creators_name: Vezerides, Kostis
creators_name: Kehagias, Athanasios
creators_id: 
creators_id: kehagiat
type: preprint
datestamp: 2003-10-04
lastmod: 2011-03-11 08:55:21
metadata_visibility: show
title: The Liar and Related Paradoxes:Fuzzy Truth Value Assignment for Collections of Self-Referential Sentences
subjects: cog-psy
subjects: phil-logic
full_text_status: public
keywords: Self-reference, liar paradox, truth, fuzzy logic, nonlinear equations, root finding algorithms
abstract: 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
date_type: published
refereed: FALSE
citation:   Vezerides, Kostis and Kehagias, Dr. Athanasios  (2003) The Liar and Related Paradoxes:Fuzzy Truth Value Assignment for Collections of Self-Referential Sentences.  [Preprint]     
document_url: http://cogprints.org/3171/1/FL1025.ps