will discuss the problem of expressing and dealing with logical knowledge using neural network in this paper. A novel neuron model (triple- or multiple-valued logical neuron, or TMLN) is presented. It can express triple-valued and even multiple-valued logical knowledge. There are two TMLNs, TMLN-AND (triple- or multiple-valued "logical and" neuron) and TMLN-OR (triple- or multiple-valued "logical or" neuron). TMLN-AND can deal with triple- or multiple-valued "logical and" while TMLN-OR can deal with triple- or multiple-valued "logical or". Two simplified TMLNs are presented also. A multi-layer neural network (TMLNN) made up of TMLNs can implement a triple- or multiple-valued logical inference system. The training algorithm for TMLNN is presented and it is proved to converge. Triple- or multiple-valued logical rules can be extracted from TMLNN with easy. TMLNN is a base for expressing logical knowledge using neural network.