Automated Theory Formation Applied to Four Learning Tasks

Automated theory formation involves amongst other things the production of examples concepts and statements relating the concepts The HR program has been developed to form theo ries in mathematical domains by calculating examples inventing concepts making conjectures and settling conjectures using the Otter theorem prover and MACE model generator In addition to providing a plausible model for automated the ory formation in pure mathematics HR has been applied to other problems in Arti cial Intelligence We discuss HR s application to inducing de nitions from examples scienti c discovery prob lem solving and puzzle generation For each problem we look at how a theory formation approach can be applied and men tion some initial results from the application of HR Our aim is not to describe the applications in great detail but rather to provide an overview of how HR is used for these problems This will facilitate a comparison of the problems and discussion of the e ectiveness of theory formation for these tasks Our second aim is to compare HR with the Progol machine learning program We do this rst by looking at the con cept formation these programs perform Also by suggesting how Progol could be used for the applications mentioned above we compare the programs in terms of how they can be applied