Dynamic Approximation of Self-Referential Sentences

Abstract

Non-classical logic via approximation of self-referential sentences by dynamical systems are consistently presented. The new 6-valued truth values <T, va, A.V. av,F> (here A=Liar, V=TruthTeller) are presented as a function of the classical truth values & € (0,1), which resulted in a philosophical standpoint known as Suszko's Thesis. Three-valuedtruth tables were created corresponding to Priest's tables of the same name. In the process of constructing 4-valued truth tables, two more new truth values (va, av) were revealed that do not coincide with the four original ones. Therefore, the closed tables turned out to be 6-valued. Prof Dunn's 4-valued truth tables are compared with our 4-valued truth tables.De Morgan's laws are confirmed by six-valued truth tables. Constructed 3-, 4- and 6-valued lattices obeying De Morgan's laws. Keywords: self-reference, dynamic, Liar, TruthTeller.