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I'm interested in knowing if there is a specific term for the phenomenon (in English) where a word with a positive connotation can be modified to create a word or phrase with a negative connotation (or, perhaps, vice versa). I can think of two examples to illustrate: namely, preceding a word with "not" or prefixing it with "un."

kind -> unkind
intelligent -> unintelligent
pretty -> not pretty
happy -> not happy

(It seems easier to think of positive-to-negative examples, and I'm guessing this may be more common in English.)

Is there a specific term to indicate this transformation? Thanks!

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    Negation (linguistics), a grammatical operation by which a proposition is replaced by one that states the opposite, as by the addition of not
    – bytebuster
    Jun 23 '16 at 20:22
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    @bytebuster Although negation usually revereses the meaning, negating an adjective doesn't necessarily lead to the opposite meaning: not pretty is not automatically ugly, not hot is not automatically cold etc. Especially for adjectives that can be described as scale of meanings - like hot - warm - lukewarm - cool - cold and infinitely many steps in betweeen - negation results in negating the positive end of the scale, but usually not in expressing the opposite end of the scale.
    – lemontree
    Jun 23 '16 at 20:41
  • You could even claim that by saying not hot, the absolute opposite is excluded: Although, semantically seen, saying not hot would include cold, you can infer that it's not meant to mean cold by pragmatic reasoning - the speaker should try to be as informative as he can so if he could have said something stronger, he would have done so, but since he didn't, he must think that the stronger propositoin is not true etc; this would be the reasoning along the lines of Gricean conversational implicatures, or theories of speaker and hearer economy.
    – lemontree
    Jun 23 '16 at 20:44
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    (Of course, this is not always as simple; you could now argue that not pretty will indeed often be used to express ugly for reasons of e.g. politeness; in that way, using a euphemism will eventually lead to the more neutral expression receiving a more negative meaning - which takes us back to perjoration.)
    – lemontree
    Jun 23 '16 at 20:49
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Change in connotation

If it's about connotation:
A word receiving a more negative connotation is called pejoration.
A word receiving a more positive connotation is called melioration.

However, those two terms are perhaps not perfectly suitable, at least I'm not aware of an alternative terminology that would express more precisely what you mean:
Pejoration and melioration is more about a single word undergoing a change in meaning over time; e.g. silly used to mean something like happy, unworried in Middle English and over time received the meaning of stupid or ridiculous, so the word itself changed its meaning or, if you want to call it like this, connotation.
In the examples that you gave, one could not really speak of such a semantic change, since you modify the expression (by adding un- or not) so as to express something different, while the orignial word itself retains its meaning.
So there might be the need of a different terminology here, depending on how narrow you set the definition of pejoration and melioration, but I doubt there is an actual term that expresses modification with respect to connotation for the following reason:

I would like to comment that "connotation" is a term that is not so easy to define and probably not that often used in semantics, rather maybe in pragmatics (some may even say it's outdated; I recently read a comment to some question here on Ling.SE (don't remember who it was though) saying that connotation is more of a rhetorical term that was already used by the Ancient Greeks and not something that you could use as a neutral scientific term nowadays).
This, and the choice of the clearly negating morphemes not and un-, is why I'd go with a simpler description:


Negation

If it's not about the rather vague notions like positive or negative but simply negating its meaning1 by using not or un- like in the examples you gave, this can semantically be captured conciselier, e.g. by truth conditions, and is then simply called negation.
The linguistic means that are used to express negation can be negation affixes (such as un-), negation particles (such as not) or, less common across the languages of the world, e.g. a negation verb (such as ei in Finnish and Estonian).


About the distribution of positive and negative adjectives

Regarding your observation that positive --> negative seems to b a more common thing to do than the other way round:
This is indeed so; languages tend to have the more "positive" term (although it is now of course very hard to define again what "posivitve" should be, but see my paragraph below) in their vocabulary and derive the negative word from the positive one (by use of the various negation tools I mentioned), much less frequently the other way round:
"positive" now explicitely not primarily referring to connotation, but positive in the sense of presence of a property - someone is either pretty or you can not assign him the property of being especially pretty, physically there is no actual coldness but only the absence of heat, something is loud or less loud but you wouldn't perceive this as different intensity of quietness, and so on; you can do this for maybe not all2, but many adjectives, at least the ones that have meaningful alternatives3 or a scalar meaning space, and there are some studies investigating what those "default" concepts are across the languages of the world and what is more or less universal in human perception of standards/positives of such properties.
You'll see this especially in languages with smaller vocabulary, most noteably perhaps constructed languages, and among those especially ones that try to be very minimalist (like Toki Pona, which has a basic vocabularly of just slightly over 100 words!) or logical (like Loglan/Lojban, aUI and others). Of course, conlangs can not be granted the same status as natlangs when it comes to linguistic universals, but I'd say that someone explicitely thinking about how to build up a language's lexicon gives even more significant evidence of what humans consider to be the basic notions.


Footnotes

1 This may sometimes correspond to the opposite, but especially for words like pretty or hot which are scalar adjectives you won't necessarily receive the exact opposite like ugly or cold, but rather not pretty, but not exactly ugly or not hot, but not actually cold either - see my comment under the question.

2 The phenomenon for example doesn't apply for adjectives like dead, you can not be "deader" or so, although something could certainly be taller, heavier, older, ...
Also you couldn't really make judgements about adjectives like alleged in John is an alleged murderer, being alleged is not a property that applies or doesn't apply to an individual.
There are some more examples; just saying that the concept of something like positive values for adjectives has its restrictions.

3 By "meaningful alternatives", I mean alternatives that form a kind of natural class - you can certainly assume that the set of small [-tall] things forming something like a natural class, but it is implausibel to assume that there are any common features among the things that are not glued apart from not being glued, so adjectives like glued could i.m.o. be regareded as a more privative feature whose absence does not result in the formation of a natural class of meaningful alternatives.
Just like in phonology, where it is perfectly fine to have a class of voiced [+voice] and a class of unvoiced [-voice] sounds, while on the other hand, you could form a class of all sounds that carry the feature [PHARYNGEAL], but it makes no sense to speak of the class of all sounds that are not pharyngeal because they don't have anything in common appart from being not pharyngeal.
I think the distinction of privative features as opposed to, e.g., binary features roughly captures what I mean by an adjective not having "meaningful alternatives".
But certainly, not every adjective can be regareded as a binary feature either, in fact I think that a strict partition throughout the whole domain between two meaningful alternatives [+property]/[-property] without any values additionally or in between is a very uncommon, if not impossible meaning for adjectives to carry.


Sorry for the long post, it got longer that I had originally planned and probably not every detail is immediately important to the question. I just like giving some advanced information, felt that my original three-sentence answer didn't address the question in enough accuracy and hopefully visually distinguished the side information sufficiently.

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    I appreciate you taking the time for a thorough answer. Obviously, I had some trouble forming the question and don't know too much about linguistics. "Negation" seems to be what I was looking for—the rest is a bonus.
    – Mario
    Jun 24 '16 at 12:43

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