ERG vs. MRS Algebra for non-scopal modification with pre-nominal adjectives

My project, POGG, aims to build MRSs from scratch by adhering to composition as it is defined in the MRS Algebra paper and then pass these MRSs to the ERG for generation.

It has been explained to me before that the algebra wasn’t really meant to be used in isolation like this, so naturally I’ve run into a few snags.

One of the big issues I’m having is setting the HOOK on the result of composition.

Per the algebra, the HOOK of the result comes from the HOOK of the semantic functor:

In order to adhere to this, I was “cheating” with adjectives and when I created a starter SEMENT with just one adjectival predicate in the RELS list I would set the INDEX to be the ARG1 of that adjective, so that after being composed with a noun the resulting INDEX would be the ARG0 of that noun.

In order to illustrate this I’m going to consider the sentence “the white cat sleeps.”

; cat 
[
    LTOP: h0
    INDEX: x1
    RELS: <[
        _cat_n_1
        LBL: h0
        ARG0: x1
    ]>
    HCONS <>  
]

; white 
[
    LTOP: h3
    INDEX: x5 <-- comes from ARG1 rather than ARG0
    RELS: <[
        _white_a_1
        LBL: h3
        ARG0: e4
        ARG1: x5
    ]>
    HCONS <>  
]

; white cat 
; establish equality between x1 and x5 so that white.ARG1 = cat.ARG0
; LTOP comes from 'white' 
; INDEX also comes from 'white' which has been cheesed to be ARG0 of cat because of how I created the starter SEMENT for 'white'
[
    LTOP: h3
    INDEX: x1
    RELS: <[
        _white_a_1
        LBL: h3
        ARG0: e1
        ARG1: x1
    ],
    [
        _cat_n_1
        LBL: h0
        ARG0: x1
    ]>
    HCONS <>  
]

There are a few problems with this.

  1. As far as I know, the LTOPs of two SEMENTs should be identified during composition, but I don’t see where in the algebra this gets established. All I’m able to find is that the resulting hook comes from the functor, but not that the LTOP between the functor and argument are identified.
  2. This hack does not work in more complex cases like “the extremely white cat.”
    • The starter SEMENT for “extremely” states its INDEX is its ARG1
    • The starter SEMENT for “white” states its INDEX is its ARG1
    • When composing “extremely white” with “extremely” as the functor, it will plug the ARG1 slot with the INDEX of “white” which is now pointing to what white modifies, when the ARG1 of “extremely” needs to be the “white” situation itself.

In trying to figure out a potential solution, I dug around in the ERG to see how this construction is handled there, and I am confused about what I’m seeing.

From what I can tell, the rule that composes “white cat” (adj_n_rule) has the constraint (or at least one of its supertypes does) that LOCAL.CONT.HOOK is identified with the following:

  • C-CONT.HOOK
  • ARGS.FIRST.SYNSEM.LOCAL.CAT.HEAD.MOD.FIRST.LOCAL.CONT.HOOK (the HOOK of what the non-head daughter, “white”, modifies, i.e. “cat”)
  • ARGS.REST.FIRST.SYNSEM.LOCAL.CONT.HOOK (the HOOK of the head daughter, “cat”)

So the HOOK of the mother node comes from “cat,” which is the syntactic head, but it was my understanding that in the algebra the HOOK should come from the semantic head/functor, which here would be “white.”

It does make more sense to me that ultimately the INDEX of “white cat” should be coming from “cat” because that is the variable we probably want in further composition, but why would the algebra be defined the other way around? And why does the ERG not follow the algebra here (even though it seems to make more sense to me that it wouldn’t)?