Subminimal negation

Colacito, Almudena; de Jongh, Dick; Vargas, A. L. (2017). Subminimal negation. Soft computing, 21(1), pp. 165-174. Springer 10.1007/s00500-016-2391-8

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Minimal logic, i.e., intuitionistic logic without the ex falso principle, is investigated in its original form with a negation symbol instead of a symbol denoting the contradiction. A Kripke semantics is developed for minimal logic and its sublogics with a still weaker negation by introducing a function on the upward closed sets of the models. The basic logic is a logic in which the negation has no properties but the one of being a unary operator. A number of extensions is studied of which the most important ones are contraposition logic and negative ex falso, a weak form of the ex falso principle. Completeness is proved, and the created semantics is further studied. The negative translation of classical logic into intuitionistic logic is made part of a chain of translations by introducing translations from minimal logic into contraposition logic and intuitionistic logic into minimal logic, the latter having been discovered in the correspondence between Johansson and Heyting. Finally, as a bridge to the work of Franco Montagna a start is made of a study of linear models of these logics.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics

UniBE Contributor:

Colacito, Almudena

Subjects:

500 Science > 510 Mathematics

ISSN:

1432-7643

Publisher:

Springer

Language:

English

Submitter:

George Metcalfe

Date Deposited:

26 Apr 2017 12:57

Last Modified:

26 Apr 2017 12:57

Publisher DOI:

10.1007/s00500-016-2391-8

BORIS DOI:

10.7892/boris.92781

URI:

https://boris.unibe.ch/id/eprint/92781

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