Evolutionary construction of derivations in classical propositional logic using a symbolic-connectionist representation

This report introduces a way derivations in classical propositional logic can be constructed using evolutionary algorithms. The derivations are represented by connectionist systems. There are three kinds of nodes constituting these systems: formula nodes that generate signal in the form of strings of symbols, "modus ponens" nodes that transform incoming signal according to the "modus ponens" rule, and substitution nodes that transform incoming signal by applying the substitution rule. This work presents initial research on an approach that is a part of our quest for efficient construction of derivations using various logics and constrained in various ways. The final part of this report outlines limitations encountered in our initial experiments and the ways the proposed approach can be improved.