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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.
Two of them also use emphasis to make the meaning clearer. The last example is a popular example of a double negative that resolves to a positive. This is because the verb 'to doubt' has no intensifier which effectively resolves a sentence to a positive. Had we added an adverb thus: I never had no doubt this sentence is false.
Corner quotes, also called “Quine quotes”; for quasi-quotation, i.e. quoting specific context of unspecified (“variable”) expressions; [3] also used for denoting Gödel number; [4] for example “āGā” denotes the Gödel number of G. (Typographical note: although the quotes appears as a “pair” in unicode (231C and 231D), they ...
Syntactically, (1) and (2) are derivable from each other via the rules of contraposition and double negation. Semantically, (1) and (2) are true in exactly the same models (interpretations, valuations); namely, those in which either Lisa is in Denmark is false or Lisa is in Europe is true. (Note that in this example, classical logic is assumed
A negative literal is the negation of an atom (e.g., ). The polarity of a literal is positive or negative depending on whether it is a positive or negative literal. In logics with double negation elimination (where ¬ ¬ x ≡ x {\displaystyle \lnot \lnot x\equiv x} ) the complementary literal or complement of a literal l {\displaystyle l} can ...
In C (and some other languages descended from C), double negation (!!x) is used as an idiom to convert x to a canonical Boolean, ie. an integer with a value of either 0 or 1 and no other. Although any integer other than 0 is logically true in C and 1 is not special in this regard, it is sometimes important to ensure that a canonical value is ...
In logic, a rule of replacement [1] [2] [3] is a transformation rule that may be applied to only a particular segment of an expression.A logical system may be constructed so that it uses either axioms, rules of inference, or both as transformation rules for logical expressions in the system.
De Morgan's laws represented with Venn diagrams.In each case, the resultant set is the set of all points in any shade of blue. In propositional logic and Boolean algebra, De Morgan's laws, [1] [2] [3] also known as De Morgan's theorem, [4] are a pair of transformation rules that are both valid rules of inference.