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Dualising Intuitionistic Negation

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Author(s): Graham Priest

Journal: Principia : an International Journal of Epistemology
ISSN 1414-4247

Volume: 13;
Issue: 2;
Start page: 165;
Date: 2009;
Original page

Keywords: Da Costa | paraconsistency | intuitionism | C! | Kripke semantics | Brouwerian algebras | closed set logic | negation

ABSTRACT
One of Da Costa’s motives when he constructed the paraconsistent logic C! 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 C!. 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’.
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