PP-2016-23: Subminimal Negation

PP-2016-23: Colacito, Almudena and de Jongh, Dick and Vargas, Ana Lucia (2016) Subminimal Negation. [Report]

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Abstract

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 intutionistic 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: Report
Report Nr: PP-2016-23
Series Name: Prepublication (PP) Series
Year: 2016
Uncontrolled Keywords: intuitionistic logic, minimal logic, negation, ex falso, contraposition
Subjects: Logic
Date Deposited: 12 Oct 2016 14:37
Last Modified: 12 Oct 2016 14:37
URI: https://eprints.illc.uva.nl/id/eprint/559

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