## First order jk-clausal theories are PAC-learnable (1994)

Venue: | Artificial Intelligence |

Citations: | 65 - 27 self |

### BibTeX

@ARTICLE{Raedt94firstorder,

author = {Luc De Raedt},

title = {First order jk-clausal theories are PAC-learnable},

journal = {Artificial Intelligence},

year = {1994},

volume = {70},

pages = {375--392}

}

### Years of Citing Articles

### OpenURL

### Abstract

We present positive PAC-learning results for the nonmonotonic inductive logic programming setting. In particular, we show that first order range-restricted clausal theories that consist of clauses with up to k literals of size at most j each are polynomialsample polynomial-time PAC-learnable with one-sided error from positive examples only. In our framework, concepts are clausal theories and examples are finite interpretations. We discuss the problems encountered when learning theories which only have infinite non-trivial models and propose a way to avoid these problems using a representation change called flattening. Finally, we compare our results to PAC-learnability results for the normal inductive logic programming setting. 1

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(Show Context)
Citation Context ... problem. Example 3 Suppose our target theory is T = {sort([A|B], S) ← partition(A, B, C, D), sort(C, E), sort(D, F ), append(E, [B|F ], S)}. The interpretation (set of ground facts) I = {append([1], =-=[2]-=-, [1, 2]), partition(2, [1], [1], []), sort([], []), sort([1], [1]), sort([2, 1], [1, 2])} is a model (i.e. a positive example) for the target theory T . We have used the PROLOG notation for lists her... |

9 | The many faces of inductive logic programming - Raedt, Lavra - 1993 |

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1 |
Declarative bias for bottom-up ILP systems
- Adé, Raedt, et al.
- 1994
(Show Context)
Citation Context ...econd problem. Example 3 Suppose our target theory is T = {sort([A|B], S) ← partition(A, B, C, D), sort(C, E), sort(D, F ), append(E, [B|F ], S)}. The interpretation (set of ground facts) I = {append(=-=[1]-=-, [2], [1, 2]), partition(2, [1], [1], []), sort([], []), sort([1], [1]), sort([2, 1], [1, 2])} is a model (i.e. a positive example) for the target theory T . We have used the PROLOG notation for list... |

1 | Generalization and learnability: a case study of constrained atoms - Page, Frisch - 1992 |