Formal semantics (Montague, type-theoretical) of adverbial clauses

Partee has nice summary about the formal semantics of relative clause http://people.umass.edu/partee/MGU_2005/MGU05Lec10.pdf (subordinate adjectival clause). E.g. `At least one boy who Mary loves is happy` has semantics `∃x (boy(x) & loves(x)(Mary) & happy(x))`

My question is - is it possible to represent adverbial clauses in such manner? AS far as I know, then https://link.springer.com/article/10.1007/s10849-017-9246-2 is the most up-to-date analysis of adverbs but it does not include analysis of adverbial clauses which seems to be quite intricate thing: it seems to me that entire clause modifies the verb. E.g. `you can sit where you like` - the entire clause `you like` modifies the verb `sit`. And it is big difference from relative clause - relative clause can be separated as standalone clause which has anaphoric pronoun and this separate clause can be added to the knowledge base. But it is quite different - it seems to me - with adverbial clause which is not understandable if it is taken as separate sentence. I.e. - what to do with the word `which`?

• Note that the semantics given above does not distinguish between what is asserted and what is presupposed (i.e, the relative clause). The sentence does not assert `loves(x)(Mary)`. Commented May 3, 2018 at 0:25
• @jlawler, It doesn't? ∃x (boy(x) & loves(x)(Mary) & happy(x)) does imply ∃x (loves(x)(Mary)) Commented May 3, 2018 at 3:07
• The logical analysis asserts that there is such a boy; the relative clause presupposes it. One of the differences between language and logic; logic is just a stick-figure model of meaning. Commented May 3, 2018 at 3:22
• It is only the relative clauses of definite constructions which are presupposed (because if the relative clause is false, the definite NP fails to refer). But this is an indefinite construction, so what you say is not so. Commented May 3, 2018 at 10:16
• It's not an adverbial clause. "You can sit where you like" is a fused relative construction (the free choice kind) in which "where" combines the functions of antecedent and relativised element. It's very close in meaning to the integrated relative "You can sit anywhere you like". Commented May 3, 2018 at 12:07