Discrete Mathematics - First Japan Conference on Graph Theory and Applications
Discovering mathematical operator definitions
Proceedings of the sixth international workshop on Machine learning
C4.5: programs for machine learning
C4.5: programs for machine learning
Maple V by example
Theories for mutagenicity: a study in first-order and feature-based induction
Artificial Intelligence - Special volume on empirical methods
Machine Learning - special issue on inductive logic programming
On the notion of interestingness in automated mathematical discovery
International Journal of Human-Computer Studies - Special issue on Machine Discovery
Readings in Knowledge Representation
Readings in Knowledge Representation
Automated Theory Formation in Pure Mathematics
Automated Theory Formation in Pure Mathematics
Discovery of frequent DATALOG patterns
Data Mining and Knowledge Discovery
Journal of Automated Reasoning
Automatic Identification of Mathematical Concepts
ICML '00 Proceedings of the Seventeenth International Conference on Machine Learning
Finding Relations in Polynomial Time
IJCAI '99 Proceedings of the Sixteenth International Joint Conference on Artificial Intelligence
Automatic Invention of Integer Sequences
Proceedings of the Seventeenth National Conference on Artificial Intelligence and Twelfth Conference on Innovative Applications of Artificial Intelligence
Constraint Generation via Automated Theory Formation
CP '01 Proceedings of the 7th International Conference on Principles and Practice of Constraint Programming
Making Conjectures about Maple Functions
AISC '02/Calculemus '02 Proceedings of the Joint International Conferences on Artificial Intelligence, Automated Reasoning, and Symbolic Computation
Employing Theory Formation to Guide Proof Planning
AISC '02/Calculemus '02 Proceedings of the Joint International Conferences on Artificial Intelligence, Automated Reasoning, and Symbolic Computation
The HR Program for Theorem Generation
CADE-18 Proceedings of the 18th International Conference on Automated Deduction
Computing Prime Implicates Incrementally
CADE-11 Proceedings of the 11th International Conference on Automated Deduction: Automated Deduction
Combining superposition, sorts and splitting
Handbook of automated reasoning
Automatic Construction and Verification of Isotopy Invariants
Journal of Automated Reasoning
Structured machine learning: the next ten years
Machine Learning
Boosting Descriptive ILP for Predictive Learning in Bioinformatics
Inductive Logic Programming
Automatic invention of fitness functions with application to scene generation
Evo'08 Proceedings of the 2008 conference on Applications of evolutionary computing
Automatic construction and verification of isotopy invariants
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
Mathematical practice, crowdsourcing, and social machines
CICM'13 Proceedings of the 2013 international conference on Intelligent Computer Mathematics
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The application of Inductive Logic Programming to scientific datasets has been highly successful. Such applications have led to breakthroughs in the domain of interest and have driven the development of ILP systems. The application of AI techniques to mathematical discovery tasks, however, has largely involved computer algebra systems and theorem provers rather than machine learning systems. We discuss here the application of the HR and Progol machine learning programs to discovery tasks in mathematics. While Progol is an established ILP system, HR has historically not been described as an ILP system. However, many applications of HR have required the production of first order hypotheses given data expressed in a Prolog-style manner, and the core functionality of HR can be expressed in ILP terminology. In Colton (2003), we presented the first partial description of HR as an ILP system, and we build on this work to provide a full description here. HR performs a novel ILP routine called Automated Theory Formation, which combines inductive and deductive reasoning to form clausal theories consisting of classification rules and association rules. HR generates definitions using a set of production rules, interprets the definitions as classification rules, then uses the success sets of the definitions to induce hypotheses from which it extracts association rules. It uses third party theorem provers and model generators to check whether the association rules are entailed by a set of user supplied axioms.HR has been applied successfully to a number of predictive, descriptive and subgroup discovery tasks in domains of pure mathematics. We survey various applications of HR which have led to it producing number theory results worthy of journal publication, graph theory results rivalling those of the highly successful Graffiti program and algebraic results leading to novel classification theorems. To further promote mathematics as a challenge domain for ILP systems, we present the first application of Progol to an algebraic domain--we use Progol to find algebraic properties of quasigroups, semigroups and magmas (groupoids) of varying sizes which differentiate pairs of non-isomorphic objects. This development is particularly interesting because algebraic domains have been an important proving ground for both deduction systems and constraint solvers. We believe that AI programs written for discovery tasks will need to simultaneously employ a variety of reasoning techniques such as induction, abduction, deduction, calculation and invention. We argue that mathematics is not only a challenging domain for the application of ILP systems, but that mathematics could be a good domain in which to develop a new generation of systems which integrate various reasoning techniques.