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I'm currently writing a term paper where I am comparing if... then..., only if..., and if... only then... statements.

I've noticed that only if p q and if p, only then q have the same truth conditions (namely q implies p). Additionally, unlike if... then... statements, both show a preference for subject-verb inversion:

If Mary tells John (then) it will ruin the surprise.
*If Mary tells John (then) will it ruin the surprise.

Only if Mary tells John will it ruin the surprise.
*Only if Mary tells John it will ruin the surprise.

If Mary tells John, only then will it ruin the surprise.
*If Mary tells John, only then it will ruin the surprise.

However, there are differences. While if... then... seems to allow "then" to be elided at will, only if... seems to strictly ban "then" while if... only then... seems to strictly require it:

If Mary tells John (then) it will ruin the surprise.
?Only if Mary tells John then will it ruin the surprise.
*If Mary tells John, only will it ruin the surprise.

My intuition is that only if... and if... only then... share the same syntactic structure but undergo different overt raisings and that the differences in "then" insertion are due to those raisings.

UPDATE - According to the link in Alex B.'s comment, "if" is a complementizer and the related CP is simply adjuncted on to a VP. That VP is embedded in an IP (where "then" is an inflectional). Also, the CP headed by "if" has the potential to raise to SpecIP. So far so good.

I am assuming that the "only" phrase must scope immediately over the "if" CP because if it scopes immediately over IP then we incorrectly predict the following struture is possible:
I am guessing that the "only" phrase must come immediately over the IP since it is the only way to explain the following structure:

only (?then) q if p
(You should) only call the police if you see something suspicious
If you see something suspicious, only then (should you) call the police

This still leaves me with the problem of what the "only" phrase is. It is modifying an IP, thus cannot be adjectival nor adverbial.

Also, I still have the issue of "then" support. This isn't that big a deal. It seems analoguous to the problem of why C is null for non-embedded CP (in English).

NOTE - Although this is related to my term paper, this is not the topic of my term paper. Still, I understand if some people do not want to give overt answers.

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    see examples (93a-c) in www-bcf.usc.edu/~pancheva/bhatt-pancheva_syncom.pdf
    – Alex B.
    Jun 21, 2012 at 16:20
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    "Sentence-final IF-clause are adjoined to VP of the main clause. Iatridou also demonstrates that IF-clauses are base-generated in this lower position and then A’-move to sentence-initial position, adjoined to IP." see p. 6 for a tree diagram ling.umd.edu/~htaylor/papers/Taylor_Conditionals.pdf
    – Alex B.
    Jun 21, 2012 at 16:46
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    Assuming LF means logical form, no. The sentences you ask about could be logically equivalent, but the sentence structures are clearly different. Maybe you mean to ask whether their deep (or remote) structures are the same?
    – Greg Lee
    Jul 28, 2018 at 11:01
  • @AlexB. She argues that and provides some evidence, but I think she falls somewhat short of showing it!
    – Araucaria - him
    Aug 28, 2022 at 10:52
  • Long past its usefulness to you, but I have long disagreed with the claim that the consequent clauses of Only if conditionals exclude then. It seems to me that almost any adjunct which can occur in both clause-initial and post-auxiliary position must come in the latter in only if conditionals. For example: Only if she finishes here homework, later she will be able to go to the party (ungrammatical), versus Only if she finishes her homework will she later be able to go to the party. Same thing goes for the prepositional adjunct then. (1/2)
    – Araucaria - him
    Aug 28, 2022 at 10:59

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