Some definitions of negation leading to paraconsistent logics

Studia Logica 43 (1-2):75 - 78 (1984)
Abstract
In positive logic the negation of a propositionA is defined byA X whereX is some fixed proposition. A number of standard properties of negation, includingreductio ad absurdum, can then be proved, but not the law of noncontradiction so that this forms a paraconsistent logic. Various stronger paraconsistent logics are then generated by putting in particular propositions forX. These propositions range from true through contingent to false.
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DOI 10.1007/BF00935741
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On the Theory of Inconsistent Formal Systems.Newton C. A. Da Costa - 1974 - Notre Dame Journal of Formal Logic 15 (4):497-510.
Alpha-Models and Systems T and T.Newton C. A. da Costa - 1974 - Notre Dame Journal of Formal Logic 15:443.

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