An explanatory framework for human theorem proving

Abstract

Along the line of the science of reasoning proposed by Alan Bundy [8], we present in this paper a computational theory accounting for human formal deductive competence. Our goal is primarily twofold. For one thing, it is aimed to establish an explanatory framework for human theorem proving. Devised as a computational theory, for another thing, it should also set up a theoretical foundation for deductive systems which simulate the way in which human beings carry out reasoning tasks. As such, the hope is to arrive at systems which learn and plan, which share their experiences with human users in high level communications. The last requirement, we believe, makes such systems ultimately useful. As a computational model, we cast the cognitive activities involved in theorem proving as an interleaving process of metalevel planning and object level verification. Within such a framework, emphasis is put on three kinds of tactics concerning three kinds of declarative knowledge structures. We also account for the acquisition of new tactics and methods, as well as the modifications of existing tactics and methods to suit novel problems. While the fundamental framework is sketched out formally, the mechanisms manipulating tactics and methods are only intended to be suggestive, achieved with the help of examples.

This work was supported by the Deutsche Forschungsgemeinschaft, SFB 3I4 (D2, D3)