We investigate the appropriate design and implementation of an Inductive Learning Alogrithm with a Neural Network in order to solve both inconsistent indexing and incomplete query problems on the web. Specifically, the proposed system based queries and documents in the field of Mathematics shows how inductive learning method and neural networks can apply to information retreival. Also, this study examines all of parameters of the neural networks -- the number of node in input and output, hidden layer size and learning parameters etc. -- which are significant in determining how well the neural network will converge.