Combining multiple answers for learning mathematical structures from visual observation

Learning general truths from the observation of simple domains and, further, learning how to use this knowledge are essential capabilities for any intelligent agent to understand and execute informed actions in the real world. The aim of this work is the investigation of the automatic learning of mathematical structures from visual observation. This research was conducted upon a system that combines computer vision with inductive logic programming that was first designed to learn protocol behaviour from observation. In this paper we show how transitivity, reflexivity and symmetry axioms could be induced from the noisy data provided by the vision system. Noise in the data accounts for the generation of a large number of possible generalisations by the ILP system, most of which do not represent interesting concepts about the observed domain. In order to automatically choose the best answers among those generated by induction, we propose a method for combining the results of multiple ILP processes by ranking the most interesting answers.