Reconciling First-Order Logic to Algebra

Registro completo de metadados
MetadadosDescriçãoIdioma
Autor(es): dc.contributorUniversidade Estadual de Campinas (UNICAMP)-
Autor(es): dc.contributorUniversidade de São Paulo (USP)-
Autor(es): dc.contributorUniversidade Estadual Paulista (Unesp)-
Autor(es): dc.creatorCarnielli, Walter-
Autor(es): dc.creatorLuiz Mariano, Hugo-
Autor(es): dc.creatorMatulovic, Mariana [UNESP]-
Data de aceite: dc.date.accessioned2022-02-22T00:46:51Z-
Data de disponibilização: dc.date.available2022-02-22T00:46:51Z-
Data de envio: dc.date.issued2021-06-25-
Data de envio: dc.date.issued2021-06-25-
Data de envio: dc.date.issued2018-01-01-
Fonte completa do material: dc.identifierhttp://dx.doi.org/10.1007/978-3-319-98797-2_13-
Fonte completa do material: dc.identifierhttp://hdl.handle.net/11449/206358-
Fonte: dc.identifier.urihttp://educapes.capes.gov.br/handle/11449/206358-
Descrição: dc.descriptionWe start from the algebraic method of theorem-proving based on the translation of logic formulas into polynomials over finite fields, and adapt the case of first-order formulas by employing certain rings equipped with infinitary operations. This paper defines the notion of M-ring, a kind of polynomial ring that can be naturally associated to each first-order structure and each first-order theory, by means of generators and relations. The notion of M-ring allows us to operate with some kind of infinitary version of Boolean sums and products, in this way expressing algebraically first-order logic with a new gist. We then show how this polynomial representation of first-order sentences can be seen as a legitimate algebraic semantics for first-order logic, an alternative to cylindric and polyadic algebras and closer to the primordial forms of algebraization of logic. We suggest how the method and its generalization could be lifted successfully to n-valued logics and to other non-classical logics helping to reconcile some lost ties between algebra and logic.-
Descrição: dc.descriptionDepartment of Philosophy and Centre for Logic Epistemology and the History of Science University of Campinas-Unicamp-
Descrição: dc.descriptionInstitute of Mathematics and Statistics University of São Paulo-
Descrição: dc.descriptionFaculty of Science and Engineering São Paulo State University (UNESP)-
Descrição: dc.descriptionFaculty of Science and Engineering São Paulo State University (UNESP)-
Formato: dc.format273-305-
Idioma: dc.languageen-
Relação: dc.relationTrends in Logic-
???dc.source???: dc.sourceScopus-
Título: dc.titleReconciling First-Order Logic to Algebra-
Aparece nas coleções:Repositório Institucional - Unesp

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