On the notion of interestingness in automated mathematical discovery
International Journal of Human-Computer Studies - Special issue on Machine Discovery
Automated Theory Formation in Pure Mathematics
Automated Theory Formation in Pure Mathematics
Journal of Automated Reasoning
Automatic Identification of Mathematical Concepts
ICML '00 Proceedings of the Seventeenth International Conference on Machine Learning
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
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
Cooperating reasoning processes: more than just the sum of their parts
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
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We describe a flexible approach to automated reasoning, where non-theorems can be automatically altered to produce proved results which are related to the original. This is achieved in the TM system through an interaction of the HR machine learning program, the Otter theorem prover and the Mace model generator. Given a non-theorem, Mace is used to generate examples which support the non-theorem, and examples which falsify it. HR then invents concepts which categorise these examples and TM uses these concepts to modify the original non-theorem into specialised theorems which Otter can prove. The methods employed by TM are inspired by the piecemeal exclusion, strategic withdrawal and counterexample barring methods described in Lakatos's philosophy of mathematics. In addition, TM can also determine which modified theorems are likely to be interesting and which are not. We demonstrate the effectiveness of this approach by modifying non-theorems taken from the TPTP library of first order theorems. We show that, for 98 non-theorems, TM produced meaningful modifications for 81 of them. This work forms part of two larger projects. Firstly, we are working towards a full implementation both of the reasoning and the social interaction notions described by Lakatos. Secondly, we are aiming to show that the combination of reasoning systems such as those used in TM will lead to a new generation of more powerful AI systems.