Learning in the Presence of Partial Explanations

Abstract 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 a 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 additional information in the scientific process. It is shown that the 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, a more sophisticated model of science, are demonstrated. Inadequacies in Gold's paradigm of language learning are investigated. It is argued that Gold's model fails to incorporate certain additional information that children get from their environment. Children are sometimes told about some grammatical rule that enumerates elements of the language. It is argued that these rules are a kind of additional information. They enable children to see in advance elements that are yet to appear in their environments. Also, children are being given some information about what is not in the language. Sometimes, they are rebuked for making incorrect utterances, or are told of a rule that enumerates certain non-elements of the language. An attempt has been made to extend Gold's model to incorporate both the above types of additional information. It is shown that either type of additional information enhances the learning capability of formal language learning devices.