This paper presents an algorithm for extract ing propositions from trained neural networks. The algorithm is a decompositional approach which can be applied to any neural network whose output function is monotone such as sig moid function. Therefore, the algorithm can be applied to multi-layer neural networks, re current neural networks and so on. The algorithm does not depend on training methods. The algorithm is polynomial in computational complexity. The basic idea is that the units of neural networks are approximated by Boolean functions. But the computational complexity of the approximation is exponential, so a poly nomial algorithm is presented. The authors have applied the algorithm to several problems to extract understandable and accurate propositions. This paper shows the results for votes data and mushroom data. The algorithm is extended to the continuous domain, where extracted propositions are continuous Boolean functions. Roughly speaking, the representa tion b...