Lukasiewicz logic arrays

Abstract

Lukasiewicz logic arrays (LLAs) are massively parallel analog computers organized as binary trees of identical processing elements performing either implication, negated implication, or both. The authors have designed and built working 31-cell CMOS VLSI LLA whose cells perform implication. They discuss the representation completeness of Lukasiewicz logic with respect to other multiple-valued logics; describe the architecture of the prototype LLA, its relationship to cellular automata and its VLSI implementation; show how the prototype LLA is programmed; and report on results obtained by programming the prototype LLA as a fuzzy function generator. Because LLAs have both an algebraic and a logical operational semantics, they can be used to implement approximate reasoning systems, including expert systems and neural networks.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>