I know that grammaticality differs from acceptability, but what about acceptability versus felicity? All emboldenings are mine.
Besides grammaticality, notions such as felicity (first used in Austin 1975) and acceptability (first discussed in Quirk and Svartvik 1966) are also frequently used judging tools in theoretical linguistics, which deserve the solid empirical foundation to be properly used in linguistic discussions.
Jieun Kiaer, Pragmatic Syntax 2014. Anyone know the page number?
Matters of preference are not as clear cut as matters of grammaticality. Accordingly, researchers have referred to discourse acceptability, appropriateness or felicity as graded notions, whereas for grammatical phenomena, sentences are seen as either grammatical or ungrammatical (the ✓/* convention).
Mira Ariel, Defining Pragmatics 2010, p. 42.
A third issue that has attracted much attention in recent linguistic scholarship is gradience (see Fanselow, Féry, Vogel and Schlesewsky (eds.) 2006). Variants may not all enjoy the same degree of grammaticality, semantic acceptability or pragmatic felicity. While it has long been known that some grammatical variants are, in some contexts of occurrence or irrespective of context, judged better than others, the implications of gradience for variationist methodology and for grammatical description in general have only recently begun to be taken seriously. Some directions for dealing with gradience, and for complementing the study of linguistic variation by comparing production and perception, are indicated in the contributions by Abraham, Cornips, Salzmann, and Schiering.
Describing and Modeling Variation in Grammar 2009, p. 5.
Despite arguments over a great many details in these proposals, one basic assumption remains unchanged: to the extent that there is order in lin- guistic actions/ behaviour, it is to be sought at the level of linguistic knowledge/norms. It is a common belief among linguists that the meaning of an utterance is 'given' in the rules, conditions, norms and maxims that govern or guide linguistic behaviour, independently of the actual, situated, occasioned contingencies surrounding their occurrence. Knowledge or norms provides, in this view, mechanisms that would determine the grammaticality, acceptability, appropriateness, or felicity of linguistic actions (performance, speech acts, behaviour, use), and a basis for the possibility of communication.
Kang Kwong Luke, Utterance Particles in Cantonese Conversation 1990, p. 30.