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--- 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. altloc: [] chapter: ~ commentary: ~ commref: ~ confdates: ~ conference: ~ confloc: ~ contact_email: ~ creators_id: - '' - 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 department: ~ dir: disk0/00/00/31/71 edit_lock_since: ~ edit_lock_until: ~ edit_lock_user: ~ editors_id: [] editors_name: [] eprint_status: archive eprintid: 3171 fileinfo: /style/images/fileicons/application_postscript.png;/3171/1/FL1025.ps full_text_status: public importid: ~ institution: ~ isbn: ~ ispublished: ~ issn: ~ item_issues_comment: [] item_issues_count: 0 item_issues_description: [] item_issues_id: [] item_issues_reported_by: [] item_issues_resolved_by: [] item_issues_status: [] item_issues_timestamp: [] item_issues_type: [] keywords: 'Self-reference, liar paradox, truth, fuzzy logic, nonlinear equations, root finding algorithms' lastmod: 2011-03-11 08:55:21 latitude: ~ longitude: ~ metadata_visibility: show note: ~ number: ~ pagerange: ~ pubdom: TRUE publication: ~ publisher: ~ refereed: FALSE referencetext: ~ relation_type: [] relation_uri: [] reportno: ~ rev_number: 10 series: ~ source: ~ status_changed: 2007-09-12 16:48:49 subjects: - cog-psy - phil-logic succeeds: ~ suggestions: ~ sword_depositor: ~ sword_slug: ~ thesistype: ~ title: The Liar and Related Paradoxes:Fuzzy Truth Value Assignment for Collections of Self-Referential Sentences type: preprint userid: 4320 volume: ~