Abstract
The “laws” in science are not the relations established by only the objective features of the nature. They have to be consistent with the assumptions and the operations commonly used in the study of scientists identifying these relations. Upon this consistency, they become communicable among the scientists. The objectives of this literature are to discuss a mathematical foundation of the communicability of the “scientific law equation” and to demonstrate “Smart Discovery System (SDS)” to discover the law equations based on the foundation. First, the studies of the scientific law equation discovery are briefly reviewed, and the need to introduce an important communicability criterion called “Mathematical Admissibility” is pointed out. Second, the axiomatic foundation of the mathematical admissibility in terms of measurement processes and quantity scale-types are discussed. Third, the strong constraints on the admissible formulae of the law equations are shown based on the criterion. Forth, the SDS is demonstrated to discover law equations by successively composing the relations that are derived from the criterion and the experimental data. Fifth, the generic criteria to discover communicable law equations for scientists are discussed in wider view, and the consideration of these criteria in the SDS is reviewed.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Beaumont, A.P., Knowles, J.D., Beuamont, G.P.: Statistical tests: An introduction with minitab commentary. Prentice Hall, Upper Saddle River (1996)
Bridgman, P.W.: Dimensional analysis. Yale University Press, New Haven (1922)
Buckingham, E.: On physically similar systems; Illustrations of the use of dimensional equations. Physical Review IV(4), 345–376 (1914)
Descartes, R.: Discours de la Methode/Discourse on the Method. Notre Dame. In: University of Notre Dame Press. Bilingual edition (1637/1994)
Džeroski, S., Todorovski, L.: Discovering dynamics: From inductive logic programming to machine discovery. Journal of Intelligent Information Systems 4, 89–108 (1995)
Falkenhainer, B.C., Michalski, R.S.: Integrating quantitative and qualitative discovery: The ABACUS system. Machine Learning 1, 367–401 (1986)
Feynman, R.P.: The character of physical law. MIT Press, Boston, MA (1965)
Kan, M., Miyata, N., Watanabe, K.: Research on spaciousness. Japanese Journal of Architecture 193, 51–57 (1972)
Koehn, B., Zytkow, J.M.: Experimeting and theorizing in theory formation. In: Proceedings of the International Symposium on Methodologies for Intelligent Systems, Knoxville, pp. 296–307 (1986)
Kokar, M.M.: Determining arguments of invariant functional descriptions. Machine Learning 1, 403–422 (1986)
Kouzou, T.: Material on heat transfer engineering. The Japan Society of Mechanical Engineers (JSME) Ch. 2 1, 55–56 (1986)
Krantz, D.H., Luce, R.D., Suppes, P., Tversky, A.: Fundations of measurement. Academic Press, New York (1971)
Langley, P.W., Simon, H.A., Bradshaw, G., Zytkow, J.M.: Scientific discovery: Computational explorations of the creative process. MIT Press, Cambridge, MA (1985)
Luce, R.D.: On the possible psychological laws. The Psychological Review 66, 81–95 (1959)
Newton, I.: Principia, vol.II, The System of the World. Translated into English by Motte, A (1729). University of California Press, Berkeley, CA Copyright 1962 (1686)
Rissanen, J.: Modeling by shortest data description. Automatica 14, 465–471 (1978)
Simon, H.A.: Models of discovery. D. Reidel Publishing Company, Dordrecht, Holland (1977)
Stevens, S.S.: On the theory of scales of measurement. Science 103, 677–680 (1946)
Todorovski, L., Džeroski, S.: Declarative bias in equation discovery. In: Proceedings of the Fourteenth International Conference on Machine Learning, Nashville, TN, pp. 376–384 (1997)
Washio, T., Motoda, H.: Discovering admissible models of complex systems based on scale-types and identity constraints. In: Proceedings of Fifteenth International Joint Conference on Artificial Intelligence, Nagoya, Japan, pp. 810–817 (1997)
Washio, T., Motoda, H.: Discovering admissible simultaneous equations of large scale systems. In: Proceedings of Fifteenth National Conference on Artificial Intelligence, Madison, WI, pp. 189–196 (1998)
Washio, T., Motoda, H., Niwa, Y.: Discovering admissible model equations from observed data based on scale-types and identity constraints. In: Proceedings of Sixteenth International Joint Conference on Artificial Intelligence, Stockholm, Sweden, pp. 772–779
Washio, T., Motoda, H., Niwa, Y.: Enhancing the plausibility of law equation discovery. In: Proceedings of the Seventeenth International Conference on Machine Learning, Stanford, CA, pp. 1127–1134 (2000)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Washio, T., Motoda, H. (2007). Communicability Criteria of Law Equations Discovery. In: Džeroski, S., Todorovski, L. (eds) Computational Discovery of Scientific Knowledge. Lecture Notes in Computer Science(), vol 4660. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73920-3_5
Download citation
DOI: https://doi.org/10.1007/978-3-540-73920-3_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-73919-7
Online ISBN: 978-3-540-73920-3
eBook Packages: Computer ScienceComputer Science (R0)