A connectionist approach for rule-based inference using an improved relaxation method

A connectionist mechanism for an inference problem alternative to the usual chaining method is described. The inference problem is within the scope of propositional logic that contains no variables and with some enhanced knowledge representation facilities. The method is an application of mathematical programming where knowledge and data are transformed into constraint equations. In the network, the nodes represent propositions and constraint equations, and the violation of constraints is formulated as an energy function. The inference is realized as a minimization process of the energy function using the relaxation method to search for a truth value distribution that achieves the optimum consistency with the given knowledge and data. A modified relaxation method is proposed to improve the computational inefficiencies associated with the optimization process. The behavior of the method is analyzed through examples of deductive and abductive inference and of inference with unorganized knowledge