Dualising Intuitionictic Negation

Graham Priest


One of Da Costa's motives when he constructed the paraconsistent logic Cw was to dualise the negation of intuitionistic logic. In this paper I explore a different way of going about this task. A logic is defined by taking the Kripke semantics for intuitionistic logic, and dualising the truth conditions for negation. Various properties of the logic are established, including its relation to CWo Tableau and natural deduction systems for the logic are produced, as are appropriate algebraic structures. The paper then investigates dualising the intuitionistic conditional in the same way. This establishes various connections between the logic, and a logic called in the literature 'Brouwerian logic' or 'closed-set logic'.


Da Costa; Paraconsistency; Intuitionism; Kripke semantics; Brouwerian algebras; Closed set logic; Negation

DOI: https://doi.org/10.5007/1808-1711.2009v13n2p165

Copyright (c)


Principia: an internationnal journal of epistemology
Published by NEL - Epistemology and Logic Research Group
Federal University of Santa Catarina - UFSC
Center of Philosophy and Human Sciences – CFH
Campus Reitor João David Ferreira Lima
Florianópolis, Santa Catarina - Brazil
CEP: 88040-900

 ISSN: 1414-4217
EISSN: 1808-171

e-mail: principia@contato.ufsc.br