On negation: Pure local rules

✍ Scribed by João Marcos

• Publisher: Elsevier Science
• Year: 2005
• Tongue: English
• Weight: 296 KB
• Volume: 3
• Category: Article
• ISSN: 1570-8683
• DOI: 10.1016/j.jal.2004.07.017

✦ Synopsis

This is an initial systematic study of the properties of negation from the point of view of abstract deductive systems. A unifying framework of multiple-conclusion consequence relations is adopted so as to allow us to explore symmetry in exposing and matching a great number of positive contextual sub-classical rules involving this logical constant-among others, well-known forms of proof by cases, consequentia mirabilis and reductio ad absurdum. Finer definitions of paraconsistency and the dual paracompleteness can thus be formulated, allowing for pseudo-scotus and ex contradictione to be differentiated and for a comprehensive version of the Principle of Non-Triviality to be presented. A final proposal is made to the effect that-pure positive rules involving negation being often fallible-a characterization of what most negations in the literature have in common should rather involve, in fact, a reduced set of negative rules.