Logical controls via Boolean rule matrix transformations

Abstract

The model described uses Boolean rule matrices that are equivalent to implication digraphs to transform truth states associated with rule conditions into deduced or abduced truth states. Such transformations realize prepositional logic to deduce controls for complex real-time noninteractive systems. The algorithm runs in deterministically polynomial time and is simple for easy implementation. The rule matrix is decomposable into subsystems with rule submatrices for distributed processing in multiple microprocessors. A single transformation of a truth state fires every entire implication path for which the initial, i. e., root, condition is true, whereas a user interactive production system fires a single rule at a time and uses the output in the firing of other rules. Predicate logic is more powerful but is too slow. It also has the fatal flaw of being unending when a solution does not exist in the data space. Our method will perform stimulus-response type control that humans use to perform such amazing feats as fly airplanes, ride bicycles, or control nuclear reactors. It promises to bring low-cost automation to complex real-time systems.