Sweet classifies the words in several ways. They are sentence-modifying adverbs, adverbs that act as modifiers to an entire sentence. They are also sentence words, when standing alone. They may, as question responses, also be absolute forms that correspond to what would otherwise be the not in a negated echo response.
For example, a "No." in response to the question "Is he here?" is equivalent to the echo response "He is not here." Sweet observes that there is no correspondence with a simple yes in the latter situation, although the sentence-word "Certainly." provides an absolute form of an emphatic echo response "He is certainly here." Many other adverbs can also be used as sentence words in this way.
Unlike yes, no can also be an adverb of degree, applying to adjectives solely in the comparative (e.g. no greater, no sooner, but not no soon or no soonest), and an adjective when applied to nouns (e.g. "He is no fool." and Dyer's "No clouds, no vapours intervene.").
Grammarians of other languages have created further, similar, special classifications for these types of words. Tesnière classifies the French oui and non as phrasillons logiques (along with voici). Fonagy observes that such a classification may be partly justified for the former two, but suggests that pragmatic holophrases is more appropriate.