Abstract
This chapter discusses the applications of mathematical logic in new generation computing. In computer design and testing, artificial intelligence, and supercomputing many problems are expressed as a sequence of operations on Boolean functions. With the binary system, a computer can evaluate the truth value of logic expressions by making use of three logic gates, NOT, AND, and OR. While conventional computers are built around an adder that sums up binary numbers, matrix logic processors must be built around multiplicative gates that multiply binary vectors. Multiplicative processors find applications for a wide range of problems. Matrix logic algebra forms a foundation for multiplicative processors, just as Boolean logic algebra formed a foundation for conventional additive processors. Matrix logic serves to unify the fields of logic programming and artificial intelligence and, is the missing link between knowledge engineering and parallel computer architecture.
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