Edit: More Context: At least one other Indo-European language (Latvian) uses a morphological conditional mood for the politely enquiring about desired future states: vai tu gribētu … ? Is equivalent to "Would you like … ?" and the verb is in the conditional mood. This prompted me to consider whether (and how) "Would you … " is in the conditional mood in English.
Edit: Not a duplicate:
Not a duplicate of Which dialects of English consider "would" to be a polite form of "will"? because that question deals with cases in which would is directly substituted for will. No such substitution can be made for "Would you like to dance?" – "Will you dance?" has a different meaning and *"Will you like to dance?".
Question:
Most explanations of the conditional mood (e.g. WP) are statements not questions, and the examples they give generally include both the the apodosis and protasis.
I am looking for an analysis of expressions like:
Would you like to dance?
(in which I assume to like is in the conditional mood).
Possible Explanation 1
Does it have an implied dependent clause? E.g.
[If I had opportunity], I would like to dance.
[If you had the opportunity], you would like to dance.
And then as a question:
[If you had the opportunity], would you like to dance?
[If it was with me], would you like to dance?
Possible Explanation 2
I am not 100% satisfied with those examples though, because to me any condition is specific, and omitting the dependent clause also omits any "specificity". Which makes me wonder if lack of specificity is the whole point of omitting the dependent clause, for example:
[There exists a condition under which] I would like to dance.
[Does there exist a condition under which] you would like to dance?
[*Does there exist a condition under which] would you like to dance?
Edit: Possible Explanation 3
Replying to comments I thought of some constructions that demonstrate the probable conditionality of "Would you like … ?"
Take an unambigious conditional like:
If it happened, you would like it.
We can step towards "Would you like …"
If we danced, you would like it.
If we danced, you would like to dance.
Now question the truth of that statement:
If we danced, you would like to dance?
But the statement has some redundancy, let's remove it
[If we danced] you would like to dance?
You would like to dance?
Would you like to dance?
Or maybe "Would you … ?" is not in the conditional mood at all?
Best Answer
I agree with the above "if-dependency" comment by msam.
Modals have many uses. The 'polite form usage' is relevant here:
"We can use certain modal verbs, especially the past forms of the modal verbs can, may, shall and will (could, might, should and would), to be more polite or less direct."
(source: https://dictionary.cambridge.org/grammar/british-grammar/functions/politeness)
In your example, it does not seem to be a conditional because there is no condition imposed. "Would you like to dance?" is an invitation, yes/no reply.