Abstract: A digital set theoretic system is disclosed that expands the reasoning capability from reasoning with probability measures to reasoning with set theory measures and other Venn diagram type operations using linear transformations and power series transformations, and appropriate hardware and software implementations. This expansion also leads to an increase in precision of the output which can be provided by a hardwired power series expansion. A recursive power series expansion increases this precision while reducing the spatial requirements. The system also enhances flexibility by allowing the constants of the power series expansion to be selectable.

Abstract: The present system performs linear transformations on input probabilities and produces outputs which indicate the likelihood of one or more events. The transformation performed is a product of linear transforms such as P.sub.o =[A.sub.j P.sub.j +B.sub.j ].multidot.[A.sub.k P.sub.k +B.sub.k ] where P.sub.j and P.sub.k are input probabilities, P.sub.o is an output event probability and A.sub.j, B.sub.j, A.sub.k and B.sub.k are transformation constants. The system includes a basic processing unit or computational unit which performs a probabilistic gate operation to convert two input probability signals into one output probability signal where the output probability is equal to the product of linear transformations of the input probabilities. By appropriate selection of transformation constants logical and probabilistic gates performing the functions of AND, NAND, OR, NOR, XOR, NOT, IMPLIES and NOT IMPLIES can be created.

Abstract: A preprocessing device is disclosed which performs a linear transformation or power series expansion transformation on the input signals to a neural network node. The outputs of the preprocessing device are combined as a product of these linear transformations and compared to a threshold. This processing element configuration, combining a transformation with a product and threshold comparison, performs non-linear transformations between input data and output results. As a result, this processing element will, by itself, produce both linearly and non-linearly separable boolean logic functions. When this processing element is configured in a network, a two layer neural network can be created which will solve any arbitrary decision making function. This element can be configured in a probability based binary tree neural network which is validatable and verifiable in which the threshold comparison operation can be eliminated. The element can also be implemented in binary logic for ultra high speed.

Abstract: This application discloses a system that optimizes a neural network by generating all of the discrete weights for a given neural node by creating a normalized weight vector for each possible weight combination. The normalized vectors for each node define the weight space for that node. This complete set of weight vectors for each node is searched using a direct search method during the learning phase to optimize the network. The search evaluates a node cost function to determine a base point from which a pattern more within the weight space is made. Around the pattern mode point exploratory moves are made which are cost function evaluated. The pattern move is performed by eliminating from the search vectors with lower commonality.