The class of all 3-valued natural conditional variants of RM3 that are Plumwood Algebras
- Blanco, Jose Miguel 1
- Lopez, Sandra M. 3456
- Recio, Marcos M. 2
- 1 Faculty of Informatics, Masaryk University
- 2 Facultad de Filosofía, Universidad de Salamanca
- 3 Universidad de Valladolid (2022)
- 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 Programa Ramón y Cajal
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6
Universidad de Salamanca
info
ISSN: 1448-5052
Ano de publicación: 2023
Volume: 20
Número: 2
Páxinas: 188-218
Tipo: Artigo
Outras publicacións en: The Australasian Journal of Logic
Resumo
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.