Sorted Downward Refinement: Building Background Knowledge into a Refinement Operator for Inductive Logic Programming

The main operations in Inductive Logic Programming (ILP) are generalization and specialization, which only make sense in a generality order. In ILP, the three most important generality orders are subsumption, implication and implication relative to background knowledge. The two languages used most often are languages of clauses and languages of only Horn clauses. This gives a total of six different ordered languages. In this paper, we give a systematic treatment of the existence or non-existence of least generalizations and greatest specializations of finite sets of clauses in each of these six ordered sets. We survey results already obtained by others and also contribute some answers of our own. Our main new results are, firstly, the existence of a computable least generalization under implication of every finite set of clauses containing at least one non-tautologous function-free clause (among other, not necessarily function-free clauses). Secondly, we show that such a least generalization need not exist under relative implication, not even if both the set that is to be generalized and the background knowledge are function-free. Thirdly, we give a complete discussion of existence and non-existence of greatest specializations in each of the six ordered languages.

Download Full-text

Turning 30: New Ideas in Inductive Logic Programming

Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence ◽

10.24963/ijcai.2020/673 ◽

2020 ◽

Cited By ~ 2

Author(s):

Andrew Cropper ◽

Sebastijan Dumančić ◽

Stephen H. Muggleton

Keyword(s):

Machine Learning ◽

Logic Programming ◽

Inductive Logic Programming ◽

Inductive Logic ◽

Background Knowledge ◽

Training Data ◽

Future Research ◽

Logic Programs ◽

Recursive Programs ◽

New Ideas

Common criticisms of state-of-the-art machine learning include poor generalisation, a lack of interpretability, and a need for large amounts of training data. We survey recent work in inductive logic programming (ILP), a form of machine learning that induces logic programs from data, which has shown promise at addressing these limitations. We focus on new methods for learning recursive programs that generalise from few examples, a shift from using hand-crafted background knowledge to learning background knowledge, and the use of different technologies, notably answer set programming and neural networks. As ILP approaches 30, we also discuss directions for future research.

Download Full-text

Learning logic programs with structured background knowledge☆☆An extended abstract of this paper appeared in: L. De Raedt (Ed.), Proceedings of the Fifth International Workshop on Inductive Logic Programming, Tokyo, Japan, 1995, pp. 53–76, Scientific Report of the Department of Computer Science, Katholieke Universiteit Leuven, and also in the post-conference volume: L. De Raedt (Ed.), Advances in Inductive Logic Programming, IOS Press, Amsterdam/Ohmsha, Tokyo, 1996, pp. 172–191.

Artificial Intelligence ◽

10.1016/s0004-3702(01)00062-5 ◽

2001 ◽

Vol 128 (1-2) ◽

pp. 31-97 ◽

Cited By ~ 11

Author(s):

Tamás Horváth ◽

György Turán

Keyword(s):

Logic Programming ◽

Computer Science ◽

Inductive Logic Programming ◽

International Workshop ◽

Inductive Logic ◽

Background Knowledge ◽

Logic Programs ◽

Scientific Report ◽

Learning Logic

Download Full-text

Forgetting to Learn Logic Programs

Proceedings of the AAAI Conference on Artificial Intelligence ◽

10.1609/aaai.v34i04.5776 ◽

2020 ◽

Vol 34 (04) ◽

pp. 3676-3683

Author(s):

Andrew Cropper

Keyword(s):

Logic Programming ◽

Inductive Logic Programming ◽

Inductive Logic ◽

Background Knowledge ◽

Experimental Results ◽

Learning Performance ◽

Sample Complexity ◽

Logic Programs ◽

Hypothesis Space ◽

Alternative Approaches

Most program induction approaches require predefined, often hand-engineered, background knowledge (BK). To overcome this limitation, we explore methods to automatically acquire BK through multi-task learning. In this approach, a learner adds learned programs to its BK so that they can be reused to help learn other programs. To improve learning performance, we explore the idea of forgetting, where a learner can additionally remove programs from its BK. We consider forgetting in an inductive logic programming (ILP) setting. We show that forgetting can significantly reduce both the size of the hypothesis space and the sample complexity of an ILP learner. We introduce Forgetgol, a multi-task ILP learner which supports forgetting. We experimentally compare Forgetgol against approaches that either remember or forget everything. Our experimental results show that Forgetgol outperforms the alternative approaches when learning from over 10,000 tasks.

Download Full-text