Composition and Verb Frames

I mentioned verb frames before.
I use (Fillmore 68) as the citation here.
Linguists really think of compositional semantics this way.
I haven't trawled the psych lit for this, but I'm pretty sure it's got really good back up.
Note that people can remember the semantics of a system, but they can't remember the syntax.
You can just align your (single state) FSA with specific frames.
You could also have a state for the base verb, a state for each slot, and do this a couple of times for embedded sentences.
That would cover most sentences, particularly short ones.
However, to do this a psychologically plausible way, you need variable binding.