# Validating fuzzy logic values

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The first known classical logician who didn't fully accept the law of excluded middle was Aristotle (who, ironically, is also generally considered to be the first classical logician and the "father of logic").

For example, the preserved property could be justification, the foundational concept of intuitionistic logic.IX), but he didn't create a system of multi-valued logic to explain this isolated remark.Until the coming of the 20th century, later logicians followed Aristotelian logic, which includes or assumes the law of the excluded middle.Thus, a proposition is not true or false; instead, it is justified or flawed.A key difference between justification and truth, in this case, is that the law of excluded middle doesn't hold: a proposition that is not flawed is not necessarily justified; instead, it's only not proven that it's flawed.The 20th century brought back the idea of multi-valued logic.

The Polish logician and philosopher Jan Łukasiewicz began to create systems of many-valued logic in 1920, using a third value, "possible", to deal with Aristotle's paradox of the sea battle. Post (1921), also introduced the formulation of additional truth degrees with n ≥ 2, where n are the truth values.

In logic, a many-valued logic (also multi- or multiple-valued logic) is a propositional calculus in which there are more than two truth values.

Traditionally, in Aristotle's logical calculus, there were only two possible values (i.e., "true" and "false") for any proposition.

For example, in a three-valued logic, sometimes the two greatest truth-values (when they are represented as e.g.

positive integers) are designated and the rules of inference preserve these values.

The key difference is the determinacy of the preserved property: One may prove that P is justified, that P is flawed, or be unable to prove either.