## Characterizations of Monotonic and Dual Monotonic Language Learning (1995)

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Venue: | Information and Computation |

Citations: | 20 - 7 self |

### BibTeX

@ARTICLE{Zeugmann95characterizationsof,

author = {Thomas Zeugmann and Steffen Lange and Shyam Kapur},

title = {Characterizations of Monotonic and Dual Monotonic Language Learning},

journal = {Information and Computation},

year = {1995},

volume = {120},

pages = {155--173}

}

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### Abstract

The present paper deals with monotonic and dual monotonic language learning from positive as well as from positive and negative examples. The three notions of monotonicity reflect different formalizations of the requirement that the learner has to produce better and better generalizations when fed more and more data on the concept to be learned.

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Citation Context ... is infinite and all but finitely many terms of it are equal to j, or (M(oe x )) x2IN is non-empty and finite, and its last term is j. Now we are ready to define learning in the limit. Definition 1. (=-=Gold, 1967-=-) Let L be an indexed family, L 2 L, and let G = (G j ) j2IN be a hypothesis space. An IIM M CLIM--TXT- [CLIM--INF ]-identifies L from text [ informant ] with respect to G iff for every text t [inform... |

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Citation Context ...y have not seen data contradicting them. 8 Hence, whenever a conservative IIM performs a mind change it is because it has perceived clear inconsistency between its guess and the input. Definition 5. (=-=Angluin, 1980-=-b) Let L be an indexed family, L 2 L, and let G = (G j ) j2IN be a hypothesis space. An IIM M CCONSERVATIVE--TXT- [CCONSERVATIVE--INF ]-identifies L from text [ from informant ] with respect to G iff ... |

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Citation Context ...y have not seen data contradicting them. 8 Hence, whenever a conservative IIM performs a mind change it is because it has perceived clear inconsistency between its guess and the input. Definition 5. (=-=Angluin, 1980-=-b) Let L be an indexed family, L 2 L, and let G = (G j ) j2IN be a hypothesis space. An IIM M CCONSERVATIVE--TXT- [CCONSERVATIVE--INF ]-identifies L from text [ from informant ] with respect to G iff ... |

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Citation Context ...with respect to G. CCONS0TXT and CCONS0INF are defined analogously as above. Now we are ready to formally define the three types of monotonic language learning introduced in Section 1. Definition 4. (=-=Jantke, 1991-=-a, Wiehagen, 1991) Let L be an indexed family, L 2 L, and let G = (G j ) j2IN be a hypothesis space. An IIM M is said to identify a language L from text [informant ] with respect to G (A) strong-monot... |

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Citation Context ...with respect to G. CCONS0TXT and CCONS0INF are defined analogously as above. Now we are ready to formally define the three types of monotonic language learning introduced in Section 1. Definition 4. (=-=Jantke, 1991-=-a, Wiehagen, 1991) Let L be an indexed family, L 2 L, and let G = (G j ) j2IN be a hypothesis space. An IIM M is said to identify a language L from text [informant ] with respect to G (A) strong-monot... |

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