|A general semantics for logics of affirmation and negation|
Assertion and Proof special issue
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.