Modeling and Stability Analysis of a Truth Maintenance System Neural Network
Artificial intelligence expert systems problems are shown to be solved by the novel use of a new neural network formulation, the Boolean neural network. Following the Truth Maintenance System form of knowledge representation, known facts are represented by neurons and the interconnections among the neurons form the actual knowledge base. The network finds valid solutions (equilibrium points) representing a consistent set of facts provided such a solution exits. The hardware implementation of such a network operates asynchronously with the use of simple discrete components and converges to (possibly non-zero) equilibrium points provided these points exist. In order to prove the stability of such candidate equilibrium points, the asynchronous Boolean logic system is mathematically transformed to a synchronous algebraic set of dynamic equations which retain the original candidate equilibrium points. These equilibrium points are translated to the origin to use a Lyapunov stability criterion for discrete systems. Examples are shown which model different knowledge bases, and steps are also given to analyze the stability of such knowledge bases.