TMLNN: triple-valued or multiple-valued logic neural network

Abstract

We discuss the problem of representing and processing triple-valued or multiple-valued logic knowledge using neural network in this paper. A novel neuron model, triple-valued or multiple-valued logic neuron (TMLN), is presented. Each triple-valued or multiple-valued logic neuron can represent a triple-valued or multiple-valued logic rule by itself. We will show that there are two triple-valued or multiple-valued logic neurons: TMLN-AND (triple-valued or multiple-valued "logic and" neuron) and TMLN-OR (triple-valued or multiple-valued "logic or" neuron). TMLN-AND can realize triple-valued or multiple-valued "logic and" while TMLN-OR can realize triple-valued or multiple-valued "logic or." Two simplified triple-valued or multiple-valued logic neuron models are also presented. We can show that a multiple-layer neural network (TMLNN) made up of triple-valued or multiple-valued logic neurons can implement a triple-valued or multiple-valued logic inference system. The training algorithm for TMLNN is presented and can be shown to converge. In our model, triple-valued or multiple-valued logic rules can be extracted from TMLNN with ease. TMLNN can thus form a base for representing logic knowledge using neural network.