Improving the time efficiency of proving theorems using a learning mechanism

Abstract

In this paper, we develop a new approach for enhancing the time efficiency of proving theorems by using a learning mechanism. A system is proposed for analyzing a set of theorems and observing those features that often affect the speed at which the theorems are proved. The system uses the learning mechanism for choosing between two well known theorem-provers, namely, Resolution–Refutation (TGTP) and Semantic Trees (HERBY). A three-step process has been implemented. The first step is to prove a set of theorems using the above two theorem provers. A training set of two classes of theorems is thus created. Each class represents those theorems that have been proven in less time using a particular theorem prover. The second step is to train neural networks on both classes of theorems in order to construct an internal representation of the decision boundary between the two classes. In the last step, a voting scheme is invoked in order to combine the decisions of the individual neural networks into a final decision. The results achieved by the system when working on the standard theorems of the Stickel Test Set are shown. Those results confirm the feasibility of our approach to inte-grate a learning mechanism into the process of automated theorem proving.