Grounding Fingers, Words and Numbers in a Cognitive Developmental Robot Alessandro Di Nuovo a,b , Vivian M. De La Cruz c , Angelo Cangelosi a a Centre for Robotics and Neural Systems, Plymouth University, UK b Faculty of Engineering and Architecture, Kore University, Italy c University of Messina, Italy Abstract— The young math learner must make the transition from a concrete number situation, such as that of counting objects (fingers often being the most readily available), to that of using a written symbolic form that stands for the quantities the sets of objects come to represent. This challenging process is often coupled to that of learning a verbal number system that is not always transparent to children. A number of theoretical approaches have been advanced to explain aspects of how this transition takes place in cognitive development. The results obtained with the model presented here, show that a symbol grounding approach can be used to implement aspects of this transition in a cognitive robot. In the current extended version, the model develops finger and word representations, through the use of finger counting and verbal counting strategies, together with the visual representations of learned number symbols, which it uses to perform basic arithmetic operations. In the final training phases, the model is able to do this using only the number symbols as addends. We consider this an example of symbolic grounding, in that through the direct sensory experience with the body (finger counting), a category of linguistic symbol is learned (number words), and both types of representations subsequently serve to ground higher level (numerical) symbols, which are later used exclusively to perform the arithmetic operations. Keywords—symbol grounding; cognitive developmental robotics; number learning. I. INTRODUCTION Thanks to recent technological advances and the increasing interest in the Cognitive Developmental Robotics (CDR) paradigm [1], many popular platforms for scientific research have been designed in order to resemble the shape of the human body. The motivation behind this strongly humanoid design is the embodied cognition hypothesis, which affirms that all aspects of cognition are shaped by aspects of the body. Thus CDR is based on a synthetic approach that aims to provide new understanding on how human beings develop their higher cognitive functions. To implement the CDR paradigm, bodies of many new popular robotic platforms for research (e.g. iCub [2], NAO [3]) are designed to resemble the shape of a human body, and in particular that of a child. The motivation behind this strongly humanoid design is the embodied cognition hypothesis, that human-like manipulation plays a vital role in the development of human cognition. A baby learns many cognitive skills, with one of the most important being how to use language for example, by interacting with its environment and other humans, by using its senses (as a number of disembodied artificial neural network models have shown, e.g. [4], [5]), but also through the use of its limbs. Consequently, the form of the human body also plays a significant role in determining its internal model of the world. A humanoid robot is, thus, designed to test this hypothesis by allowing cognitive learning scenarios to be acted out by an accurate reproduction of the perceptual system and the movements of a small child, so that it can interact with the world in the same way that a child does. The use of humanoid platforms can help scientists studying cognitive development and working in disciplines such as developmental psychology or epigenetic robotics, increase their understanding of cognitive systems. However, in experiments with robotic platforms, there are many situations in which realistic computer simulation is preferred to the use of real platforms. Among the advantages, we recall that computer simulation allows one to study the behavior of several types of embodied agents without facing the problem of building in advance, and maintaining, a complex hardware device, it can be used as a tool for testing algorithms in order to quickly check for any major problems prior to using the physical robot, drastically reducing the time of the experiments such as in evolutionary robotics and reinforcement learning. For these reasons researchers often use computer simulation as the “physical” body for their cognitive models, e.g. [6], [7]. In this context, we use the iCub humanoid robot platform, both real and simulated, as the body for an artificial neural network model with the aim of exploring whether finger counting and the association of number words (or tags) to the fingers, could serve to bootstrap the representation of numbers and number symbols in the cognitive robot. In this paper, we discuss the experimental results of the design and implementation with the iCub platform simulator of an extension of the cognitive model presented in [8]. The rest of the paper is organized as follows: Section II introduces the related work giving particular emphasis to other connectionist models; Section III presents the material and methods used in this work; Section IV details the experiments and discuss the numerical results obtained; Section V 978-1-4799-4549-8/14/$31.00 ©2014 IEEE 9