Learning in the Presence of Partial Explanations 1

The effect of a partial explanation as additional information in the learning process is investigated. A scientist performs experiments to gather experimental data about some phenomenon, and then, tries to construct an explanation (or theory) for the phenomenon. A plausible model for the practice of science is an inductive inference machine (scientist) learning a program (explanation) from graph (set of experiments) of a recursive function (phenomenon). It is argued that this model of science is not an adequate one, as scientists, in addition to performing experiments, make use of some approximate partial explanation based on the "state of the art " knowledge about that phenomenon. An attempt has been made to model this partial explanation as an additional information in the scientific process. It is shown that inference capability of machines is improved in the presence of such a partial explanation. The quality of this additional information is modeled using certain "density " notions. It is shown that additional information about a "better " quality partial explanation enhances the inference capability of learning machines as scientists more than a "not so good " partial explanation. Similar enhancements to inference of approximations