Aristotelian Logic vs. Modern Logics

For example, let's consider the axioms of a group. Let's take the existence of a neutral element axiom. To S-deny the existence of a neutral element we can find group elements e1, e2, ..., en that have as neutral element n1, and other group elements that have as neutral element with respect to the same algebraic law the element n2, and other group elements that have no neutral element. S-denying is alike the Smarandache geometries.

Aristotelian Logic vs. Modern Logics

Florentin Smarandache I think we cannot use the Aristotelian logic to judge the modern logics, since in Aristotelian logic one has the law of excluded middle, while in modern logics you have the law of included middle, and in neutrosophic logic even more: the law of included multiple-middle. Selçuk Topal My main aim is to open a door in natural logic for your theory and to provide to find applications of the theory in the natural language studies (for the areas of Logic,

Language, and Information).

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