Dualising Intuitionictic Negation


  • Graham Priest Universities of Melbourne and St Andrews




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'.

Author Biography

Graham Priest, Universities of Melbourne and St Andrews

Graham Priest[1]  (born 1948, London) is Boyce Gibson Professor of Philosophy  at the University of Melbourne and a distinguished professor of philosophy at the CUNY Graduate Center, as well as a regular visitor at St. Andrews University. He was educated at the University of Cambridge and the London School of Economics. His thesis advisor was John Lane Bell.Departments of Philosophy Universities of Melbourne, St Andrews, and the Graduate Center, City University of New York