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Revised version of
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Vol. 4(4), 2004 (Section Logic)
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On Negation: Pure local rules
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João Marcos
Personal web-page
 
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Date Posted: August, 05th 2004
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Abstract
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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.
Keywords: negation, abstract deductive systems, multiple-conclusion logic, paraconsistency
1991 MSC: 03B22, 03B53, 03B60.
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