3値M-演算系とその標準形

概要

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This paper presents new normal forms in 3-valued logic. The normal forms are based on the M-AND (Modified-AND), M-MID (Modified-MIDDLE), M-OR (Modified-OR) and NOT operations. Especially, we present M-MID operation, but other logical operations introduced by J.Lukasiewiez, are defined as follows, [numerical formula] where x_i, x_j are 3-valued variables, and + is the ordinary addition. We show some properties between the M-AND, M-OR and NOT operations and prove that the set {M-AND, M-MID, M-OR, NOT} forms functionally complete. Furthermore, the normal form of the 3-valued logical function can be expressed as follows, f(x_1, x_2, ・・・, x_n) = [numerical formula] where [numerical formula] is M-OR operation over (a_1, a_2, ・・・, a_n) ∈ L^n and II^^n__(i=1) is M-AND operation on i. Also we present a synthesis algorithm to construct any 3-valued function by using the normal form, and describe the way to simplify this function.
北海道東海大学の論文
2004-03-25