Automated Theory Formation in Pure Mathematics
Automated Theory Formation in Pure Mathematics
Automatic Generation of Implied Constraints
Proceedings of the 2006 conference on ECAI 2006: 17th European Conference on Artificial Intelligence August 29 -- September 1, 2006, Riva del Garda, Italy
Automated conjecture making in number theory using HR, Otter and Maple
Journal of Symbolic Computation
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Stand-alone Artificial Intelligence systems for performing specific types of reasoning - such as automated theorem proving and symbolic manipulation in computer algebra systems - are numerous, highly capable and constantly improving. Moreover, systems which combine various forms of reasoning have repeatedly been shown to be more effective than stand-alone systems. For example, the ICARUS system for reformulating constraint satisfaction problems [1] and the HOMER system for conjecture making in number theory [2]. However, in general, such combinations have been ad-hoc in nature and designedwith a specific task in mind. With little general design consideration or a suitable framework for combining reasoning, in general every new combination has to be built from scratch and the resulting system is often inflexible and difficult to manage. We believe it is imperative that generic frameworks are developed if the field of combining reasoning systems is to progress. Such generic frameworkswould provide standardised rule sets and toolkits to simplify the development of combined systems.