Contrariety and Subcontrariety: The Anatomy of Negation (with Special Reference to an Example of J.-Y. Béziau)

Theoria 71 (3):241-262 (2008)
We discuss aspects of the logic of negation bearing on an issue raised by Jean-Yves Béziau, recalled in §1. Contrary- and subcontrary-forming operators are introduced in §2, which examines some of their logical behaviour, leading on naturally to a consideration in §3 of dual intuitionistic negation (as well as implication), and some further operators related to intuitionistic negation. In §4, a historical explanation is suggested as to why some of these negation-related connectives have attracted more attention than others. The remaining sections (§§5, 6) briefly address a question about a certain notion of global contrariety and the provision of Kripke semantics for the various operators in play in our discussion.
Keywords contraries  Negation  dual intuitionistic negation  intuitionistic logic  consequence ralations
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DOI 10.1111/j.1755-2567.2005.tb00886.x
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Lloyd Humberstone (2013). Logical Relations. Philosophical Perspectives 27 (1):175-230.

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