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The k-valued Kleene functions over Kleene algebra (instead of over Post algebra) are defined. Multivalued logic and fuzzy logic are studied in the light of lattice theory. It is shown that all Kleene k-valued logic (k = 3 or more) have the same algebraic structure as fuzzy logic through lattice isomorphism. As a by-product, an asymptotic formula and upper bound for enumeratinlg fuzzy switching functions of n variables is obtained. Some conditions for minimizing Kleene functions are discussed, and an efficient generalized Karnaught map method is described. An application is made of the above Kleene multivalued logic to the fault diagnosis of combinational circuits. The fault norm of a combinational circuit is introduced and it is shown that this norm contains all the information about the fault situation of the circuit, and can hence be used to solve such problems as fault analysis, fault diagnosis, and detection of circuit redundance and fault masking.
Date of Publication: July 1984