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%A Kostis Vezerides %A Dr. Athanasios Kehagias %T The Liar and Related Paradoxes:Fuzzy Truth Value Assignment for Collections of Self-Referential Sentences %X We study self-referential sentences of the type related to the Liar paradox. In particular, we consider the problem of assigning consistent fuzzy truth values to collections of self-referential sentences. We show that the problem can be reduced to the solution of a system of nonlinear equations. Furthermore, we prove that, under mild conditions, such a system always has a solution (i.e. a consistent truth value assignment) and that, for a particular implementation of logical ``and'', ``or'' and ``negation'', the ``mid-point'' solution is always consistent. Next we turn to computational issues and present several truth-value assignment algorithms; we argue that these algorithms can be understood as generalized sequential reasoning. In an Appendix we present a large number of examples of self-referential collections (including the Liar and the strengthened Liar), we formulate the corresponding truth value equations and solve them analytically and/ or numerically. %D 2003 %K Self-reference, liar paradox, truth, fuzzy logic, nonlinear equations, root finding algorithms %L cogprints3171