Algebraic Study of Two Deductive Systems of Relevance Logic
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Algebraic Study of Two Deductive Systems of Relevance Logic
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| Id. |
979882 |
| Idioma |
inglés
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| Titulo |
Algebraic Study of Two Deductive Systems of Relevance Logic |
| Autor(es) |
Font, Josep Maria
Rodríguez, Gonzalo
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| Localización |
http://projecteuclid.org/euclid.ndjfl/1040511344
Notre Dame J. Formal Logic 35, no. 3 (1994), 369-397
doi:10.1305/ndjfl/1040511344
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| Versión |
1.0 |
| Estado |
Final
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| Descripción |
In this paper two deductive systems (i.e., two consequence
relations) associated with relevance logic are studied from an algebraic point of
view. One is defined by the familiar, Hilbert-style, formalization of R; the
other one is a weak version of it, called WR, which appears as the semantic
entailment of the Meyer-Routley-Fine semantics, and which has already been
suggested by Wójcicki for other reasons. This weaker consequence is first defined
indirectly, using R, but we prove that the first one turns out to be an
axiomatic extension of WR. Moreover we provide WR with a natural Gentzen
calculus (of a classical kind). It is proved that both deductive systems have the
same associated class of algebras but different classes of models on these
algebras. The notion of model used here is an abstract logic, that is, a closure
operator on an abstract algebra; the abstract logics obtained in the case of WR
are also the models, in a natural sense, of the given Gentzen calculus.
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| Tipo |
application/pdf
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| Palabras clave |
03B46
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| Tipo de recurso |
Text
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| Tipo de Interactividad |
Expositivo
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| Nivel de Interactividad |
muy bajo
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| Audiencia |
Estudiante
Profesor
Autor
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| Estructura |
Atomic |
| Coste |
no
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| Copyright |
sí
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Copyright 1994 Duke University Press |
| Formatos |
application/pdf
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| Requerimientos técnicos |
Browser: Any
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| Fecha de contribución |
21-nov-2008 |
| Contacto |
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