verlag, 1995.
Seiichiro Sakurai and Makoto Haraguchi. Towards learning by abstraction. In Proc. 2nd Internat. Workshop on Algorithmic Learning Theory, pages 288–298, 1991.
Ehud Y. Shapiro. Inductive inference of theories from facts. Technical Report 192, Yale University Computer Science Dept., 1981.
Birgit Tausend and Siegfried Bell. Analogical reasoning for logic programming. In Inductive Logic Programming, pages 397–408. ACADEMIC PRESS, 1992.
Patrick R.J. van der Laag and Shan-Hwei Nienhuys-Cheng. Subsumption and refinement in model inference. In Proc. 6th European Conference on Machine Learning, pages 95–114. Springer-Verlag, 1993.
Akihiro Yamamoto. Procedural semantics and negative information of elementary formal system. J. Logic Programming, 13:89–97, 1992.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1995 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Sadohara, K., Haraguchi, M. (1995). Analogical logic program synthesis algorithm that can refute inappropriate similarities. In: Jantke, K.P., Shinohara, T., Zeugmann, T. (eds) Algorithmic Learning Theory. ALT 1995. Lecture Notes in Computer Science, vol 997. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60454-5_45
Download citation
DOI: https://doi.org/10.1007/3-540-60454-5_45
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-60454-9
Online ISBN: 978-3-540-47470-8
eBook Packages: Springer Book Archive