The class of all 3-valued natural conditional variants of RM3 that are Plumwood Algebras

  1. Blanco, Jose Miguel 1
  2. Lopez, Sandra M. 3456
  3. Recio, Marcos M. 2
  1. 1 Faculty of Informatics, Masaryk University
  2. 2 Facultad de Filosofía, Universidad de Salamanca
  3. 3 Universidad de Valladolid (2022)
  4. 4 (Departamento de Filosofía (Filosofía, Lógica y Filosofía de la Ciencia, Teoría e Historia de la Educación, Filosofía Moral, Estética y Teoría de las Artes))
  5. 5 Programa Ramón y Cajal
  6. 6 Universidad de Salamanca
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    Universidad de Salamanca

    Salamanca, España

    ROR https://ror.org/02f40zc51

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Revista:
The Australasian Journal of Logic

ISSN: 1448-5052

Año de publicación: 2023

Volumen: 20

Número: 2

Páginas: 188-218

Tipo: Artículo

DOI: 10.26686/AJL.V29I2.8285 GOOGLE SCHOLAR lock_openAcceso abierto editor

Otras publicaciones en: The Australasian Journal of Logic

Resumen

Valerie Plumwood introduced in Some false laws of logic [15] a series of arguments on how the rules Exported Syllogism, Disjunctive Syllogism, Commutation, and Exportation are not acceptable. Based on this we define the class of Plumwood algebras, logical matrices that do not verify any of these theses. Afterwards we provide conditional variants of the characteristic matrix of the logic RM3 that are also Plumwood algebras. These matrices are given an axiomatization based on First Degree Entailment and are endowed with Belnap-Dunn Semantics. Finally we provide results of Soundness and Completeness in the strong sense for each of the defined variants.

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Información de financiación

Sandra M. Lopez’s work is co-financed by the European NextGenerationEU Fund, Spanish “Plan de Recuperacion, Transformacion y Resilencia” Fund, Spanish Ministry of Universities, and University of Salamanca. (“Ayudas para la recualificacion del sistema universitario espanol 2021-2022”.)

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