The MacLaurin's and Taylor's series expansions of the symbolic multiple valued logic functions

Generally, multiple valued logic algebra is based on the number system of modulo-M. In this paper, characters a, b, c,... each of which represents the independent state, are regarded as the elements of the symbolic multiple valued logic. By using set theory, the symbolic multiple valued logic and their functions are defined. Variations of the symbolic logic function due to the variation of a variable and their properties are suggested and analyzed. With these variations, the MacLaurin's and Taylor's series expansions of the symbolic multiple valued logic functions are proposed and proved. The theory and properties may be available in the design and modeling of the hardware or intelligent system.