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The Liar and Related Paradoxes:Fuzzy Truth Value Assignment for Collections of Self-Referential Sentences
The Liar and Related Paradoxes:Fuzzy Truth Value Assignment for Collections of Self-Referential Sentences (Postscript)
The Liar and Related Paradoxes:Fuzzy Truth Value Assignment for Collections of Self-Referential Sentences (Image (PNG))
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.
2003-09
The Liar and Related Paradoxes:Fuzzy Truth Value Assignment for Collections of Self-Referential Sentences
Cognitive Psychology
Logic
Vezerides
Kostis
Kostis Vezerides
Kehagias
Athanasios
Athanasios Kehagias