Set-driven and rearrangement-independent learning of recursive languages
The present paper deals with the learnability of indexed families of uniformly recursive languages from positive data under various postulates of naturalness. In particular, we consider set-driven and rearrangement-independent learners, i.e., learning devices whose output exclusively depends on the range and on the range and length of their input, respectively. The impact of set-drivenness and rearrangement-independence on the behavior of learners to their learning power is studied in dependence on the hypothesis space the learners may use. Furthermore, we consider the influence of set-drivenness and rearrangementindependence for learning devices that realize the subset principle to different extents. Thereby we distinguish between strong-monotonic, monotonic and weak-monotonic or conservative learning.
The results obtained are twofold. First, rearrangement-independent learning does not constitute a restriction except the case of monotonic learning. Second, we prove that for all but one of the considered learning models set-drivenness is a severe restriction. However, set-driven conservative learning is exactly as powerful as unrestricted conservative learning provided the hypothesis space is appropriately chosen. These results considerably extend previous work done in the field (cf. e.g. Schäfer-Richter (1984) and Fulk (1990)).
Unable to display preview. Download preview PDF.
- Angluin, D. (1980), Inductive inference of formal languages from positive data, Information and Control45, 117–135.Google Scholar
- Berwick, R. (1985), “The Acquisition of Syntactic Knowledge,” Cambridge, Mass.: MIT Press.Google Scholar
- Fulk, M. (1990), Prudence and other restrictions in formal language learning, Information and Computation85, 1–11.Google Scholar
- Gold, E.M. (1967), Language identification in the limit, Information and Control10, 447–474.Google Scholar
- Hopcroft, J.E., and Ullman, J.D. (1969), “Formal Languages and their Relation to Automata,” Addison-Wesley, Reading, Massachusetts.Google Scholar
- Jantke, K.P. (1991) Monotonic and non-monotonic inductive inference, New Generation Computing8, 349–360.Google Scholar
- Lange, S., and Zeugmann, T. (1992), Types of monotonic language learning and their characterization, in “Proceedings 5th Annual ACM Workshop on Computational Learning Theory,” July 27–29, Pittsburgh, pp. 377–390, ACM Press.Google Scholar
- Lange, S., and Zeugmann, T. (1993a), Monotonic versus non-monotonic language learning, in “Proceedings 2nd International Workshop on Nonmonotonic and Inductive Logic,” December 1991, Reinhardsbrunn, (G. Brewka, K.P. Jantke and P.H. Schmitt, Eds.), Lecture Notes in Artificial Intelligence 659, pp. 254–269, Springer-Verlag, Berlin.Google Scholar
- Lange, S., and Zeugmann, T. (1993b), Language learning in dependence on the space of hypotheses, in “Proceedings 6th Annual ACM Conference on Computational Learning Theory,” Santa Cruz, July 1993, pp. 127–136, ACM Press, New York.Google Scholar
- Lange, S., and Zeugmann, T. (1993c), The learnability of recursive languages in dependence on the hypothesis space, GOSLER-Report 20/93, FB Mathematik, Informatik und Naturwissenschaften, HTWK Leipzig.Google Scholar
- Lange, S., and Zeugmann, T. (1993d), On the impact of order independence to the learnability of recursive languages, ISIS-RR-93-17E, ISIS FUJITSU Labs., Numazu.Google Scholar
- Machtey, M., and Young, P. (1978) “An Introduction to the General Theory of Algorithms,” North-Holland, New York.Google Scholar
- Osherson, D., Stob, M., and Weinstein, S. (1986), “Systems that Learn, An Introduction to Learning Theory for Cognitive and Computer Scientists,” MITPress, Cambridge, Massachusetts.Google Scholar
- Schäfer-Richter, G. (1984), “Über Eingabeabhängigkeit und Komplexität von Inferenzstrategien.” Dissertation, Rheinisch Westfälische Technische Hochschule Aachen.Google Scholar
- Wexler, K. (1992), The subset principle is an intensional principle, in “Knowledge and Language: Issues in Representation and Acquisition,” (E. Reuland and W. Abraham, Eds.), Kluwer Academic Publishers.Google Scholar
- Wexler, K., and Culicover, P. (1980), “Formal Principles of Language Acquisition,” Cambridge, Mass.: MIT Press.Google Scholar
- Wiehagen, R. (1991), A thesis in inductive inference, in “Proceedings First International Workshop on Nonmonotonic and Inductive Logic,” December 1990, Karlsruhe, (J. Dix, K.P. Jantke and P.H. Schmitt, Eds.), Lecture Notes in Artificial Intelligence Vol. 543, pp. 184–207, Springer-Verlag, Berlin.Google Scholar