Traditional approaches for the analysis of stability of neural networks are quanti tative such as analysis of weight matrixes.This paper presents a logical method based on inference and contradiction analysis and reveals what partial/local structures are unstable factors

which is useful in the design and analysis of neural networks.In the paper

a logical theory of binary neural networks（BNNs） is first presented.Then

the qualitative analysis of the stability of BNNs is given.Finally

the formation of contradiction loops with full-constraint and semi-constraint rules is discussed.The analysis indicates that the existence of contradictory loops inside BNNs is a neces sary condition for BNNs to be unstable

so that it is possible to study the global properties of net works by only analyzing their partial/local structures.