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TY - GEN ID - cogprints3171 UR - http://cogprints.org/3171/ A1 - Vezerides, Kostis A1 - Kehagias, Dr. Athanasios TI - The Liar and Related Paradoxes:Fuzzy Truth Value Assignment for Collections of Self-Referential Sentences Y1 - 2003/09// N2 - 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. AV - public KW - Self-reference KW - liar paradox KW - truth KW - fuzzy logic KW - nonlinear equations KW - root finding algorithms ER -