Intrinsic Lexical Intentionality and the Mathematics of Homomorphism

Abstract

Moisl [1, 2] proposed a model of how the brain implements intrinsic intentionality with respect to lexical and sentence meaning, where 'intrinsic' is understood as 'independent of interpretation by observers external to the cognitive agent'. The discussion in both was mainly philosophical and qualitative; the present paper gives a mathematical account of the distance structure preservation that underlies the proposed mechanism of intrinsic intentionality. The three-layer autoassociative multilayer perceptron (aMLP) architecture with nonlinear hidden and linear output layers is the component in the model which generates representations homomorphic with the environment. The discussion first cites existing work which identifies the aMLP as an implementation architecture for principal component analysis (PCA), and then goes on to argue that the homomorphism characteristic of linear functions like PCA extends to aMLPs with nonlinear activation functions in the hidden layer. The discussion is in two main parts: the first part outlines the model, and the second presents the mathematical account.