Abstract
An elementary formal system (EFS) is a logic program such as a Prolog program, for instance, that directly manipulates strings. Arikawa and his co-workers proposed elementary formal systems as a unifying framework for formal language learning.
In the present paper, we introduce advanced elementary formal systems (AEFSs), i.e., elementary formal systems which allow for the use of a certain kind of negation, which is nonmonotonic, in essence, and which is conceptually close to negation as failure.
We study the expressiveness of this approach by comparing certain AEFS definable language classes to the levels in the Chomsky hierarchy and to the language classes that are definable by EFSs that meet the same syntactical constraints.
Moreover, we investigate the learnability of the corresponding AEFS definable language classes in two major learning paradigms, namely in Gold’s model of learning in the limit and Valiant’s model of probably approximately correct learning. In particular, we show which learnability results achieved for EFSs extend to AEFSs and which do not.
This work has been partially supported by the German Ministry of Economics and Technology (BMWi) within the joint project LExIKON under grant 01 MD 949.
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References
D. Angluin, Inductive inference of formal languages from positive data, Information and Control 45 (1980) 117–135.
D. Angluin, C. H. Smith, A survey of inductive inference: Theory and methods, Computing Surveys 15 (1983) 237–269.
S. Arikawa, Elementary formal systems and formal languages-Simple formal systems, Memoirs of Faculty of Science, Kyushu University, Series A, Mathematics 24 (1970) 47–75.
S. Arikawa, S. Miyano, A. Shinohara, T. Shinohara, A. Yamamoto, Algorithmic learning theory with elementary formal systems, IEICE Trans. Inf. & Syst. E75-D 4 (1992) 405–414.
S. Arikawa, T. Shinohara, A. Yamamoto, Elementary formal systems as a unifying framework for language learning, in: Proc. Second Annual Workshop on Computational Learning Theory, Morgan Kaufmann, 1989, pp. 312–327.
S. Arikawa, T. Shinohara, A. Yamamoto, Learning elementary formal systems, Theoretical Computer Science 95 (1992) 97–113.
A. Blumer, A. Ehrenfeucht, D. Hausler, M. Warmuth, Learnability and the Vapnik-Chervonenkis dimension, Journal of the ACM 36 (1989) 929–965.
G. Grieser, K. P. Jantke, S. Lange, B. Thomas, A unifying approach to HTML wrapper representation and learning, in: Proc. Third Int. Conference on Discovery Science, LNAI 1967, Springer-Verlag, 2000, pp. 50–64.
E. M. Gold, Language identification in the limit, Information and Control 14 (1967) 447–474.
J. E. Hopcroft, J. D. Ullman, Formal Languages and their Relation to Automata, Addison-Wesley Publishing Company, 1979.
S. Jain, D. Osherson, J. Royer, A. Sharma, Systems that Learn-2nd Edition, An Introduction to Learning Theory, MIT Press, 1999.
N. Kushmerick, Wrapper induction: efficiency and expressiveness, Artificial Intelligence 118 (2000) 15–68.
V. Lifschitz, Foundations of logic programming, in: Principles of knowledge representation, G. Brewka (ed.), CSLI Publications, 1996, pp. 69–127.
S. Miyano, A. Shinohara, T. Shinohara, Polynomial-time learning of elementary formal systems, New Generation Computing 18 (2000) 217–242.
B. K. Natarajan, On learning sets and functions, Machine Learning 4 (1989) 67–97.
B. K. Natarajan, Machine Learning-A Theoretical Approach, Morgan Kaufmann Publ., 1991.
H. Rogers Jr., Theory of Recursive Functions and Effective Computability, MIT Press, 1987.
T. Shinohara, Inductive inference of monotonic formal systems from positive data, New Generation Computing 8 (1991) 371–384.
T. Shinohara, Rich classes inferable from positive data: Length-bounded elementary formal systems, Information and Computation 108 (1994) 175–186.
R. M. Smullyan, Theory of Formal Systems, Annals of Mathematical Studies, No. 47, Princeton University, 1961.
S. Soderland, Learning information extraction rules from semi-structured and free text, Machine Learning 34 (1997) 233–272.
B. Thomas, Token-Templates and Logic Programs for IntelligentWeb Search, Journal of Intelligent Information Systems 14 (2000) 241–261.
L. Valiant, A theory of the learnable, Communications of the ACM 27 (1984) 1134–1142.
A. Yamamoto, Procedural semantics and negative information of elementary formal systems, Journal of Logic Programming 13 (1992) 89–97.
C. Zeng, S. Arikawa, Applying inverse resolution to EFS language learning, in: Proc. Int. Conference for Young Computer Scientists, Int. Academic Publishers, 1999, pp. 480–487.
T. Zeugmann, S. Lange, A guided tour across the boundaries of learning recursive languages, in: Algorithmic Learning for Knowledge-Based Systems, K. P. Jantke and S. Lange (eds), LNAI 961, Springer-Verlag, 1995, pp. 190–258.
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Lange, S., Grieser, G., Jantke, K.P. (2001). Extending Elementary Formal Systems. In: Abe, N., Khardon, R., Zeugmann, T. (eds) Algorithmic Learning Theory. ALT 2001. Lecture Notes in Computer Science(), vol 2225. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45583-3_25
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DOI: https://doi.org/10.1007/3-540-45583-3_25
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