A summary of investigations into three and four valued logics
George Epstein · International Symposium on Multiple-Valued Logic · 1978
There are a number of basic 3 and 4-valued relationships which have been neglected in the literature. Some of these are relationships which involve key connectives such as strong negation. The latter operation has logical properties corresponding to electrical properties of inverters which are used today in the design of all binary computers (and also used indirectly through the use of NAND or NOR circuits, at the feedback paths within flip-flop circuits, and at the inner inversion points of certain cascaded amplifiers). The reason for such neglect seems to be two-fold: (1) The technical development for general n camouflages specifics for certain low values, such as n=2, 3, or 4; and (2) The concommitant avoidance of immediate practical applications, encourages neglect of practical relationships which are needed by the computer scientist or engineer.The theoretical background for this work occurs as early as 1941, with the algebras of G. Moisil. The inability of these algebras to model Łukasiewicz logics with more than 4 values was noted in 1968 by A. Rose. There are similar results for the P-algebras of Epstein and Horn with either the Meskhi or Cignoli conditions, as reported in the Bulletin of the Section of Logic, Polish Academy of Sciences, 6, #4, pp.156-160, 1977.The practical reason for focus on the 3 and 4-valued cases is the continuing interest in 3-valued digital circuitry and computers, evidenced in our 8 annual symposia on multiple-valued logic of this decade, and the most recent application to 4-valued digital circuitry by Signetics Corporation, reported in May, 1977 at the Seventh International Symposium on Multiple-valued Logic at Charlotte, North Carolina. This encourages a fresh look at interconnections and relationships which hold for the 3 and 4-valued cases, with special emphasis on the key connectives which appear in practical applications.