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Andrew Cropper

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29 papers

2 author rows

AAAI Conference 2026 Conference Paper

Can Humans Teach Machines to Code?

Celine Hocquette
Johannes Langer
Andrew Cropper
Ute Schmid

The goal of inductive program synthesis is for a machine to automatically generate a program from user-supplied examples. A key underlying assumption is that humans can provide sufficient examples to teach a concept to a machine. To evaluate the validity of this assumption, we conduct a study where human participants provide examples for six programming concepts, such as finding the maximum element of a list. We evaluate the generalisation performance of five program synthesis systems trained on input-output examples (i) from a human group, (ii) from a gold standard set, and (iii) randomly sampled. Our results suggest that human-provided examples are typically insufficient for a program synthesis system to learn an accurate program.

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AAAI Conference 2026 Conference Paper

Efficient Rule Induction by Ignoring Pointless Rules

Andrew Cropper
David M. Cerna

The goal of inductive logic programming (ILP) is to find a set of logical rules that generalises training examples and background knowledge. We introduce an ILP approach that identifies pointless rules. A rule is pointless if it contains a redundant literal or cannot discriminate against negative examples. We show that ignoring pointless rules allows an ILP system to soundly prune the hypothesis space. Our experiments on multiple domains, including visual reasoning and game playing, show that our approach can reduce learning times by 99% whilst maintaining predictive accuracies.

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JAIR Journal 2026 Journal Article

Honey, I Shrunk the Hypothesis Space (Through Logical Preprocessing)

Andrew Cropper
Filipe Gouveia
David M. Cerna

Inductive logic programming (ILP) is a form of logical machine learning. The goal is to search a hypothesis space for a hypothesis that generalises training examples and background knowledge. We introduce an approach that shrinks the hypothesis space before an ILP system searches it. Our approach uses background knowledge to find rules that cannot be in an optimal hypothesis regardless of the training examples. For instance, our approach discovers relationships such as even numbers cannot be odd and prime numbers greater than 2 are odd. It then removes violating rules from the hypothesis space. We implement our approach using answer set programming and use it to shrink the hypothesis space of a constraint-based ILP system. Our experiments on multiple domains, including visual reasoning and game playing, show that our approach can substantially reduce learning times whilst maintaining predictive accuracies. For instance, given just 10 seconds of preprocessing time, our approach can reduce learning times from over 10 hours to only 2 seconds.

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AAAI Conference 2026 Conference Paper

Symmetry Breaking for Inductive Logic Programming

Andrew Cropper
David M. Cerna
Matti Järvisalo

The goal of inductive logic programming (ILP) is to search for a hypothesis that generalises training data and background knowledge. The challenge is searching vast hypothesis spaces, which is exacerbated because many logically equivalent hypotheses exist. To address this challenge, we introduce a method to break symmetries in the hypothesis space. We implement our idea in answer set programming. Our experiments on multiple domains, including visual reasoning and game playing, show that our approach can reduce solving times from over an hour to just 17 seconds.

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IJCAI Conference 2025 Conference Paper

Relational Decomposition for Program Synthesis

Céline Hocquette
Andrew Cropper

We introduce a relational approach to program synthesis. The key idea is to decompose synthesis tasks into simpler relational synthesis subtasks. Specifically, our representation decomposes a training input-output example into sets of input and output facts respectively. We then learn relations between the input and output facts. We demonstrate our approach using an off-the-shelf inductive logic programming (ILP) system on four challenging synthesis datasets. Our results show that (i) our representation can outperform a standard one, and (ii) an off-the-shelf ILP system with our representation can outperform domain-specific approaches.

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AAAI Conference 2025 Conference Paper

Scalable Knowledge Refactoring Using Constrained Optimisation

Minghao Liu
David M. Cerna
Filipe Gouveia
Andrew Cropper

Knowledge refactoring compresses logic programs by replacing them with new rules. Current approaches struggle to scale to large programs. To overcome this limitation, we introduce a constrained optimisation refactoring approach. Our first key idea is to encode the problem with decision variables based on literals rather than rules. Our second key idea is to focus on linear invented rules. Our empirical results on multiple domains show that our approach can refactor programs quicker and with more compression than the previous state-of-the-art approach, sometimes by 60%.

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AAAI Conference 2024 Conference Paper

Generalisation through Negation and Predicate Invention

David M. Cerna
Andrew Cropper

The ability to generalise from a small number of examples is a fundamental challenge in machine learning. To tackle this challenge, we introduce an inductive logic programming (ILP) approach that combines negation and predicate invention. Combining these two features allows an ILP system to generalise better by learning rules with universally quantified body-only variables. We implement our idea in NOPI, which can learn normal logic programs with predicate invention, including Datalog programs with stratified negation. Our experimental results on multiple domains show that our approach can improve predictive accuracies and learning times.

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IJCAI Conference 2024 Conference Paper

Learning Big Logical Rules by Joining Small Rules

Céline Hocquette
Andreas Niskanen
Rolf Morel
Matti Järvisalo
Andrew Cropper

A major challenge in inductive logic programming is learning big rules. To address this challenge, we introduce an approach where we join small rules to learn big rules. We implement our approach in a constraint-driven system and use constraint solvers to efficiently join rules. Our experiments on many domains, including game playing and drug design, show that our approach can (i) learn rules with more than 100 literals, and (ii) drastically outperform existing approaches in terms of predictive accuracies.

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IJCAI Conference 2024 Conference Paper

Learning Logic Programs by Discovering Higher-Order Abstractions

Céline Hocquette
Sebastijan Dumancic
Andrew Cropper

We introduce the higher-order refactoring problem, where the goal is to compress a logic program by discovering higher-order abstractions, such as map, filter, and fold. We implement our approach in Stevie, which formulates the refactoring problem as a constraint optimisation problem. Our experiments on multiple domains, including program synthesis and visual reasoning, show that refactoring can improve the learning performance of an inductive logic programming system, specifically improving predictive accuracies by 27% and reducing learning times by 47%. We also show that Stevie can discover abstractions that transfer to multiple domains.

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ECAI Conference 2024 Conference Paper

Learning Logic Programs by Finding Minimal Unsatisfiable Subprograms

Andrew Cropper
Céline Hocquette

The goal of inductive logic programming (ILP) is to search for a logic program that, with given background knowledge, generalises training examples. We introduce an ILP approach that identifies minimal unsatisfiable subprograms (MUSPs). We show that finding MUSPs allows us to efficiently and soundly prune the search space. Our experiments on multiple domains, including program synthesis and game playing, show that our approach can reduce learning times by 99%.

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AAAI Conference 2024 Conference Paper

Learning MDL Logic Programs from Noisy Data

Céline Hocquette
Andreas Niskanen
Matti Järvisalo
Andrew Cropper

Many inductive logic programming approaches struggle to learn programs from noisy data. To overcome this limitation, we introduce an approach that learns minimal description length programs from noisy data, including recursive programs. Our experiments on several domains, including drug design, game playing, and program synthesis, show that our approach can outperform existing approaches in terms of predictive accuracies and scale to moderate amounts of noise.

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ECAI Conference 2023 Conference Paper

Learning Logic Programs by Combining Programs

Andrew Cropper
Céline Hocquette

The goal of inductive logic programming is to induce a logic program (a set of logical rules) that generalises training examples. Inducing programs with many rules and literals is a major challenge. To tackle this challenge, we introduce an approach where we learn small non-separable programs and combine them. We implement our approach in a constraint-driven ILP system. Our approach can learn optimal and recursive programs and perform predicate invention. Our experiments on multiple domains, including game playing and program synthesis, show that our approach can drastically outperform existing approaches in terms of predictive accuracies and learning times, sometimes reducing learning times from over an hour to a few seconds.

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AAAI Conference 2023 Conference Paper

Learning Logic Programs by Discovering Where Not to Search

Andrew Cropper
Céline Hocquette

The goal of inductive logic programming (ILP) is to search for a hypothesis that generalises training examples and background knowledge (BK). To improve performance, we introduce an approach that, before searching for a hypothesis, first discovers "where not to search". We use given BK to discover constraints on hypotheses, such as that a number cannot be both even and odd. We use the constraints to bootstrap a constraint-driven ILP system. Our experiments on multiple domains (including program synthesis and inductive general game playing) show that our approach can (i) substantially reduce learning times by up to 97%, and (ii) can scale to domains with millions of facts.

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AAAI Conference 2023 Conference Paper

Relational Program Synthesis with Numerical Reasoning

Céline Hocquette
Andrew Cropper

Learning programs with numerical values is fundamental to many AI applications, including bio-informatics and drug design. However, current program synthesis approaches struggle to learn programs with numerical values. An especially difficult problem is learning continuous values from multiple examples, such as intervals. To overcome this limitation, we introduce an inductive logic programming approach which combines relational learning with numerical reasoning. Our approach, which we call NumSynth, uses satisfiability modulo theories solvers to efficiently learn programs with numerical values. Our approach can identify numerical values in linear arithmetic fragments, such as real difference logic, and from infinite domains, such as real numbers or integers. Our experiments on four diverse domains, including game playing and program synthesis, show that our approach can (i) learn programs with numerical values from linear arithmetical reasoning, and (ii) outperform existing approaches in terms of predictive accuracies and learning times.

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AAAI Conference 2023 Conference Paper

The Automatic Computer Scientist

Andrew Cropper

Algorithms are ubiquitous: they track our sleep, help us find cheap flights, and even help us see black holes. However, designing novel algorithms is extremely difficult, and we do not have efficient algorithms for many fundamental problems. The goal of my research is to accelerate algorithm discovery by building an automatic computer scientist. To work towards this goal, my research focuses on inductive logic programming, a form of machine learning in which my collaborators and I have demonstrated major advances in automated algorithm discovery over the past five years. In this talk and paper, I survey these advances.

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JAIR Journal 2022 Journal Article

Inductive Logic Programming At 30: A New Introduction

Andrew Cropper
Sebastijan Dumančić

Inductive logic programming (ILP) is a form of machine learning. The goal of ILP is to induce a hypothesis (a set of logical rules) that generalises training examples. As ILP turns 30, we provide a new introduction to the field. We introduce the necessary logical notation and the main learning settings; describe the building blocks of an ILP system; compare several systems on several dimensions; describe four systems (Aleph, TILDE, ASPAL, and Metagol); highlight key application areas; and, finally, summarise current limitations and directions for future research.

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AAAI Conference 2022 Conference Paper

Learning Logic Programs Though Divide, Constrain, and Conquer

Andrew Cropper

We introduce an inductive logic programming approach that combines classical divide-and-conquer search with modern constraint-driven search. Our anytime approach can learn optimal, recursive, and large programs and supports predicate invention. Our experiments on three domains (classification, inductive general game playing, and program synthesis) show that our approach can increase predictive accuracies and reduce learning times.

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AAAI Conference 2021 Conference Paper

Knowledge Refactoring for Inductive Program Synthesis

Sebastijan Dumancic
Tias Guns
Andrew Cropper

Humans constantly restructure knowledge to use it more efficiently. Our goal is to give a machine learning system similar abilities so that it can learn more efficiently. We introduce the knowledge refactoring problem, where the goal is to restructure a learner’s knowledge base to reduce its size and to minimise redundancy in it. We focus on inductive logic programming, where the knowledge base is a logic program. We introduce Knorf, a system which solves the refactoring problem using constraint optimisation. A key feature of Knorf is that, rather than simply removing knowledge, it also introduces new knowledge through predicate invention. We evaluate our approach on two domains: building Lego structures and real-world string transformations. Our experiments show that learning from refactored knowledge can improve predictive accuracies fourfold and reduce learning times by half.

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AAAI Conference 2020 Conference Paper

Forgetting to Learn Logic Programs

Andrew Cropper

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.

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AAAI Conference 2020 Conference Paper

Learning Higher-Order Programs through Predicate Invention

Andrew Cropper
Rolf Morel
Stephen H. Muggleton

A key feature of inductive logic programming (ILP) is its ability to learn ﬁrst-order programs, which are intrinsically more expressive than propositional programs. In this paper, we introduce ILP techniques to learn higher-order programs. We implement our idea in Metagolho, an ILP system which can learn higher-order programs with higher-order predicate invention. Our experiments show that, compared to ﬁrst-order programs, learning higher-order programs can signiﬁcantly improve predictive accuracies and reduce learning times.

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IJCAI Conference 2020 Conference Paper

Learning Large Logic Programs By Going Beyond Entailment

Andrew Cropper
Sebastijan Dumančic

A major challenge in inductive logic programming (ILP) is learning large programs. We argue that a key limitation of existing systems is that they use entailment to guide the hypothesis search. This approach is limited because entailment is a binary decision: a hypothesis either entails an example or does not, and there is no intermediate position. To address this limitation, we go beyond entailment and use 'example-dependent' loss functions to guide the search, where a hypothesis can partially cover an example. We implement our idea in Brute, a new ILP system which uses best-first search, guided by an example-dependent loss function, to incrementally build programs. Our experiments on three diverse program synthesis domains (robot planning, string transformations, and ASCII art), show that Brute can substantially outperform existing ILP systems, both in terms of predictive accuracies and learning times, and can learn programs 20 times larger than state-of-the-art systems.

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IJCAI Conference 2020 Conference Paper

Turning 30: New Ideas in Inductive Logic Programming

Andrew Cropper
Sebastijan Dumančić
Stephen H. Muggleton

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.

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IJCAI Conference 2019 Conference Paper

Playgol: Learning Programs Through Play

Andrew Cropper

Children learn though play. We introduce the analogous idea of learning programs through play. In this approach, a program induction system (the learner) is given a set of user-supplied build tasks and initial background knowledge (BK). Before solving the build tasks, the learner enters an unsupervised playing stage where it creates its own play tasks to solve, tries to solve them, and saves any solutions (programs) to the BK. After the playing stage is finished, the learner enters the supervised building stage where it tries to solve the build tasks and can reuse solutions learnt whilst playing. The idea is that playing allows the learner to discover reusable general programs on its own which can then help solve the build tasks. We claim that playing can improve learning performance. We show that playing can reduce the textual complexity of target concepts which in turn reduces the sample complexity of a learner. We implement our idea in Playgol, a new inductive logic programming system. We experimentally test our claim on two domains: robot planning and real-world string transformations. Our experimental results suggest that playing can substantially improve learning performance.

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JELIA Conference 2019 Conference Paper

SLD-Resolution Reduction of Second-Order Horn Fragments

Sophie Tourret
Andrew Cropper

Abstract We present the derivation reduction problem for SLD-resolution, the undecidable problem of finding a finite subset of a set of clauses from which the whole set can be derived using SLD-resolution. We study the reducibility of various fragments of second-order Horn logic with particular applications in Inductive Logic Programming. We also discuss how these results extend to standard resolution.

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JELIA Conference 2019 Conference Paper

Typed Meta-interpretive Learning of Logic Programs

Rolf Morel
Andrew Cropper
C. -H. Luke Ong

Abstract Meta-interpretive learning (MIL) is a form of inductive logic programming that learns logic programs from background knowledge and examples. We claim that adding types to MIL can improve learning performance. We show that type checking can reduce the MIL hypothesis space by a cubic factor. We introduce two typed MIL systems: Metagol \(_{T}\) and HEXMIL \(_{T}\), implemented in Prolog and Answer Set Programming (ASP), respectively. Both systems support polymorphic types and can infer the types of invented predicates. Our experimental results show that types can substantially reduce learning times.

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IJCAI Conference 2016 Conference Paper

Learning Higher-Order Logic Programs through Abstraction and Invention

Andrew Cropper
Stephen H. Muggleton

Many tasks in AI require the design of complex programs and representations, whether for programming robots, designing game-playing programs, or conducting textual or visual transformations. This paper explores a novel inductive logic programming approach to learn such programs from examples. To reduce the complexity of the learned programs, and thus the search for such a program, we introduce higher-order operations involving an alternation of Abstraction and Invention. Abstractions are described using logic program definitions containing higher-order predicate variables. Inventions involve the construction of definitions for the predicate variables used in the Abstractions. The use of Abstractions extends the Meta-Interpretive Learning framework and is supported by the use of a user-extendable set of higher-order operators, such as map, until, and ifthenelse. Using these operators reduces the textual complexity required to express target classes of programs. We provide sample complexity results which indicate that the approach leads to reductions in the numbers of examples required to reach high predictive accuracy, as well as significant reductions in overall learning time. Our experiments demonstrate increased accuracy and reduced learning times in all cases. We believe that this paper is the first in the literature to demonstrate the efficiency and accuracy advantages involved in the use of higher-order abstractions.

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IJCAI Conference 2016 Conference Paper

Logic-Based Inductive Synthesis of Efficient Programs

Andrew Cropper

Inductive programming approaches typically rely on an Occamist bias to select hypotheses with minimal textual complexity. This approach, however, fails to distinguish between the efficiencies of hypothesised programs, such as merge sort (O(n log n)) and bubble sort (O(n2)). We address this issue by introducing techniques to learn logic programs with minimal resource complexity. We describe an algorithm proven to learn minimal resource complexity robot strategies, and we propose future work to generalise the approach to a broader class of programs.

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IJCAI Conference 2015 Conference Paper

Learning Efficient Logic Programs

Andrew Cropper

Most logic-based machine learning algorithms rely on an Occamist bias where textual simplicity of hypotheses is optimised. This approach, however, fails to distinguish between the efficiencies of hypothesised programs, such as quick sort (O(n log n)) and bubble sort (O(n2 )). We address this issue by considering techniques to minimise both the resource complexity and textual complexity of hypothesised programs. We describe an algorithm proven to learn optimal resource complexity robot strategies, and we propose future work to generalise this approach to a broader class of logic programs.

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IJCAI Conference 2015 Conference Paper

Learning Efficient Logical Robot Strategies Involving Composable Objects

Andrew Cropper
Stephen H. Muggleton

Most logic-based machine learning algorithms rely on an Occamist bias where textual complexity of hypotheses is minimised. Within Inductive Logic Programming (ILP), this approach fails to distinguish between the efficiencies of hypothesised programs, such as quick sort (O(n log n)) and bubble sort (O(n2 )). This paper addresses this issue by considering techniques to minimise both the textual complexity and resource complexity of hypothesised robot strategies. We develop a general framework for the problem of minimising resource complexity and show that on two robot strategy problems, 1) Postman 2) Sorter (recursively sort letters for delivery), the theoretical resource complexities of optimal strategies vary depending on whether objects can be composed within a strategy. The approach considered is an extension of Meta-Interpretive Learning (MIL), a recently developed paradigm in ILP which supports predicate invention and the learning of recursive logic programs. We introduce a new MIL implementation, MetagolO, and prove its convergence, with increasing numbers of randomly chosen examples to optimal strategies of this kind. Our experiments show that MetagolO learns theoretically optimal robot sorting strategies, which is in agreement with the theoretical predictions showing a clear divergence in resource requirements as the number of objects grows. To the authors’ knowledge this paper is the first demonstration of a learning algorithm able to learn optimal resource complexity robot strategies and algorithms for sorting lists.

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