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FL1025.ps

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We study selfreferential sentences of the type related to the Liar paradox. In particular, we consider the problem of assigning consistent fuzzy truth values to collections of selfreferential 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 ``midpoint''
solution is always consistent. Next we turn to computational issues and present several truthvalue 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 selfreferential collections (including the Liar and the strengthened Liar), we formulate the corresponding truth value equations and solve them analytically and/ or numerically.

Vezerides
Kostis

Kehagias
Athanasios
Dr.
kehagiat
Selfreference, liar paradox, truth, fuzzy logic, nonlinear equations, root finding algorithms
TRUE
FALSE
 cogpsy
 phillogic
The Liar and Related Paradoxes:Fuzzy Truth Value Assignment for Collections of SelfReferential Sentences
published
200309
public