# Mind change complexity of learning logic programs

Jain, Sanjay & Sharma, Arun
(2002)
Mind change complexity of learning logic programs.
*Theoretical Computer Science*, *284*(1), pp. 143-160.

## Abstract

The present paper motivates the study of mind change complexity for learning minimal models of length-bounded logic programs. It establishes ordinal mind change complexity bounds for learnability of these classes both from positive facts and from positive and negative facts. Building on Angluin’s notion of finite thickness and Wright’s work on finite elasticity, Shinohara defined the property of bounded finite thickness to give a sufficient condition for learnability of indexed families of computable languages from positive data. This paper shows that an effective version of Shinohara’s notion of bounded finite thickness gives sufficient conditions for learnability with ordinal mind change bound, both in the context of learnability from positive data and for learnability from complete (both positive and negative) data. Let Omega be a notation for the first limit ordinal. Then, it is shown that if a language defining framework yields a uniformly decidable family of languages and has effective bounded finite thickness, then for each natural number m >0, the class of languages defined by formal systems of length <= m:

• is identifiable in the limit from positive data with a mind change bound of Omega (power)m; • is identifiable in the limit from both positive and negative data with an ordinal mind change bound of Omega × m.

The above sufficient conditions are employed to give an ordinal mind change bound for learnability of minimal models of various classes of length-bounded Prolog programs, including Shapiro’s linear programs, Arimura and Shinohara’s depth-bounded linearly covering programs, and Krishna Rao’s depth-bounded linearly moded programs. It is also noted that the bound for learning from positive data is tight for the example classes considered.

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ID Code: | 37256 |
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Item Type: | Journal Article |

Refereed: | Yes |

Keywords: | Inductive inference, Computational learning theory, Mind change complexity, Logic programs |

DOI: | 10.1016/S0304-3975(01)00084-6 |

ISSN: | 0304-3975 |

Subjects: | Australian and New Zealand Standard Research Classification > INFORMATION AND COMPUTING SCIENCES (080000) > COMPUTATION THEORY AND MATHEMATICS (080200) |

Divisions: | Current > QUT Faculties and Divisions > Division of Research and Commercialisation |

Deposited On: | 27 Sep 2010 01:51 |

Last Modified: | 10 Aug 2011 14:54 |

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