Computation of Fuzzy Truth Values for The Liar and Related Self-Referential Systems

Ath. Kehagias and K. Ezerides

We study the Liar paradox and related systems of self-referential sentences. Specifically, we consider the problem of assigning consistent fuzzy truth values to systems of self-referential sentences. We show that this problem can be reduced to the solution of a system of nonlinear equations and we prove that,under certain conditions, a solution (i.e. a consistent truth value assignment) always exists. Furthermore, we show that, for the min/max implementation of logical “and ”/“or” and the standard negation, the “mid-point” solution is always consistent.