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In logic, a set of symbols is commonly used to express logical representation. The following table lists many common symbols, together with their name, how they should be read out loud, and the related field of mathematics.
Affirmation and negation are a crucial building blocks for language. The presence of negation is the absence of affirmation, where affirmation functions individually. [1] There are three main aspects to the concept of affirmation and negation; Cognitive, psychological and philosophical (Schopenhauers theory or Nietzschean affirmation).
A negation is a negative polarity item, abbreviated NPI or NEG. The linguistic environment in which a polarity item appears is a licensing context. In the simplest case, an affirmative statement provides a licensing context for a PPI, while negation provides a licensing context for an NPI. However, there are many complications, and not all ...
The affirmative and negative responses to positively phrased questions are da and nu, respectively. But in responses to negatively phrased questions they are prefixed with ba (i.e. ba da and ba nu). nu is also used as a negation adverb, infixed between subject and verb. Thus, for example, the affirmative response to the negatively phrased ...
The logical quality of a proposition is whether it is affirmative (the predicate is affirmed of the subject) or negative (the predicate is denied of the subject). Thus "every man is a mortal" is affirmative, since "mortal" is affirmed of "man". "No men are immortals" is negative, since "immortal" is denied of "man". [1]
Negation: the symbol appeared in Heyting in 1930 [3] [4] (compare to Frege's symbol ⫟ in his Begriffsschrift [5]); the symbol appeared in Russell in 1908; [6] an alternative notation is to add a horizontal line on top of the formula, as in ¯; another alternative notation is to use a prime symbol as in ′.
The formulations here use implication and negation {,} as functionally complete set of basic connectives. Every logic system requires at least one non-nullary rule of inference. Classical propositional calculus typically uses the rule of modus ponens:
In logic, negation, also called the logical not or logical complement, is an operation that takes a proposition to another proposition "not ", written , , ′ [1] or ¯. [citation needed] It is interpreted intuitively as being true when is false, and false when is true.