Extraction of Low Order Boolean Rules from Trained Neural Networks using a Computer Algebra System

Abstract:  This paper deals with the extraction of low order and hence meaningful Boolean rules from trained neural networks. Tsukimoto and Morita [1] have developed a scalar algebraic model for classical logic and an algorithm for extracting the nearest Boolean rule from the units of a neural network. We deal with its implementation in the computer algebra system Derive for Windows and discuss the further development of the algorithm to networks whose variables are not necessarily Booleanly `high' or `low'. In essence a Boolean function can be expressed as a multi-linear function which in turn can be expressed as a logic vector, for example, the Boolean expression x y x y xy = + - in the scalar model, which can be written as xy x y y x + - + - ( ) ( ) 1 1 . In turn this can be represented as a vector of atoms, where xy = [ , , , ] 1 0 0 0 and x y = [ , , , ] 1 0 0 0 etc. Hence the logic vector for x y = [ , , , ] 1110 , which is of course the truth table for x y . The unit of a neural network...