A General Semantics for Logics of Affirmation and Negation

Journal of Applied Logics - IfCoLoG Journal of Logics and Their Applications 8 (2):593-609 (2021)
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A general framework for translating various logical systems is presented, including a set of partial unary operators of affirmation and negation. Despite its usual reading, affirmation is not redundant in any domain of values and whenever it does not behave like a full mapping. After depicting the process of partial functions, a number of logics are translated through a variety of affirmations and a unique pair of negations. This relies upon two preconditions: a deconstruction of truth-values as ordered and structured objects, unlike its mainstream presentation as a simple object; a redefinition of the Principle of Bivalence as a set of four independent properties, such that its definition does not equate with normality.

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Fabien Schang
Université de Lorraine (PhD)


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