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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 linguistics, negative raising is a phenomenon that concerns the raising of negation from the embedded or subordinate clause of certain predicates to the matrix or main clause. [1] The higher copy of the negation, in the matrix clause, is pronounced; but the semantic meaning is interpreted as though it were present in the embedded clause. [2]
In linguistics, negative inversion is one of many types of subject–auxiliary inversion in English.A negation (e.g. not, no, never, nothing, etc.) or a word that implies negation (only, hardly, scarcely) or a phrase containing one of these words precedes the finite auxiliary verb necessitating that the subject and finite verb undergo inversion. [1]
To signal negation, as well as other semantic relation, these negation particles combine with different aspects of the verb. [10] These pre-verb negatory particles can also be used to convey tense, mood, aspect, and polarity (negation), and in some cases can be used to convey more than one of these features. [10]
A conditional statement used to express factual implications or predictions about real situations, as opposed to counterfactual or hypothetical statements. indirect proof A method of proof in which the negation of the statement to be proven is assumed, and a contradiction is derived, thereby proving the original statement by contradiction.
A set of axioms is (syntactically, or negation-) complete if, for any statement in the axioms' language, that statement or its negation is provable from the axioms. [2] This is the notion relevant for Gödel's first Incompleteness theorem.
In most logical systems, negation, material conditional and false are related as: ¬ p ⇔ (p → ⊥). In fact, this is the definition of negation in some systems, [8] such as intuitionistic logic, and can be proven in propositional calculi where negation is a fundamental connective.
Dialetheism (/ d aɪ ə ˈ l ɛ θ i ɪ z əm /; from Greek δι-di-'twice' and ἀλήθεια alḗtheia 'truth') is the view that there are statements that are both true and false. More precisely, it is the belief that there can be a true statement whose negation is also true. Such statements are called "true contradictions", dialetheia, or ...