What is the common MRS between "We both will have soup" / "We will both have soup" meaning "2 of us will have soup"?

I expected the two phrases:

“We both will have soup”
“We will both have soup”

To both share an (identical) MRS that means “the two of us will have soup”, along with possible other interpretations.

But the only MRS they have in common is this one:

[ "we will both have soup" /  "we both will have soup"
  TOP: h0
  INDEX: e2 [ e SF: prop TENSE: fut MOOD: indicative PROG: - PERF: - ]
  RELS: < [ pron<0:2> LBL: h4 ARG0: x3 [ x PERS: 1 NUM: pl IND: + PT: std ] ]
          [ pronoun_q<0:2> LBL: h5 ARG0: x3 RSTR: h6 BODY: h7 ]
          [ _both_a_1<8:12> LBL: h1 ARG0: i8 ARG1: e2 ]
          [ _have_v_1<13:17> LBL: h1 ARG0: e2 ARG1: x3 ARG2: x9 [ x PERS: 3 NUM: sg ] ]
          [ udef_q<18:22> LBL: h10 ARG0: x9 RSTR: h11 BODY: h12 ]
          [ _soup_n_1<18:22> LBL: h13 ARG0: x9 ] >
  HCONS: < h0 qeq h1 h6 qeq h4 h11 qeq h13 > ]

It seems like that is a different interpretation than the one I’m looking for since both_a_1 is modifying the introduced event of _have_v_1, which maybe means something like “to have both of”? Am I wrong about this?

“we both will have soup” generates an additional MRS which I believe is the interpretation I am looking for:

[ "we both will have soup"
  TOP: h0
  INDEX: e2 [ e SF: prop TENSE: fut MOOD: indicative PROG: - PERF: - ]
  RELS: < [ pron<0:2> LBL: h4 ARG0: x3 [ x PERS: 1 NUM: pl IND: + PT: std ] ]
          [ pronoun_q<0:2> LBL: h5 ARG0: x3 RSTR: h6 BODY: h7 ]
          [ appos<0:2> LBL: h4 ARG0: e8 [ e SF: prop TENSE: untensed MOOD: indicative ] ARG1: x3 ARG2: x9 [ x PERS: 3 NUM: pl ] ]
          [ _both_q<3:7> LBL: h10 ARG0: x9 RSTR: h11 BODY: h12 ]
          [ card<3:7> LBL: h13 ARG0: e15 [ e SF: prop TENSE: untensed MOOD: indicative PROG: - PERF: - ] ARG1: x9 CARG: "2" ]
          [ generic_entity<3:7> LBL: h13 ARG0: x9 ]
          [ _have_v_1<13:17> LBL: h1 ARG0: e2 ARG1: x3 ARG2: x16 [ x PERS: 3 NUM: sg ] ]
          [ udef_q<18:22> LBL: h17 ARG0: x16 RSTR: h18 BODY: h19 ]
          [ _soup_n_1<18:22> LBL: h20 ARG0: x16 ] >
  HCONS: < h0 qeq h1 h6 qeq h4 h11 qeq h13 h18 qeq h20 > ]

… but this isn’t generated from “we will both have soup”, so it doesn’t seem right either (or it would be available from both phrases)

Does anyone know which of the two MRSs above really does mean “the two of us will have soup”?

@Dan, any thoughts here?

The second analysis of “we both will have soup” is probably the one you want, where “both” combines with “we” to form the subject NP. This MRS is not readily possible for the sentence “we will both have soup” since “both” and “we” don’t form a syntactic constituent. The other MRS, which is available for both sentence variants, treats “both” as a verb phrase modifier, so its meaning is something more like that of “we will have soup together”. These so-called “floating” quantifiers pose a general problem for our method of composing semantics; other examples are “we will all have soup” and “we will each have a dessert”, where again it would be nice to have the semantics of “all” or “each” combine with that of “we” to produce a meaning closer to the paraphrases “all of us” or “each of us”. It’s possible to imagine a revised analysis where the VP-modifying “both” would grab the HOOK of the VP’s subject rather than the HOOK of the VP to produce something closer to what we want, so I’ll give that some more thought.

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Rather than revising the composition to allow for floated quantifiers, let me put another perspective, which is that this might all be regarded as verb phrase modification (I think Dowty has an analysis along these lines). The observation is that “We will have soup.” has a reading which is semantically equivalent to “We will both have soup.” and (I think) the same is true of the other examples. (Just to be clear, when I say “reading” I don’t think there’s any sort of syntactic ambiguity - I’m just saying that there’s an interpretation which is equivalent in the model. So the floated quantifier is directing that you select a particular one of those available readings (more precisely, a subset of those available readings). Exactly how one does that involves thinking about the details of the event-based analysis, but I think it’s possible to do it via event modification, at least to a decent first approximation. I wrote some notes on this decades ago but I have no idea if I can retrieve them …

Thanks for the comments @Dan and @AnnC!

@AnnC, I like your approach of treating “both” as helping choose between the readings for the x variables in the verb they are modifying. The way I’ve already implemented _together_p(e,e) is by doing exactly that: limiting each of the x variables, in turn, in the targeted verb to a particular interpretation. So, doing the same with “both” is at least consistent with the direction I’ve gone so far.
It also has the practical advantage to being a form that is available to both “We both will have soup” and “We will both have soup” in the current ERG.

Since a bunch of related phrases like “both have”, “have together”, “have separately”, “each have” all generate a predication that works against the verb’s introduced event, in a form like: _both_a_1(i8, e2), _have_v_1(e2, x3, x9) (see below for two examples) it gives me a general approach I can use for them all.

[ "we will each have soup"
  TOP: h0
  INDEX: e2 [ e SF: prop TENSE: fut MOOD: indicative PROG: - PERF: - ]
  RELS: < [ pron<0:2> LBL: h4 ARG0: x3 [ x PERS: 1 NUM: pl IND: + PT: std ] ]
          [ pronoun_q<0:2> LBL: h5 ARG0: x3 RSTR: h6 BODY: h7 ]
          [ _each_a_1<8:12> LBL: h1 ARG0: i8 ARG1: e2 ]
          [ _have_v_1<13:17> LBL: h1 ARG0: e2 ARG1: x3 ARG2: x9 [ x PERS: 3 NUM: sg ] ]
          [ udef_q<18:22> LBL: h10 ARG0: x9 RSTR: h11 BODY: h12 ]
          [ _soup_n_1<18:22> LBL: h13 ARG0: x9 ] >
  HCONS: < h0 qeq h1 h6 qeq h4 h11 qeq h13 > ]

            ┌────── _soup_n_1(x9)
udef_q(x9,RSTR,BODY)               ┌────── pron(x3)
                 └─ pronoun_q(x3,RSTR,BODY)    ┌── _each_a_1(i8,e2)
                                        └─ and(0,1)
                                                 └ _have_v_1(e2,x3,x9)
[ "we will have soup separately"
  TOP: h0
  INDEX: e2 [ e SF: prop TENSE: fut MOOD: indicative PROG: - PERF: - ]
  RELS: < [ pron<0:2> LBL: h4 ARG0: x3 [ x PERS: 1 NUM: pl IND: + PT: std ] ]
          [ pronoun_q<0:2> LBL: h5 ARG0: x3 RSTR: h6 BODY: h7 ]
          [ _have_v_1<8:12> LBL: h1 ARG0: e2 ARG1: x3 ARG2: x8 [ x PERS: 3 NUM: sg ] ]
          [ udef_q<13:17> LBL: h9 ARG0: x8 RSTR: h10 BODY: h11 ]
          [ _soup_n_1<13:17> LBL: h12 ARG0: x8 ]
          [ _separate_a_from<18:28> LBL: h1 ARG0: e13 [ e SF: prop TENSE: untensed MOOD: indicative PROG: - PERF: - ] ARG1: e2 ] >
  HCONS: < h0 qeq h1 h6 qeq h4 h10 qeq h12 > ]

               ┌────── pron(x3)
pronoun_q(x3,RSTR,BODY)            ┌────── _soup_n_1(x8)
                    └─ udef_q(x8,RSTR,BODY)    ┌── _separate_a_from(e13,e2)
                                        └─ and(0,1)
                                                 └ _have_v_1(e2,x3,x8)