Satisfiability Calculus: An Abstract Formulation of Semantic Proof Systems

Autores
Lopez Pombo, Carlos Gustavo; Castro, Pablo; Aguirre, Nazareno M.; Maibaum, Thomas S.E.
Año de publicación
2019
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The theory of institutions, introduced by Goguen and Burstall in 1984, can be thought of as an abstract formulation of model theory. This theory has been shown to be particularly useful in computer science, as a mathematical foundation for formal approaches to software construction. Institution theory was extended by a number of researchers, José Meseguer among them, who, in 1989, presented General Logics, wherein the model theoretical view of institutions is complemented by providing (categorical) structures supporting the proof theory of any given logic. In other words, Meseguer introduced the notion of proof calculus as a formalisation of syntactical deduction, thus ?implementing? the entailment relation of a given logic. In this paper we follow the approach initiated by Goguen and introduce the concept of Satisfiability Calculus. This concept can be regarded as the semantical counterpart of Meseguer?s notion of proof calculus, as it provides the formal foundations for those proof systems that resort to model construction techniques to prove or disprove a given formula, thus ?implementing? the satisfiability relation of an institution. These kinds of semantic proof methods have gained a great amount of interest in computer science over the years, as they provide the basic means for many automated theorem proving techniques.
Fil: Lopez Pombo, Carlos Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigación en Ciencias de la Computación. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigación en Ciencias de la Computación; Argentina
Fil: Castro, Pablo. Universidad Nacional de Río Cuarto. Facultad de Ciencias Exactas Fisicoquímicas y Naturales. Departamento de Computación; Argentina
Fil: Aguirre, Nazareno M.. Universidad Nacional de Río Cuarto. Facultad de Ciencias Exactas Fisicoquímicas y Naturales. Departamento de Computación; Argentina
Fil: Maibaum, Thomas S.E.. Mc Master University; Canadá
Materia
Category theory
General logics
Institutions
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/123309
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/123309
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network_name_str CONICET Digital (CONICET)
spelling Satisfiability Calculus: An Abstract Formulation of Semantic Proof SystemsLopez Pombo, Carlos GustavoCastro, PabloAguirre, Nazareno M.Maibaum, Thomas S.E.Category theoryGeneral logicsInstitutionshttps://purl.org/becyt/ford/1.2https://purl.org/becyt/ford/1The theory of institutions, introduced by Goguen and Burstall in 1984, can be thought of as an abstract formulation of model theory. This theory has been shown to be particularly useful in computer science, as a mathematical foundation for formal approaches to software construction. Institution theory was extended by a number of researchers, José Meseguer among them, who, in 1989, presented General Logics, wherein the model theoretical view of institutions is complemented by providing (categorical) structures supporting the proof theory of any given logic. In other words, Meseguer introduced the notion of proof calculus as a formalisation of syntactical deduction, thus ?implementing? the entailment relation of a given logic. In this paper we follow the approach initiated by Goguen and introduce the concept of Satisfiability Calculus. This concept can be regarded as the semantical counterpart of Meseguer?s notion of proof calculus, as it provides the formal foundations for those proof systems that resort to model construction techniques to prove or disprove a given formula, thus ?implementing? the satisfiability relation of an institution. These kinds of semantic proof methods have gained a great amount of interest in computer science over the years, as they provide the basic means for many automated theorem proving techniques.Fil: Lopez Pombo, Carlos Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigación en Ciencias de la Computación. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigación en Ciencias de la Computación; ArgentinaFil: Castro, Pablo. Universidad Nacional de Río Cuarto. Facultad de Ciencias Exactas Fisicoquímicas y Naturales. Departamento de Computación; ArgentinaFil: Aguirre, Nazareno M.. Universidad Nacional de Río Cuarto. Facultad de Ciencias Exactas Fisicoquímicas y Naturales. Departamento de Computación; ArgentinaFil: Maibaum, Thomas S.E.. Mc Master University; CanadáIOS Press2019-04info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/123309Lopez Pombo, Carlos Gustavo; Castro, Pablo; Aguirre, Nazareno M.; Maibaum, Thomas S.E.; Satisfiability Calculus: An Abstract Formulation of Semantic Proof Systems; IOS Press; Fundamenta Informaticae; 166; 4; 4-2019; 297-3470169-2968CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://content.iospress.com/articles/fundamenta-informaticae/fi1804info:eu-repo/semantics/altIdentifier/doi/10.3233/FI-2016-0000info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:12:40Zoai:ri.conicet.gov.ar:11336/123309instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 10:12:41.187CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Satisfiability Calculus: An Abstract Formulation of Semantic Proof Systems
title Satisfiability Calculus: An Abstract Formulation of Semantic Proof Systems
spellingShingle Satisfiability Calculus: An Abstract Formulation of Semantic Proof Systems
Lopez Pombo, Carlos Gustavo
Category theory
General logics
Institutions
title_short Satisfiability Calculus: An Abstract Formulation of Semantic Proof Systems
title_full Satisfiability Calculus: An Abstract Formulation of Semantic Proof Systems
title_fullStr Satisfiability Calculus: An Abstract Formulation of Semantic Proof Systems
title_full_unstemmed Satisfiability Calculus: An Abstract Formulation of Semantic Proof Systems
title_sort Satisfiability Calculus: An Abstract Formulation of Semantic Proof Systems
dc.creator.none.fl_str_mv Lopez Pombo, Carlos Gustavo
Castro, Pablo
Aguirre, Nazareno M.
Maibaum, Thomas S.E.
author Lopez Pombo, Carlos Gustavo
author_facet Lopez Pombo, Carlos Gustavo
Castro, Pablo
Aguirre, Nazareno M.
Maibaum, Thomas S.E.
author_role author
author2 Castro, Pablo
Aguirre, Nazareno M.
Maibaum, Thomas S.E.
author2_role author
author
author
dc.subject.none.fl_str_mv Category theory
General logics
Institutions
topic Category theory
General logics
Institutions
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.2
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv The theory of institutions, introduced by Goguen and Burstall in 1984, can be thought of as an abstract formulation of model theory. This theory has been shown to be particularly useful in computer science, as a mathematical foundation for formal approaches to software construction. Institution theory was extended by a number of researchers, José Meseguer among them, who, in 1989, presented General Logics, wherein the model theoretical view of institutions is complemented by providing (categorical) structures supporting the proof theory of any given logic. In other words, Meseguer introduced the notion of proof calculus as a formalisation of syntactical deduction, thus ?implementing? the entailment relation of a given logic. In this paper we follow the approach initiated by Goguen and introduce the concept of Satisfiability Calculus. This concept can be regarded as the semantical counterpart of Meseguer?s notion of proof calculus, as it provides the formal foundations for those proof systems that resort to model construction techniques to prove or disprove a given formula, thus ?implementing? the satisfiability relation of an institution. These kinds of semantic proof methods have gained a great amount of interest in computer science over the years, as they provide the basic means for many automated theorem proving techniques.
Fil: Lopez Pombo, Carlos Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigación en Ciencias de la Computación. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigación en Ciencias de la Computación; Argentina
Fil: Castro, Pablo. Universidad Nacional de Río Cuarto. Facultad de Ciencias Exactas Fisicoquímicas y Naturales. Departamento de Computación; Argentina
Fil: Aguirre, Nazareno M.. Universidad Nacional de Río Cuarto. Facultad de Ciencias Exactas Fisicoquímicas y Naturales. Departamento de Computación; Argentina
Fil: Maibaum, Thomas S.E.. Mc Master University; Canadá
description The theory of institutions, introduced by Goguen and Burstall in 1984, can be thought of as an abstract formulation of model theory. This theory has been shown to be particularly useful in computer science, as a mathematical foundation for formal approaches to software construction. Institution theory was extended by a number of researchers, José Meseguer among them, who, in 1989, presented General Logics, wherein the model theoretical view of institutions is complemented by providing (categorical) structures supporting the proof theory of any given logic. In other words, Meseguer introduced the notion of proof calculus as a formalisation of syntactical deduction, thus ?implementing? the entailment relation of a given logic. In this paper we follow the approach initiated by Goguen and introduce the concept of Satisfiability Calculus. This concept can be regarded as the semantical counterpart of Meseguer?s notion of proof calculus, as it provides the formal foundations for those proof systems that resort to model construction techniques to prove or disprove a given formula, thus ?implementing? the satisfiability relation of an institution. These kinds of semantic proof methods have gained a great amount of interest in computer science over the years, as they provide the basic means for many automated theorem proving techniques.
publishDate 2019
dc.date.none.fl_str_mv 2019-04
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/123309
Lopez Pombo, Carlos Gustavo; Castro, Pablo; Aguirre, Nazareno M.; Maibaum, Thomas S.E.; Satisfiability Calculus: An Abstract Formulation of Semantic Proof Systems; IOS Press; Fundamenta Informaticae; 166; 4; 4-2019; 297-347
0169-2968
CONICET Digital
CONICET
url http://hdl.handle.net/11336/123309
identifier_str_mv Lopez Pombo, Carlos Gustavo; Castro, Pablo; Aguirre, Nazareno M.; Maibaum, Thomas S.E.; Satisfiability Calculus: An Abstract Formulation of Semantic Proof Systems; IOS Press; Fundamenta Informaticae; 166; 4; 4-2019; 297-347
0169-2968
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://content.iospress.com/articles/fundamenta-informaticae/fi1804
info:eu-repo/semantics/altIdentifier/doi/10.3233/FI-2016-0000
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv IOS Press
publisher.none.fl_str_mv IOS Press
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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