An Interpretation of Sheldon Klein's Four Valued Analogical Transformational Operator

Abstract

This paper presents a machine implemented encoding of a versatile analogical four-valued n-adic control logic designed for parallelized expert systems as suggested in the works of Klein. The logic allows for a benign dynamic analogical encoding of both syntactic and semantic information into a common notation, the testing of N conditionals in theoretic time O(C), while maintaining the linear growth of information as stressed by Klein. The computer model, a novel formalism of the analytic techniques of Harris, Herdan, Kleene and Levi-Strauss is specifically tailored for natural language processing but may be viewed as a general theorem prover for its applicability in other areas of computer science. Similar logical formulizations using the Klein-4 group in meta-mathematical considerations made independently by both Dubarle and Belnap will be briefly discussed.