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Some Definitions of Negation Leading to Paraconsistent Logics
M. W. Bunder
Studia Logica: An International Journal for Symbolic Logic
Vol. 43, No. 1/2, Paraconsistent Logics (1984), pp. 75-78
Published by: Springer
Stable URL: http://www.jstor.org/stable/20015150
Page Count: 4
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In positive logic the negation of a proposition A is defined by $A\supset X$ where X is some fixed proposition. A number of standard properties of negation, including reductio 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 for X. These propositions range from true through contingent to false.
Studia Logica: An International Journal for Symbolic Logic © 1984 Springer