David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Topoi 18 (2):141-148 (1999)
Of the various accounts of negation that have been offered by logicians in the history of Western logic, that of negation as cancellation is a very distinctive one, quite different from the explosive accounts of modern "classical" and intuitionist logics, and from the accounts offered in standard relevant and paraconsistent logics. Despite its ancient origin, however, a precise understanding of the notion is still wanting. The first half of this paper offers one. Both conceptually and historically, the account of negation as cancellation is intimately connected with connexivist principles such as ¬( ¬). Despite this, standard connexivist logics incorporate quite different accounts of negation. The second half of the paper shows how the cancellation account of negation of the first part gives rise to a semantics for a simple connexivist logic.
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Sara L. Uckelman, Jesse Alama & Aleks Knoks (2014). A Curious Dialogical Logic and its Composition Problem. Journal of Philosophical Logic 43 (6):1065-1100.
Thomas Macaulay Ferguson (2015). Logics of Nonsense and Parry Systems. Journal of Philosophical Logic 44 (1):65-80.
Andreas Kapsner (2012). Strong Connexivity. Thought: A Journal of Philosophy 1 (2):141-145.
Nissim Francez (2014). Bilateral Relevant Logic. Review of Symbolic Logic 7 (2):250-272.
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