Abstract:
In Aristotelian logic, categorical propositions are divided in Universal Affirmative, Universal Negative, Particular Affirmative and Particular Negative. Possible relations between two of the mentioned type of propositions are encoded in the square of opposition. The square expresses the essential properties of monadic first order quantification which, in an algebraic approach, may be represented taking into account monadic Boolean algebras.More precisely, quantifiers are considered as modal operators acting on a Boolean algebra and the square of opposition is represented by relations between certain terms of the language in which the algebraic structure is formulated. This representation is sometimes called the modal square of opposition. Several generalizations of the monadic first order logic can be obtained by changing the underlying Boolean structure by another one giving rise to new possible interpretations of the square. © Springer Basel 2012. All rights reserved.
Registro:
| Documento: |
Parte de libro
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| Título: | The square of opposition in orthomodular logic |
| Autor: | Freytes, H.; De Ronde, C.; Domenech, G. |
| Filiación: | Universita degli Studi di Cagliari, Via Is Mirrionis 1, Cagliari, 09123, Italy
Instituto Argentino de Matemática, Saavedra 15, Buenos Aires, Argentina
Departamento de Filosofía 'Dr. A Korn', Universidad de Buenos Aires-CONICET, Buenos Aires, Argentina
Center Leo Apostel and Foundations of the Exact Sciences, Vrije Universiteit Brussel, Krijgskundestraat 33, Brussels, 1160, Belgium
Instituto de Astronomía y Física del Espacio, CC 67, Suc 28, Buenos Aires, 1428, Argentina
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| Palabras clave: | Classical consequences; Modal orthomodular logic; Square of opposition |
| Año: | 2012
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| Página de inicio: | 193
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| Página de fin: | 200
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| DOI: |
http://dx.doi.org/10.1007/978-3-0348-0379-3_13 |
| Título revista: | Around and Beyond the Square of Opposition
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| Título revista abreviado: | Around and Beyond the Sq. of Oppos.
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| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_97830348_v_n_p193_Freytes |
Referencias:
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Citas:
---------- APA ----------
Freytes, H., De Ronde, C. & Domenech, G.
(2012)
. The square of opposition in orthomodular logic. Around and Beyond the Square of Opposition, 193-200.
http://dx.doi.org/10.1007/978-3-0348-0379-3_13---------- CHICAGO ----------
Freytes, H., De Ronde, C., Domenech, G.
"The square of opposition in orthomodular logic"
. Around and Beyond the Square of Opposition
(2012) : 193-200.
http://dx.doi.org/10.1007/978-3-0348-0379-3_13---------- MLA ----------
Freytes, H., De Ronde, C., Domenech, G.
"The square of opposition in orthomodular logic"
. Around and Beyond the Square of Opposition, 2012, pp. 193-200.
http://dx.doi.org/10.1007/978-3-0348-0379-3_13---------- VANCOUVER ----------
Freytes, H., De Ronde, C., Domenech, G. The square of opposition in orthomodular logic. Around and Beyond the Sq. of Oppos. 2012:193-200.
http://dx.doi.org/10.1007/978-3-0348-0379-3_13