Admissible equivalence systems

Detalhes bibliográficos
Autor(a) principal: Babenyshev, Sergey
Data de Publicação: 2010
Outros Autores: Martins, Manuel A.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10773/6934
Resumo: Whenever a logic is the set of theorems of some deductive system, where the latter has an equivalence system, the behavioral theorems of the logic can be determined by means of that equivalence system. In general, this original equivalence system may be too restrictive, because it su ces to check behavioral theorems by means of any admissible equivalence system (that is an equivalence system of the small- est deductive system associated with the given logic). In this paper, we present a range of examples, which show that: 1) there is an admissible equivalence system which is not an equivalence system for the initial deductive system, 2) there is a non- nitely equivalential deductive system with a nite admissible equivalence system, and 3) there is a deductive system with an admissible equivalence sys- tems, such that this deductive system is not even protoalgebraic itself. We use methods and results from algebraic and modal logic.
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spelling Admissible equivalence systemsAbstract algebraic logicEquivalence systemsAdmissible rulesLeibniz operatorBehavioral theoremsWhenever a logic is the set of theorems of some deductive system, where the latter has an equivalence system, the behavioral theorems of the logic can be determined by means of that equivalence system. In general, this original equivalence system may be too restrictive, because it su ces to check behavioral theorems by means of any admissible equivalence system (that is an equivalence system of the small- est deductive system associated with the given logic). In this paper, we present a range of examples, which show that: 1) there is an admissible equivalence system which is not an equivalence system for the initial deductive system, 2) there is a non- nitely equivalential deductive system with a nite admissible equivalence system, and 3) there is a deductive system with an admissible equivalence sys- tems, such that this deductive system is not even protoalgebraic itself. We use methods and results from algebraic and modal logic.Department of Logic, University of Lodz2012-02-27T16:27:54Z2010-01-01T00:00:00Z2010info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/6934eng0138-0680Babenyshev, SergeyMartins, Manuel A.info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2024-02-22T11:07:04Zoai:ria.ua.pt:10773/6934Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T02:43:07.130773Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv Admissible equivalence systems
title Admissible equivalence systems
spellingShingle Admissible equivalence systems
Babenyshev, Sergey
Abstract algebraic logic
Equivalence systems
Admissible rules
Leibniz operator
Behavioral theorems
title_short Admissible equivalence systems
title_full Admissible equivalence systems
title_fullStr Admissible equivalence systems
title_full_unstemmed Admissible equivalence systems
title_sort Admissible equivalence systems
author Babenyshev, Sergey
author_facet Babenyshev, Sergey
Martins, Manuel A.
author_role author
author2 Martins, Manuel A.
author2_role author
dc.contributor.author.fl_str_mv Babenyshev, Sergey
Martins, Manuel A.
dc.subject.por.fl_str_mv Abstract algebraic logic
Equivalence systems
Admissible rules
Leibniz operator
Behavioral theorems
topic Abstract algebraic logic
Equivalence systems
Admissible rules
Leibniz operator
Behavioral theorems
description Whenever a logic is the set of theorems of some deductive system, where the latter has an equivalence system, the behavioral theorems of the logic can be determined by means of that equivalence system. In general, this original equivalence system may be too restrictive, because it su ces to check behavioral theorems by means of any admissible equivalence system (that is an equivalence system of the small- est deductive system associated with the given logic). In this paper, we present a range of examples, which show that: 1) there is an admissible equivalence system which is not an equivalence system for the initial deductive system, 2) there is a non- nitely equivalential deductive system with a nite admissible equivalence system, and 3) there is a deductive system with an admissible equivalence sys- tems, such that this deductive system is not even protoalgebraic itself. We use methods and results from algebraic and modal logic.
publishDate 2010
dc.date.none.fl_str_mv 2010-01-01T00:00:00Z
2010
2012-02-27T16:27:54Z
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dc.identifier.uri.fl_str_mv http://hdl.handle.net/10773/6934
url http://hdl.handle.net/10773/6934
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 0138-0680
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eu_rights_str_mv openAccess
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dc.publisher.none.fl_str_mv Department of Logic, University of Lodz
publisher.none.fl_str_mv Department of Logic, University of Lodz
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
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repository.name.fl_str_mv Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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