Some definitions of negation leading to paraconsistent logics
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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.
KeywordsMathematical Logic Computational Linguistic Standard Property Paraconsistent Logic Positive Logic
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