Artificial intelligence and analogical demostration: strategies, solutions and educational importance

Abstract

The present communication describes the solution strategies that can be drawn from two puzzles (the jigsaw puzzle and the tangram puzzle) and the analogue reasoning from Psichology. We conclude than in all the three cases the mental activity involved is an Analogical Demostration: starts with a certain "givens" and ends up with an analogical construction very similar to the demostration in logic. The analogical demostration uses (as is the case in logic) rules in the form of definitions, principles and theorems, analogical in this case, that can lead the demostration to valid "trayectories", equivalent to forward or backward reasoning. We show in our work that occasionally the demostrator makes use of pure logical reasoning in order to find its way in the analogical demostration. Additionally in this communication we describe the heuristics that have been used in Artificial Intelligence for this kind of problems. The Al solutions are for the moment confined to the simbolic paradigm with its limitations. We propose that the use of parallelism in the form of neural nets will solve some of the present limitations. Finally we propose also that the analogical demostration can be a very valuable instrument as a pre-training for demostration in mathematics at elementary and intermediate level.