Sentence examples for natural negation from inspiring English sources

Usually (N_{I_{T,S,N}}) is called the natural negation generated from I T,S,N.

Let T be a t-norm on the complete lattice L. The function N T :L→L given by N_{T}(x) = sup { y in L | T x,y) = 0_{L} } (2). is a fuzzy negation, called natural negation of T or the negation induced by T. Similarly, we can define a natural negation of a t-conorm S as follows.

Let S be a t-conorm on the complete lattice L. The function N S :L→L given by N_{S}(x) = inf { y in L | S x,y) = 1_{L} } (3). is a fuzzy negation, called natural negation of S or the negation induced by S. Let T be a t-norm and S be a t-conorm on complete lattice L. Thus 1. if T x,y)=0 L for some x,y∈L then y≤N T (x)   2.

Not every natural language negation is a contradictory operator, or even a logical operator.

In a given natural language, contradictory negation may be expressed as a particle associated with a copula or a verb, as an inflected auxiliary verb, as a verb of negation, or as a negative suffix or prefix.

This is because the natural account of the negation of a proposition, namely that it holds on the smallest closed set containing the Boolean negation of the proposition, means that on the overlapping boundary both the proposition and its negation hold.

This is because the natural account of the negation of a proposition in such a space says that it holds on the largest open set contained in the Boolean complement of the set of points on which the original proposition held, which is in general smaller than the Boolean complement.

For Jespersen, the tendency reflected by the neg-raised interpretation of I don't think that $p$ not only illustrates the general strengthening to contrariety but also participates in a more general conspiracy in natural language to signal negation as early as possible.

The simple syntactical nature of logical negation belies the profoundly complex and subtle expression of negation in natural language, as expressed in linguistically distinct categories and parts of speech (adverbs, verbs, copulas, quantifiers, affixes).

That is the nature of negations.

But although this condition is met by the standard rules for conjunction, it is not met by the natural deduction introduction rule for negation, which must employ either another logical constant (\(\dq{\bot}\)) or another instance of the negation sign than the one being introduced.