The laws of thought are an obsolete way to refer to three logical principles: the law of identity (LOI), the law of non-contradiction (LNC), and the law of excluded middle (LEM).
In modern logic these are simply some of the class of tautologies, and are not inference rules. There is no system of logic which uses the three "laws" as axioms, and the interpretations of even just the three "laws" varies widely.
In propositional logic, the double negation of a statement states that "it is not the case that the statement is not true". In classical logic, every statement is logically equivalent to its double negation, but this is not true in intuitionistic logic; this can be expressed by the formula A ≡ ~(~A) where the sign ≡ expresses logical equivalence and the sign ~ expresses negation.
Like the law of the excluded middle, this principle is considered to be a law of thought in classical logic, but it is disallowed by intuitionistic logic. The principle was stated as a theorem of propositional logic by Russell and Whitehead in Principia Mathematica as:
View the full Wikipedia page for Double negation eliminationLaw of logic may refer to: