pulling out leads to arity mismatch in frames-of-frames

[JosephNathaniel]

sometimes we would like pulling out to change the types of arguments inside a conjunction

e.g. "Alice quickly and rapidly loves Bob", initially looks like this:

After pulling out, the composite "quickly and rapidly" becomes transitive, but each of "quickly" and "rapidly" remains intransitive

Essentially, we want the conjunction frame to maintain its X->X->X type

[JosephNathaniel]

Here is another related example -- it does not involve a conjunction, but like the example above it does contain a "higher order frame".

I.e. consider the original example "Alice quickly and rapidly loves Bob". If we call noun states 0th order, and gates 1st order, then adverbs "quickly", "rapidly" are 2nd order (i.e. basic frames), and the conjunction of adverbs "and" is 3rd order (a frame of frames).

The original example shows that pulling out leads to a mismatch in arity when 3rd order components are involved. That is, the gate "loves" has arity 2, but the adverb frames "quickly" and "rapidly" have kept their original arities of 1.

Similarly, consider the sentence "Alice very gently washes Fido". Here "washes" is 1st order, the adverb "gently" is 2nd order (basic frame), and the intensifier "very" is 3rd order (a frame of frames).

If we do pulling out on this sentence, we get a similar problem to the original example.

Here the gate "washed" has arity 2, but the adverb "gently" still keeps its original arity of 1.

There are various reasons why we would probably want the arities of the adverbs in both these examples to change to 2.

This new example suggests the problem is a conceptual one about pulling out in the presence of general 3rd order components (frames of frames), rather than to do with conjunction frames specifically.