Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9517934 | Journal of Applied Logic | 2005 | 35 Pages |
Abstract
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Logic
Authors
João Marcos,