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Contrariety and Subcontrariety: The Anatomy of Negation (with Special Reference to an Example of J.‐Y. Béziau)
Author(s) -
HUMBERSTONE LLOYD
Publication year - 2005
Publication title -
theoria
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.34
H-Index - 16
eISSN - 1755-2567
pISSN - 0040-5825
DOI - 10.1111/j.1755-2567.2005.tb00886.x
Subject(s) - negation , intuitionistic logic , negation as failure , linguistics , dual (grammatical number) , epistemology , mathematics , semantics (computer science) , philosophy , calculus (dental) , pure mathematics , computer science , medicine , propositional calculus , programming language , operational semantics , stable model semantics , dentistry
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.