Abstract
In language learning in the limit, we study computable devices (learners) learning formal languages. We consider learning tasks paired with restrictions regarding, for example, the hypotheses made by the learners. We compare such restrictions with each other in order to study their impact and depict the results in overviews, the so-called maps. In the case of explanatory learning, the literature already provides various maps.
On the other hand, in the case of behaviourally correct learning, only partial results are known. In this work, we complete these results and provide full behaviourally correct maps for different types of data presentation. In particular, in all studied settings, we observe that monotone learning implies non-U-shaped learning and that cautiousness, semantic conservativeness and weak monotonicity are equally powerful.
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Notes
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Particularly, a text (\(\mathbf {Txt}\)) provides positive information about the target language, from which Gold-style (\(\mathbf {G}\)) learners then infer their conjectures. Lastly, \(\mathbf {Ex}\) for stands for explanatory learning.
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References
Angluin, D.: Inductive inference of formal languages from positive data. Inf. Control 45, 117–135 (1980)
Baliga, G., Case, J., Merkle, W., Stephan, F., Wiehagen, R.: When unlearning helps. Inf. Comput. 206, 694–709 (2008)
Blum, L., Blum, M.: Toward a mathematical theory of inductive inference. Inf. Control 28, 125–155 (1975)
Case, J., Kötzing, T.: Strongly non-U-shaped language learning results by general techniques. Inf. Comput. 251, 1–15 (2016)
Case, J., Lynes, C.: Machine inductive inference and language identification. In: Nielsen, M., Schmidt, E.M. (eds.) ICALP 1982. LNCS, vol. 140, pp. 107–115. Springer, Heidelberg (1982). https://doi.org/10.1007/BFb0012761
Doskoč, V., Kötzing, T.: Mapping monotonic restrictions in inductive inference. In: De Mol, L., Weiermann, A., Manea, F., Fernández-Duque, D. (eds.) CiE 2021. LNCS, vol. 12813, pp. 146–157. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-80049-9_13
Doskoč, V., Kötzing, T.: Normal forms for semantically witness-based learners in inductive inference. In: De Mol, L., Weiermann, A., Manea, F., Fernández-Duque, D. (eds.) CiE 2021. LNCS, vol. 12813, pp. 158–168. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-80049-9_14
Doskoč, V., Kötzing, T.: Cautious limit learning. In: Algorithmic Learning Theory (ALT), pp. 117:251–117:276 (2020)
Fulk, M.A., Jain, S., Osherson, D.N.: Open problems in “systems that learn’’. J. Comput. Syst. Sci. 49(3), 589–604 (1994)
Gold, E.M.: Language identification in the limit. Inf. Control 10, 447–474 (1967)
Jain, S., Kötzing, T., Ma, J., Stephan, F.: On the role of update constraints and text-types in iterative learning. Inf. Comput. 247, 152–168 (2016)
Jain, S., Osherson, D., Royer, J.S., Sharma, A.: Systems that Learn: An Introduction to Learning Theory, 2nd edn. MIT Press, Cambridge (1999)
Jantke, K.: Monotonic and non-monotonic inductive inference. N. Gener. Comput. 8, 349–360 (1991)
Kinber, E.B., Stephan, F.: Language learning from texts: mindchanges, limited memory, and monotonicity. Inf. Comput. 123, 224–241 (1995)
Kötzing, T., Palenta, R.: A map of update constraints in inductive inference. Theoret. Comput. Sci. 650, 4–24 (2016)
Kötzing, T., Schirneck, M.: Towards an atlas of computational learning theory. In: Symposium on Theoretical Aspects of Computer Science (STACS), pp. 47:1–47:13 (2016)
Kötzing, T., Schirneck, M., Seidel, K.: Normal forms in semantic language identification. In: Algorithmic Learning Theory (ALT), pp. 76:493–76:516 (2017)
Lange, S., Zeugmann, T.: Monotonic versus non-monotonic language learning. In: Brewka, G., Jantke, K.P., Schmitt, P.H. (eds.) NIL 1991. LNCS, vol. 659, pp. 254–269. Springer, Heidelberg (1993). https://doi.org/10.1007/BFb0030397
Osherson, D., Stob, M., Weinstein, S.: Systems that Learn: An Introduction to Learning Theory for Cognitive and Computer Scientists. MIT Press, Cambridge (1986)
Osherson, D.N., Stob, M., Weinstein, S.: Learning strategies. Inf. Control 53, 32–51 (1982)
Osherson, D.N., Weinstein, S.: Criteria of language learning. Inf. Control 52, 123–138 (1982)
Schäfer-Richter, G.: Über eingabeabhängigkeit und komplexität von inferenzstrategien. Ph.D. thesis, RWTH Aachen University, Germany (1984)
Wexler, K., Culicover, P.W.: Formal Principles of Language Acquisition. MIT Press, Cambridge (1980)
Wiehagen, R.: A thesis in inductive inference. In: Dix, J., Jantke, K.P., Schmitt, P.H. (eds.) NIL 1990. LNCS, vol. 543, pp. 184–207. Springer, Heidelberg (1991). https://doi.org/10.1007/BFb0023324
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Doskoč, V., Kötzing, T. (2022). Maps of Restrictions for Behaviourally Correct Learning. In: Berger, U., Franklin, J.N.Y., Manea, F., Pauly, A. (eds) Revolutions and Revelations in Computability. CiE 2022. Lecture Notes in Computer Science, vol 13359. Springer, Cham. https://doi.org/10.1007/978-3-031-08740-0_9
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