enow.com Web Search

Search results

1. Results from the WOW.Com Content Network

2. Literal (mathematical logic) - Wikipedia

   en.wikipedia.org/wiki/Literal_(mathematical_logic)

   Double negation elimination occurs in classical logics but not in intuitionistic logic. In the context of a formula in the conjunctive normal form, a literal is pure if the literal's complement does not appear in the formula. In Boolean functions, each separate occurrence of a variable, either in inverse or uncomplemented form, is a literal.

3. Negation - Wikipedia

   en.wikipedia.org/wiki/Negation

   Together with double negation elimination one may infer our originally formulated rule, namely that anything follows from an absurdity. Typically the intuitionistic negation of is defined as . Then negation introduction and elimination are just special cases of implication introduction (conditional proof) and elimination (modus ponens).

4. Complete theory - Wikipedia

   en.wikipedia.org/wiki/Complete_theory

   In mathematical logic, a theory is complete if it is consistent and for every closed formula in the theory's language, either that formula or its negation is provable. That is, for every sentence φ , {\displaystyle \varphi ,} the theory T {\displaystyle T} contains the sentence or its negation but not both (that is, either T ⊢ φ ...

5. Negation normal form - Wikipedia

   en.wikipedia.org/wiki/Negation_normal_form

   Transformation into negation normal form can increase the size of a formula only linearly: the number of occurrences of atomic formulas remains the same, the total number of occurrences of and is unchanged, and the number of occurrences of in the normal form is bounded by the length of the original formula. A formula in negation normal form can ...

6. Intuitionistic logic - Wikipedia

   en.wikipedia.org/wiki/Intuitionistic_logic

   Propositions for which double-negation elimination is possible are also called stable. Intuitionistic logic proves stability only for restricted types of propositions. A formula for which excluded middle holds can be proven stable using the disjunctive syllogism, which is discussed more thoroughly below. The converse does however not hold in ...

7. Double negation - Wikipedia

   en.wikipedia.org/wiki/Double_negation

   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.