Doubts on scopal combination and passing up of INDEX

I apologize if the following is trivial or has already been asked before, although I searched and did not find any post on this.
From here, we have the this slide


In MRS composition, “The hook of a phrase is the hook of the semantic head daughter, which is determined uniquely for each construction type.” (Copestake, 2005).

I have the following questions:

  1. Here I think probably should be the semantic head daughter of the phrase probably sleeps because it supplies a slot to be filled by the other daughter sleep. However, the INDEX of probably sleeps is shown to be e_s, which is the INDEX of the non-head daughter. So, I guess I have misunderstood something here?
  2. What if the semantic head daughter has no INDEX? What would be the INDEX of the phrase?
  3. Furthermore, it seems that now all non-quantifier EPs have an intrinsic variable of type e or x, so to me it seems that INDEX can then be identified with the intrinsic variable of scopal modifiers, e.g. that of probably, what does not sound correct to me. How can one identify the EPs whose intrinsic variable can be put to INDEX if not all are allowed?

I hope the questions are not too trivial, since I have gone through quite a number of readings and tutorials on MRS already. Any reading suggestion is welcomed! Thanks in advance for the help!

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There’s no need to apologise!

You’re right that probably is the semantic head. The answer to your puzzle is that its INDEX is identified with its argument’s INDEX. If you look at slide 144, you can see the re-entrancy labelled [e].

This re-entrancy is easy to miss, so I can understand your confusion! It’s also a subtle point, because the INDEX isn’t part of anything in the RELS list.

Thank you for the clarification! However, I am still not very sure about the passing up mechanism of INDEX.
For instance, when I experiment with the phrase run fast (as in I run fast) in ACE with LUI, the phrase has its INDEX identified by the INDEX of run, which is not the semantic head daughter, and I also do not see similar coindexation in the lexical entry of fast as in that of probably which allows the INDEX of the argument of fast to take over the phrase’s INDEX. What did I miss here?

There are two distinct but related questions here:
(1) what are the rules for semantic composition with MRS?
(2) how is this done in the ERG?

For (1), there is unfortunately no definitive up-to-date document. Copestake (2007) specifically discusses composition, but some details have changed. In particular, adjectives and adverbs (including “fast”) are now analysed as having their own event variables, even when acting as modifiers. This means that they always have an intrinsic variable (e.g. there is an event variable for “furry” in both “the furry dog” and “the dog is furry”). It also allows us to model modifiers being modified (e.g. “the surprisingly furry dog”).

However, this also means that the HOOK can’t be directly passed up. (This is discussed here.) When “fast” modifies “run”, “fast” is the functor and “run” is the argument. Each of them has an event variable, which is their own INDEX. The INDEX of the composed phrase comes from “run”. The difference between scopal modification (e.g. “probably”) and non-scopal modification (e.g. “fast”) is that only scopal modifiers provide a new LTOP.

There has been some discussion about producing an updated semantic algebra (see also here), and I will try to point you to an updated document when I can. But as a brief answer to your question: the INDEX and LTOP will come from either the functor or the argument, depending on the construction.

For part (2) of your question, for the ERG v2018, the passing up of the HOOK is controlled by the syntactic rule, rather than the lexical entry. When “fast” modifies “run”, it uses the hd-aj_int-unsl_c rule, which is a subtype of phrase_or_lexrule and head_compositional. The phrase_or_lexrule type identifies SYNSEM.LOCAL.CONT.HOOK with C-CONT.HOOK, and the head_compositional type identifies C-CONT.HOOK with HD-DTR.SYNSEM.LOCAL.CONT.HOOK. So together, this means that the hook of the phrase (“run fast”) is the hook of the syntactic head daughter (“run”).

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Thanks for the informative reply! The links are on the point. You demonstrated the passing up of HOOK with an example from ERG v2018. As I am currently experimenting with the ERG v1214, is the passing up of HOOK implemented very differently in v2018 than the v1214? It would be nice if I can have an idea briefly of what is changed/improved in the v2018. Any URLs would be good, to save your time on answering. Do you suggest that I switch to v2018?

Besides, after some reading, I have the following “summary” of the mechanism of the passing up of HOOK. Forgive me for the imprecision in the terminology. Would you take a look and let me know if I got anything wrong?

First, consider the scenario where:

A word/phrase X and a word/phrase Y is unified with a syntactic rule R to give a phrase Z

From here,

INDEX always comes from the syntactic head. LTOP normally comes from the syntactic head, but comes from the modifier in scopal modifier examples (`probably sleeps’) in the dmrscomp grammar and I expect there are other cases where this will be necessary.

Given a R, the followings are uniquely determined:

  1. Whether the INDEX of Z comes from X or Y, whichever is the syntactic head as licensed by R

  2. If each of X and Y contains at least one EP (to guarantee semantic composition): whether the semantic composition is scopal (/H as in DMRS), or intersective (/EQ), or neither (/NEQ), and furthermore:

    • If intersective: LTOP of Z is equated with LTOP of X and Y
    • Else if scopal: LTOP of Z is equated with LTOP of the semantic head daughter, i.e. the scopal modifier
    • Else: LTOP of Z is equated with LTOP of either X or Y, which ever is the syntactic head as licensed by R

In other words, the mechanism of the passing up of INDEX and LTOP is encoded in R, and independent of what is in X and Y, which is different from what is described in the slide of my first post. (OR still, probably would encode such information (its INDEX is identified with its argument’s INDEX)
which is still essential to guide the passing up of HOOK's information together with R?)

I find it hard browsing for the relevant and concise documentations regarding my doubts, so I could only resort to this forum (luckily this exists!). I hope that the discussion is meaningful. Sorry for the lengthy post. Thank you for your patience!

I was referring to v2018 to be concrete, but what I said would also apply to v1214. The 2018 version is newer, so I would suggest using that if you can. For changes, see the README.

Your summary sounds correct, except that the rule R is not “independent” of X and Y. Each rule can only apply to certain kinds of phrases.

When comparing the slides you linked to and the ERG, remember that they don’t need to have exactly the same feature structures in order to perform the same semantic composition. This is why I said that there are two distinct but related questions here.

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When comparing the slides you linked to and the ERG, remember that they don’t need to have exactly the same feature structures in order to perform the same semantic composition.

I guess by this you mean that different implementation of the feature structures could lead to the same unification result, and that the ERG encodes the information about HOOK passing up in the syntactic rule applied, R, only, but the slides I referred to choose to encode such information in the lexical entries X and Y for demonstration. Does it sound right? Otherwise, if both R and (X and/or Y) store such information and contain conindexation at the HOOK, the passing up mechanism would be unclear, and even cycle may occur I guess?

As an aside, I seemed to have come up with an inaccurate description about the determination of only one type of semantic composition by a syntactic rule R, as it should possible for both intersective, scopal and neither to occur at the same time in a semantic composition during application of the rule R. For instance n_n_cmpnd_phr introduces both intersective and neither-scopal-nor-intersective combinations, where the arguments of a newly introduced predicate compound_rel are identified with the variables in X and Y through both types of combination.

Yes that sounds right.

As for types of semantic composition, it may be helpful to think of a noun-noun compound as having two semantic composition steps (one step for each argument of compound_rel). These two steps can be bundled together, for efficiency.