Learning higher-order logic programs

A key feature of inductive logic programming is its ability to learn first-order programs, which are intrinsically more expressive than propositional programs. In this paper, we introduce techniques to learn higher-order programs. Specifically, we extend meta-interpretive learning (MIL) to support l...

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Bibliographic Details
Published in:Machine learning Vol. 109; no. 7; pp. 1289 - 1322
Main Authors: Cropper, Andrew, Morel, Rolf, Muggleton, Stephen
Format: Journal Article
Language:English
Published: New York Springer US 01.07.2020
Springer Nature B.V
Subjects:
Artificial Intelligence
Complexity
Computer Science
Control
Encryption
Learning
Logic programming
Logic programs
Machine Learning
Mechatronics
Natural Language Processing (NLP)
Prolog
Robotics
Simulation and Modeling
Special Issue of the Inductive Logic Programming (ILP) 2019
ISSN:0885-6125, 1573-0565
Online Access:Get full text
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Summary:A key feature of inductive logic programming is its ability to learn first-order programs, which are intrinsically more expressive than propositional programs. In this paper, we introduce techniques to learn higher-order programs. Specifically, we extend meta-interpretive learning (MIL) to support learning higher-order programs by allowing for higher-order definitions to be used as background knowledge. Our theoretical results show that learning higher-order programs, rather than first-order programs, can reduce the textual complexity required to express programs, which in turn reduces the size of the hypothesis space and sample complexity. We implement our idea in two new MIL systems: the Prolog system Metagol ho and the ASP system HEXMIL ho . Both systems support learning higher-order programs and higher-order predicate invention, such as inventing functions for map/3 and conditions for filter/3. We conduct experiments on four domains (robot strategies, chess playing, list transformations, and string decryption) that compare learning first-order and higher-order programs. Our experimental results support our theoretical claims and show that, compared to learning first-order programs, learning higher-order programs can significantly improve predictive accuracies and reduce learning times.
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ISSN:0885-6125
1573-0565
DOI:10.1007/s10994-019-05862-7