A Note on Abstract Consequence Structures
Autor(a) principal: | |
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Data de Publicação: | 2013 |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Cognitio (São Paulo. Online) |
Texto Completo: | https://revistas.pucsp.br/index.php/cognitiofilosofia/article/view/13640 |
Resumo: | Tarski’s pioneer work on abstract logic conceived consequence structures as a pair (X, Cn) where X is a non empty set (infinite and denumerable) and Cn is a function on the power set of X, satisfying some postulates. Based on these axioms, Tarski proved a series of important results. A detailed analysis of such proofs shows that several of these results do not depend on the relation of inclusion between sets but only on structural properties of this relation, which may be seen as an ordered structure. Even the notion of finiteness, which is employed in the postulates may be replaced by an ordered substructure satisfying some constraints. Therefore, Tarski’s structure could be represented in a still more abstract setting where reference is made only to the ordering relation on the domain of the structure. In our work we construct this abstract consequence structure and show that it keeps some results of Tarski’s original construction. |
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A Note on Abstract Consequence StructuresUma Nota sobre Estruturas Abstratas de ConseqüênciaAbstract logicConsequence operatorsOrder structuresLógica abstrataOperadores de conseqüênciaEstruturas de ordemTarski’s pioneer work on abstract logic conceived consequence structures as a pair (X, Cn) where X is a non empty set (infinite and denumerable) and Cn is a function on the power set of X, satisfying some postulates. Based on these axioms, Tarski proved a series of important results. A detailed analysis of such proofs shows that several of these results do not depend on the relation of inclusion between sets but only on structural properties of this relation, which may be seen as an ordered structure. Even the notion of finiteness, which is employed in the postulates may be replaced by an ordered substructure satisfying some constraints. Therefore, Tarski’s structure could be represented in a still more abstract setting where reference is made only to the ordering relation on the domain of the structure. In our work we construct this abstract consequence structure and show that it keeps some results of Tarski’s original construction.O trabalho pioneiro de Tarski sobre lógica abstrata concebia estruturas de conseqüência como um par (X, Cn) tal que X é um conjunto não vazio e Cn é uma função definida no conjunto das partes de X, satisfazendo alguns postulados. Baseado nesses postulados, Tarski demonstra uma série de resultados importantes. Uma análise detalhada de tais demonstrações mostra que vários desses resultados não dependem da relação de inclusão entre conjuntos, mas apenas das propriedades estruturais dessa relação, que pode ser vista como uma estrutura de ordem. Mesmo a noção de finitude, que é empregada nos postulados, pode ser substituída por uma subestrutura ordenada satisfazendo alguns vínculos. Portanto, a estrutura de Tarski pode ser representada em um contexto ainda mais abstrato onde se faz referência apenas à relação de ordem sobre o domínio da estrutura. Neste trabalho, construímos essa estrutura de conseqüência abstrata e mostramos como ela mantém alguns resultados da estrutura de Tarski original.Pontifícia Universidade Católica de São Paulo2013-02-14info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://revistas.pucsp.br/index.php/cognitiofilosofia/article/view/13640Cognitio: Revista de Filosofia; Vol. 6 No. 1 (2005); 102-109Cognitio: Revista de Filosofia; v. 6 n. 1 (2005); 102-1092316-52781518-7187reponame:Cognitio (São Paulo. Online)instname:Pontifícia Universidade Católica de São Paulo (PUC-SP)instacron:PUC_SPenghttps://revistas.pucsp.br/index.php/cognitiofilosofia/article/view/13640/10143Copyright (c) 2013 http://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessSouza, Edelcio G. de2024-07-01T13:09:36Zoai:ojs.pkp.sfu.ca:article/13640Revistahttps://revistas.pucsp.br/index.php/cognitiofilosofiaPRIhttps://revistas.pucsp.br/index.php/cognitiofilosofia/oairevcognitio@gmail.com2316-52781518-7187opendoar:2024-07-01T13:09:36Cognitio (São Paulo. Online) - Pontifícia Universidade Católica de São Paulo (PUC-SP)false |
dc.title.none.fl_str_mv |
A Note on Abstract Consequence Structures Uma Nota sobre Estruturas Abstratas de Conseqüência |
title |
A Note on Abstract Consequence Structures |
spellingShingle |
A Note on Abstract Consequence Structures Souza, Edelcio G. de Abstract logic Consequence operators Order structures Lógica abstrata Operadores de conseqüência Estruturas de ordem |
title_short |
A Note on Abstract Consequence Structures |
title_full |
A Note on Abstract Consequence Structures |
title_fullStr |
A Note on Abstract Consequence Structures |
title_full_unstemmed |
A Note on Abstract Consequence Structures |
title_sort |
A Note on Abstract Consequence Structures |
author |
Souza, Edelcio G. de |
author_facet |
Souza, Edelcio G. de |
author_role |
author |
dc.contributor.author.fl_str_mv |
Souza, Edelcio G. de |
dc.subject.por.fl_str_mv |
Abstract logic Consequence operators Order structures Lógica abstrata Operadores de conseqüência Estruturas de ordem |
topic |
Abstract logic Consequence operators Order structures Lógica abstrata Operadores de conseqüência Estruturas de ordem |
description |
Tarski’s pioneer work on abstract logic conceived consequence structures as a pair (X, Cn) where X is a non empty set (infinite and denumerable) and Cn is a function on the power set of X, satisfying some postulates. Based on these axioms, Tarski proved a series of important results. A detailed analysis of such proofs shows that several of these results do not depend on the relation of inclusion between sets but only on structural properties of this relation, which may be seen as an ordered structure. Even the notion of finiteness, which is employed in the postulates may be replaced by an ordered substructure satisfying some constraints. Therefore, Tarski’s structure could be represented in a still more abstract setting where reference is made only to the ordering relation on the domain of the structure. In our work we construct this abstract consequence structure and show that it keeps some results of Tarski’s original construction. |
publishDate |
2013 |
dc.date.none.fl_str_mv |
2013-02-14 |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
https://revistas.pucsp.br/index.php/cognitiofilosofia/article/view/13640 |
url |
https://revistas.pucsp.br/index.php/cognitiofilosofia/article/view/13640 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
https://revistas.pucsp.br/index.php/cognitiofilosofia/article/view/13640/10143 |
dc.rights.driver.fl_str_mv |
Copyright (c) 2013 http://creativecommons.org/licenses/by/4.0/ info:eu-repo/semantics/openAccess |
rights_invalid_str_mv |
Copyright (c) 2013 http://creativecommons.org/licenses/by/4.0/ |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
Pontifícia Universidade Católica de São Paulo |
publisher.none.fl_str_mv |
Pontifícia Universidade Católica de São Paulo |
dc.source.none.fl_str_mv |
Cognitio: Revista de Filosofia; Vol. 6 No. 1 (2005); 102-109 Cognitio: Revista de Filosofia; v. 6 n. 1 (2005); 102-109 2316-5278 1518-7187 reponame:Cognitio (São Paulo. Online) instname:Pontifícia Universidade Católica de São Paulo (PUC-SP) instacron:PUC_SP |
instname_str |
Pontifícia Universidade Católica de São Paulo (PUC-SP) |
instacron_str |
PUC_SP |
institution |
PUC_SP |
reponame_str |
Cognitio (São Paulo. Online) |
collection |
Cognitio (São Paulo. Online) |
repository.name.fl_str_mv |
Cognitio (São Paulo. Online) - Pontifícia Universidade Católica de São Paulo (PUC-SP) |
repository.mail.fl_str_mv |
revcognitio@gmail.com |
_version_ |
1803387421305339904 |