Cogprints

The Liar and Related Paradoxes:Fuzzy Truth Value Assignment for Collections of Self-Referential Sentences

Vezerides, Kostis and Kehagias, Dr. Athanasios (2003) The Liar and Related Paradoxes:Fuzzy Truth Value Assignment for Collections of Self-Referential Sentences. [Preprint]

Full text available as:

[img]
Preview
Postscript
1051Kb

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.

Item Type:Preprint
Keywords:Self-reference, liar paradox, truth, fuzzy logic, nonlinear equations, root finding algorithms
Subjects:Psychology > Cognitive Psychology
Philosophy > Logic
ID Code:3171
Deposited By:Kehagias, Dr Athanasios
Deposited On:04 Oct 2003
Last Modified:11 Mar 2011 08:55

Metadata

Repository Staff Only: item control page