A connotation is frequently described as either positive or
negative, with regard to its pleasing or displeasing emotional
connection. For example, a stubborn person may be described as being either strong-willed or pig-headed; although these have the same literal meaning (stubborn), strong-willed connotes admiration for the level of someone's will (a positive connotation), while pig-headed connotes frustration in dealing with someone (a negative connotation).
"Connotation" branches into a mixture of different meanings. These could
include the contrast of a word or phrase with its primary, literal meaning (known as a denotation),
with what that word or phrase specifically denotes. The connotation
essentially relates to how anything may be associated with a word or
phrase, for example, an implied value judgement or feelings.
In logic and semantics, connotation is roughly synonymous with intension. Connotation is often contrasted with denotation, which is more or less synonymous with extension.
Alternatively, the connotation of the word may be thought of as the set
of all its possible referents (as opposed to merely the actual ones). A
word's denotation is the collection of things it refers to; its
connotation is what it implies about the things it is used to refer to.
The denotation of dog is (something like) four-legged canine carnivore.
So saying, "You are a dog" would connote that you were ugly or aggressive rather than literally denoting you as a canine.
