title: The Liar and Related Paradoxes:Fuzzy Truth Value Assignment for Collections of Self-Referential Sentences
creator: Vezerides, Kostis
creator: Kehagias, Dr. Athanasios
subject: Cognitive Psychology
subject: Logic
description: 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.
date: 2003-09
type: Preprint
type: NonPeerReviewed
format: application/postscript
identifier: http://cogprints.org/3171/1/FL1025.ps
identifier:   Vezerides, Kostis and Kehagias, Dr. Athanasios  (2003) The Liar and Related Paradoxes:Fuzzy Truth Value Assignment for Collections of Self-Referential Sentences.  [Preprint]     
relation: http://cogprints.org/3171/