---
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.
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  - ''
  - kehagiat
creators_name:
  - family: Vezerides
    given: Kostis
    honourific: ''
    lineage: ''
  - family: Kehagias
    given: Athanasios
    honourific: Dr.
    lineage: ''
date: 2003-09
date_type: published
datestamp: 2003-10-04
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dir: disk0/00/00/31/71
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eprint_status: archive
eprintid: 3171
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full_text_status: public
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keywords: 'Self-reference, liar paradox, truth, fuzzy logic, nonlinear equations, root finding algorithms'
lastmod: 2011-03-11 08:55:21
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rev_number: 10
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status_changed: 2007-09-12 16:48:49
subjects:
  - cog-psy
  - phil-logic
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title: The Liar and Related Paradoxes:Fuzzy Truth Value Assignment for Collections of Self-Referential Sentences
type: preprint
userid: 4320
volume: ~
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