Abstract
Several well-known inductive inference strategies change the actual hypothesis only when they discover that it “provably misclassifies” an example seen so far. This notion is made mathematically precise and its general power is characterized. In spite of its strength it is shown that this approach is not of “universal” power. Consequently, then hypotheses are considered which “unprovably misclassify” examples and the properties of this approach are studied. Among others it turns out that this type is of the same power as monotonic identification. Finally, it is shown that “universal” power can be achieved only when an unbounded number of alternations of these dual types of hypotheses is allowed.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
ANGLUIN, D. (1980), Inductive inference of formal languages from positive data, Information and Control 45, 117–135.
ANGLUIN, D., and SMITH, C. H. (1983), Inductive inference: Theory and methods, Computing Surveys 15, 237–269.
BARZDIN, J. (1971), Complexity and frequency solution of some algorithmically unsolvable problems, Doct. Diss., Novosibirsk State Univ. (Russian).
BARZDIN, J. (1974), Inductive inference of automata, functions and programs, in “Proceedings, International Congress of Mathematicians” pp.455–460.
BARZDIN, J., and FREIVALDS, R. (1972), On the prediction of general recursive functions, Soviet Math. Dokl. 13, 1224–1228.
BARZDIN, J., and FREIVALDS, R. (1974), Prediction and limit synthesis of recursively enumerable function classes, Theory of algorithms and programs, vol.1, 100–111 (Russian).
BLUM, L., and BLUM, M. (1975), Toward a mathematical theory of inductive inference, Information and Control 28, 125–155.
CASE, J., and NGO MANGUELLE, S. (1979), Refinements of inductive inference by Popperian machines, Technical Report Nr. 152, Dept. of Computer Science, State Univ. of New York at Buffalo.
CASE, J., and SMITH, C. (1983), Comparison of identification criteria for machine inductive inference, Theoretical Computer Science 25, 193–220.
FREIVALDS, R., and BARZDIN, J. (1975), Relations between predictability and identifiability in the limit, Theory of algorithms and programs vol.2, 26–34 (Russian).
FULK, M. A. (1988), Saving the phenomena: Requirements that inductive inference machines not contradict known data, Information and Computation 79, 193–209.
FULK, M. A. (1990), Robust separations in inductive inference, in “Proceedings, 31st IEEE Symposium on Foundations of Computer Science” pp.405–410.
FULK, M. A. (1991), personal communication to R. Wiehagen.
GASARCH, W., KINBER, E. B., and KUMMER, M. (1991), Degrees of inferability, Manuscript.
GOLD, E. M. (1967), Language identification in the limit, Information and Control 10, 447–474.
JANTKE, K. P. (1991), Monotonic and non-monotonic inductive inference, New Generation Computing 8, 349–360.
KINBER, E. B., and ZEUGMANN, T. (1985), Inductive inference of almost everywhere correct programs by reliably working strategies, Journal of Information Processing and Cybernetics 21, 91–100.
KLETTE, R., and WIEHAGEN, R. (1980), Research in the theory of inductive inference by GDR mathematicians—a survey, Information Sciences 22, 149–169.
OSHERSON, D. N., STOB, M., and WEINSTEIN, S. (1986), “Systems that learn: An introduction to learning theory for cognitive and computer scientists”, MIT Press, Cambridge, Mass.
PLESZKOCH, M. G., GASARCH, W. I., JAIN, S., and SOLOVAY, R. (1990), Learning via queries to an oracle, Manuscript.
PODNIEKS, K. (1974), Comparing various types of limit synthesis and prediction of functions, Theory of algorithms and programs vol.1, 68–81 (Russian).
POPPER, K. (1968), “The logic of scientific discovery”, 2nd ed. Harper Torch, New York.
ROGERS, H. (1967), “Theory of recursive functions and effective computability”, McGraw-Hill, New York.
“Theory of algorithms and programs”, vol.1, 2, 3 (1974, 1975, 1977), J. Barzdin, Ed., Latvian State Univ., Riga (Russian).
WIEHAGEN, R. (1976), Limes-Erkennung rekursiver Funktionen durch spezielle Strategien, Elektronische Informationsverarbeitung und Kybernetik 12, 93–99 (German).
WIEHAGEN, R. (1978), Zur Theorie der algorithmischen Erkennung, Diss. B, Sektion Mathematik, Humboldt-Univ. Berlin (German).
WIEHAGEN, R. (1991), A thesis in inductive inference, in “Proceedings, First International Workshop Nonmonotonic and Inductive Logic” 1990, J. Dix, K. P. Jantke, P. Schmitt, Eds., Lecture Notes in Artificial Intelligence 543, 184–207.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1993 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Freivalds, R., Kinber, E.B., Wiehagen, R. (1993). Dual types of hypotheses in inductive inference. In: Brewka, G., Jantke, K.P., Schmitt, P.H. (eds) Nonmonotonic and Inductive Logic. NIL 1991. Lecture Notes in Computer Science, vol 659. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0030395
Download citation
DOI: https://doi.org/10.1007/BFb0030395
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-56433-1
Online ISBN: 978-3-540-47557-6
eBook Packages: Springer Book Archive