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.
This research has been partially supported by the German Ministry for Research and Technology (BMFT) under grant no. 01 IW 101.
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Lange, S., Zeugmann, T. (1993). Monotonic versus non-monotonic language learning. 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/BFb0030397
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DOI: https://doi.org/10.1007/BFb0030397
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