# Monotonic versus non-monotonic language learning

- 12 Citations
- 124 Downloads

## Abstract

In the present paper strong-monotonic, monotonie and weak-monotonic reasoning is studied in the context of algorithmic language learning theory from positive as well as from positive and negative data.

*Strong-monotonicity* describes the requirement to *only* produce better and better generalizations when more and more data are fed to the inference device. *Monotonic learning* reflects the eventual interplay between generalization and restriction during the process of inferring a language. However, it is demanded that for any two hypotheses the one output later has to be at least as good as the previously produced one with respect to the language to be learnt. *Weakmonotonicity* is the analogue of cumulativity in learning theory.

We relate all these notions one to the other as well as to previously studied modes of identification, thereby in particular obtaining a strong hierarchy.

## Keywords

Initial Segment Recursive Function Inductive Inference Regular Language Positive Data## Preview

Unable to display preview. Download preview PDF.

## References

- [1]Angluin, D., (1980A), Inductive Inference of Formal Languagues from Positive Data, Information and Control 45, 117–135.Google Scholar
- [2]Angluin, D., (1980B), Finding Patterns Common to a Set of Strings, J. Computer and System Sciences 21, 46–62.Google Scholar
- [3]Angluin, D. and C.H. Smith, (1987), Formal Inductive Inference, In Encyclopedia of Artificial Intelligence, St.C. Shapiro (Ed.), Vol. 1, pp. 409–418, Wiley-Interscience Publication, New York.Google Scholar
- [4]Barzdin, Ya.M., (1974), Inductive Inference of Automata, Functions and Programs, Proc. Int. Congress of Math., Vancouver, pp. 455–460.Google Scholar
- [5]Beick, H.R., (1991), Personal Communication.Google Scholar
- [6]Bucher, W. and H. Maurer, (1984), Theoretische Grundlagen der Programmiersprachen, Automaten und Sprachen, Bibliographisches Institut AG, Wissenschaftsverlag, Zürich.Google Scholar
- [7]Case, J., (1988), The Power of Vacillation, In Proc. 1st Workshop on Computational Learning Theory, D. Haussler and L. Pitt (Eds.), pp. 196–205, Morgan Kaufmann Publishers Inc.Google Scholar
- [8]Case, J. and C. Lynes, (1982), Machine Inductive Inference and Language Identification, Proc. Automata, Languages and Programming, Ninth Colloquim, Aarhus, Denmark, M. Nielsen and E.M. Schmidt (Eds.), Lecture Notes in Computer Science 140, pp. 107–115, Springer-Verlag.Google Scholar
- [9]Fulk, M.,(1990), Prudence and other Restrictions in Formal Language Learning, Information and Computation 85, 1–11.Google Scholar
- [10]Gold, M.E., (1967), Language Identification in the Limit, Information and Control 10, 447–474.Google Scholar
- [11]Kearns, M. and L. Pitt, (1989), A Polynomial-time Algorithm for Learning kvariable Pattern Languages from Examples, In Proc. 2nd Workshop on Computational Learning Theory, R. Rivest, D. Haussler, and M.K. Warmuth (Eds.), pp. 57–70, Morgan Kaufmann Publishers Inc.Google Scholar
- [12]Jain, S. and A. Sharma, (1990), Language Learning by a ”Team”, Proc. Automata, Languages and Programming, 17th International Colloquium, Warwick University, England, M.S. Paterson (Ed.), Lecture Notes in Computer Science 443, pp. 153–166, Springer-Verlag.Google Scholar
- [13]Jantke, K.P., (1991 A), Monotonic and Non-monotonic Inductive Inference, New Generation Computing 8, 349–360.Google Scholar
- [14]Jantke, K.P., (1991B), Monotonic and Non-monotonic Inference of Functions and Patterns, in Proc. First International Workshop on Nonmonotonic and Inductive Logics, December 1990, Karlsruhe, J. Dix, K.P. Jantke and P.H. Schmitt (Eds.), Lecture Notes in Artificial Intelligence 543, pp. 161–177, Springer-Verlag.Google Scholar
- [15]Ko, K., Marron, A. and W.G. Tzeng, (1990), Learning String Patterns and Tree Patterns From Examples, Proc. 7th Conference on Machine Learning, pp. 384–391.Google Scholar
- [16]Lange, S. and R. Wiehagen, (1990), Polynomial-Time Inference of Pattern Languages, Proc. Algorithmic Learning Theory 1990, pp. 289–301, Tokyo, Ohmsha Ltd.Google Scholar
- [17]Nix, R.P., (1983), Editing by Examples, Yale University, Dept. Computer Science, Technical Report 280.Google Scholar
- [18]Osherson, D., Stob, M. and S. Weinstein, (1986), Systems that Learn, An Introduction to Learning Theory for Cognitive and Computer Scientists, MIT-Press, Cambridge, Massachusetts.Google Scholar
- [19]Shinohara, T., (1982), Polynomial Time Inference of Extended Regular Pattern Languages, RIMS Symposia on Software Science and Engineering, Kyoto, Lecture Notes in Computer Science 147, pp. 115–127, Springer-Verlag.Google Scholar
- [20]Solomonoff, R., (1964), A Formal Theory of Inductive Inference, Information and Control 7, 1–22, 234–254.Google Scholar
- [21]Wiehagen, R., (1976), Limes-Erkennung rekursiver Funktionen durch spezielle Strategien, J. Information Processing and Cybernetics (EIK) 12, 93–99.Google Scholar
- [22]Wiehagen, R., (1977), Identification of Formal Languages, Proc. Mathematical Foundations of Computer Science, Tatranska Lomnica, J. Gruska (Ed.), Lecture Notes in Computer Science 53, pp. 571–579, Springer-Verlag.Google Scholar
- [23]Wiehagen, R., (1990), Personal CommunicationGoogle Scholar
- [24]Wiehagen, R., (1991), A Thesis in Inductive Inference, in Proc. First International Workshop on Nonmonotonic and Inductive Logics, December 1990, Karlsruhe, J. Dix, K.P. Jantke and P.H. Schmitt (Eds.), Lecture Notes in Artificial Intelligence 543, pp. 184–207, Springer-Verlag.Google Scholar