Construction of a canonical model for a first-order non-Fregean logic with a connective for reference and a total truth predicate

Detalhes bibliográficos
Autor(a) principal: Lewitzka, Steffen
Data de Publicação: 2012
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UFBA
Texto Completo: http://repositorio.ufba.br/ri/handle/ri/14883
Resumo: Texto completo: acesso restrito. p. 1083-1109
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spelling Lewitzka, SteffenLewitzka, Steffen2014-04-29T17:07:43Z20121367-0751http://repositorio.ufba.br/ri/handle/ri/14883v. 84, n. 2Texto completo: acesso restrito. p. 1083-1109Logics with quantifiers that range over a model-theoretic universe of propositions are interesting for several applications. For example, in the context of epistemic logic the knowledge axioms can be expressed by the single sentences ∀x.(Kix → x), and in a truth-theoretical context an analogue to Tarski's T-scheme can be expressed by the single axiom ∀x.(x:true ↔ x). In this article, we consider a first-order non-Fregean logic, originally developed by Sträter, which has a total truth predicate and is able to model propositional self-reference. We extend this logic by a connective ‘<’ for propositional reference and study semantic aspects. φ < ψ expresses that the proposition denoted by formula ψ says something about (refers to) the proposition denoted by φ. This connective is related to a syntactical reference relation on formulas and to a semantical reference relation on the propositional universe of a given model. Our goal is to construct a canonical model, i.e. a model that establishes an order-isomorphism from the set of sentences (modulo alpha-congruence) to the universe of propositions, where syntactical and semantical reference are the respective orderings. The construction is not trivial because of the impredicativity of quantifiers: the bound variable in ∃x.φ ranges over all propositions, in particular over the proposition denoted by ∃x.φ itself. Our construction combines ideas coming from Sträter's dissertation with the algebraic concept of a canonical domain, which is introduced and studied in this article.Submitted by Edileide Reis (leyde-landy@hotmail.com) on 2014-04-29T17:07:42Z No. of bitstreams: 1 Steffen Lewitzka.pdf: 293466 bytes, checksum: d22e2339097905567f9adcf4378ad6ac (MD5)Made available in DSpace on 2014-04-29T17:07:43Z (GMT). No. of bitstreams: 1 Steffen Lewitzka.pdf: 293466 bytes, checksum: d22e2339097905567f9adcf4378ad6ac (MD5) Previous issue date: 2012http://dx.doi.org/ 10.1093/jigpal/jzr050reponame:Repositório Institucional da UFBAinstname:Universidade Federal da Bahia (UFBA)instacron:UFBANon-Fregean logicPropositional quantifiersImpredicativityPropositional (self-) referenceTruth theoryConstruction of a canonical model for a first-order non-Fregean logic with a connective for reference and a total truth predicateLogic Journal of the IGPLinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article10000-01-01info:eu-repo/semantics/openAccessengORIGINALSteffen Lewitzka.pdfSteffen Lewitzka.pdfapplication/pdf293466https://repositorio.ufba.br/bitstream/ri/14883/1/Steffen%20Lewitzka.pdfd22e2339097905567f9adcf4378ad6acMD51LICENSElicense.txtlicense.txttext/plain1345https://repositorio.ufba.br/bitstream/ri/14883/2/license.txt0d4b811ef71182510d2015daa7c8a900MD52TEXTSteffen Lewitzka.pdf.txtSteffen Lewitzka.pdf.txtExtracted texttext/plain90714https://repositorio.ufba.br/bitstream/ri/14883/3/Steffen%20Lewitzka.pdf.txt2057dc46c87c1b0f70fe11637b386fa4MD53ri/148832022-07-05 14:02:51.957oai:repositorio.ufba.br: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Repositório InstitucionalPUBhttp://192.188.11.11:8080/oai/requestopendoar:19322022-07-05T17:02:51Repositório Institucional da UFBA - Universidade Federal da Bahia (UFBA)false
dc.title.pt_BR.fl_str_mv Construction of a canonical model for a first-order non-Fregean logic with a connective for reference and a total truth predicate
dc.title.alternative.pt_BR.fl_str_mv Logic Journal of the IGPL
title Construction of a canonical model for a first-order non-Fregean logic with a connective for reference and a total truth predicate
spellingShingle Construction of a canonical model for a first-order non-Fregean logic with a connective for reference and a total truth predicate
Lewitzka, Steffen
Non-Fregean logic
Propositional quantifiers
Impredicativity
Propositional (self-) reference
Truth theory
title_short Construction of a canonical model for a first-order non-Fregean logic with a connective for reference and a total truth predicate
title_full Construction of a canonical model for a first-order non-Fregean logic with a connective for reference and a total truth predicate
title_fullStr Construction of a canonical model for a first-order non-Fregean logic with a connective for reference and a total truth predicate
title_full_unstemmed Construction of a canonical model for a first-order non-Fregean logic with a connective for reference and a total truth predicate
title_sort Construction of a canonical model for a first-order non-Fregean logic with a connective for reference and a total truth predicate
author Lewitzka, Steffen
author_facet Lewitzka, Steffen
author_role author
dc.contributor.author.fl_str_mv Lewitzka, Steffen
Lewitzka, Steffen
dc.subject.por.fl_str_mv Non-Fregean logic
Propositional quantifiers
Impredicativity
Propositional (self-) reference
Truth theory
topic Non-Fregean logic
Propositional quantifiers
Impredicativity
Propositional (self-) reference
Truth theory
description Texto completo: acesso restrito. p. 1083-1109
publishDate 2012
dc.date.issued.fl_str_mv 2012
dc.date.accessioned.fl_str_mv 2014-04-29T17:07:43Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
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status_str publishedVersion
dc.identifier.uri.fl_str_mv http://repositorio.ufba.br/ri/handle/ri/14883
dc.identifier.issn.none.fl_str_mv 1367-0751
dc.identifier.number.pt_BR.fl_str_mv v. 84, n. 2
identifier_str_mv 1367-0751
v. 84, n. 2
url http://repositorio.ufba.br/ri/handle/ri/14883
dc.language.iso.fl_str_mv eng
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