Degree of Negation of an Axiom

Details Degree of Negation of an Axiom Degree of Negation of an Axiom

2009-05-06

arxiv.org/abs/0905.0719v3

Mathematics

General Mathematics

6 pages. To appear in the Journal of Approximate Reasoning

Scientific paper

In this article we present the two classical negations of Euclid's Fifth Postulate (done by Lobachevski-Bolyai-Gauss, and respectively by Riemann), and in addition of these we propose a partial negation (or a degree of negation) of an axiom in geometry. The most important contribution of this article is the introduction of the degree of negation (or partial negation) of an axiom and, more general, of a scientific or humanistic proposition (theorem, lemma, etc.) in any field - which works somehow like the negation in fuzzy logic (with a degree of truth, and a degree of falsehood), or like in neutrosophic logic [with a degree of truth, a degree of falsehood, and a degree of neutrality (i.e. neither truth nor falsehood, but ambiguous, unknown, indeterminate)].

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