New uses of underspecified variables in the ERG 2018?

I notice that the MRS outputs of the ERG contain i variables more often than in the 1214 version. I’m used to them being used for dropped x arguments, but now I’m asking about them being used as intrinsic variables (ARG0s, abbreviated “IV” below). I show the parses from ACE using the ERG grammar images Woodley distributes. The examples are mostly taken from the mrs test suite.

Number constructions

1214 already used i for some IVs of number constructions, as below for “Twenty three dogs go” (i-id 631):

[ TOP: h0
  INDEX: e2
  RELS: < [ udef_q<0:12> LBL: h4 ARG0: x3 RSTR: h5 BODY: h6 ]
          [ card<0:6> LBL: h7 ARG0: e9 ARG1: x3 CARG: "20" ]
          [ plus<0:6> LBL: h10 ARG0: i11 ARG1: x3 ARG2: h7 ARG3: h12 ]
          [ card<7:12> LBL: h12 ARG0: i14 ARG1: x3 CARG: "3" ]
          [ _dog_n_1<13:17> LBL: h10 ARG0: x3 ]
          [ _go_v_1<18:21> LBL: h1 ARG0: e2 ARG1: x3 ] >
  HCONS: < h0 qeq h1 h5 qeq h10 > ]

But 2018 changes the distribution so card EPs use i variables and the plus is now an e.

[ TOP: h0
  INDEX: e2
  RELS: < [ udef_q<0:12> LBL: h4 ARG0: x3 RSTR: h5 BODY: h6 ]
          [ card<0:6> LBL: h7 ARG0: i9 ARG1: i10 CARG: "20" ]
          [ plus<0:6> LBL: h11 ARG0: e12 ARG1: x3 ARG2: h7 ARG3: h13 ]
          [ card<7:12> LBL: h13 ARG0: i15 ARG1: i16 CARG: "3" ]
          [ _dog_n_1<13:17> LBL: h11 ARG0: x3 ]
          [ _go_v_1<18:21> LBL: h1 ARG0: e2 ARG1: x3 ] >
  HCONS: < h0 qeq h1 h5 qeq h11 > ]

I think this is an improvement, but I’m still not certain why the cards have i IVs at all. Normally they are e in this context, as in the MRS for “Two dogs go”, although they can be x, as in “Two is a number”. I suppose if they were x-like you would not want to quantify them all, but is there more to the story?

Scopal modifiers

In 1214, scopal modifiers (by which I mean things like “probably”, or is the term “scopal operator”?) used e variables, as below for “The dog probably barked” (i-id 451):

[ TOP: h0
  INDEX: e2
  RELS: < [ _the_q<0:3> LBL: h4 ARG0: x3 RSTR: h5 BODY: h6 ]
          [ _dog_n_1<4:7> LBL: h7 ARG0: x3 ]
          [ _probable_a_1<8:16> LBL: h1 ARG0: e8 ARG1: h9 ]
          [ _bark_v_1<17:24> LBL: h10 ARG0: e2 ARG1: x3 ] >
  HCONS: < h0 qeq h1 h5 qeq h7 h9 qeq h10 > ]

But in 2018 they use i variables:

[ TOP: h0
  INDEX: e2
  RELS: < [ _the_q<0:3> LBL: h4 ARG0: x3 RSTR: h5 BODY: h6 ]
          [ _dog_n_1<4:7> LBL: h7 ARG0: x3 ]
          [ _probable_a_1<8:16> LBL: h1 ARG0: i8 ARG1: h9 ]
          [ _bark_v_1<17:24> LBL: h10 ARG0: e2 ARG1: x3 ] >
  HCONS: < h0 qeq h1 h5 qeq h7 h9 qeq h10 > ]

If this is an intentional change and it’s linguistically sound, then maybe we should describe it as a new criterion for well-formed MRSs. Doing so would allow me to improve a couple semantic operations I do in PyDelphin (which I won’t get into here).

I note that the ERG already did this for neg in 1214, as for “Don’t bark!” (i-id 1061)

[ TOP: h0
  INDEX: e2
  RELS: < [ pronoun_q<0:5> LBL: h4 ARG0: x5 RSTR: h6 BODY: h7 ]
          [ pron<0:5> LBL: h8 ARG0: x5 ]
          [ neg<0:5> LBL: h1 ARG0: i9 ARG1: h10 ]
          [ _bark_v_1<6:11> LBL: h11 ARG0: e2 ARG1: x5 ] >
  HCONS: < h0 qeq h1 h6 qeq h8 h10 qeq h11 > ]

and things like addressee, as in “It rained, Abrams” from the esd test suite (i-id 1151):

[ TOP: h0
  INDEX: e2
  RELS: < [ _rain_v_1<3:10> LBL: h1 ARG0: e2 ]
          [ addressee<11:18> LBL: h1 ARG0: i4 ARG1: x5 ARG2: e2 ]
          [ proper_q<11:18> LBL: h6 ARG0: x5 RSTR: h7 BODY: h8 ]
          [ named<11:18> LBL: h9 ARG0: x5 CARG: "Abrams" ] >
  HCONS: < h0 qeq h1 h7 qeq h9 > ]

Summary

There are plenty of other examples in Redwoods but I’ll stop here. I just want to know if there was some new principle applied in the ERG’s MRS outputs to explain these changes, since I didn’t notice anything about it in the release announcement. Or maybe we can categorize when we should expect to see i variables: (1) dropped x arguments; (2) underspecified x/e; (3) scopal modifiers; (4) ???. I also note that there are no p-variable IVs in Redwoods, although they appear in other argument positions for dropped scopal arguments. And if dropped e arguments are possible (all my examples insert ellipses or unknowns), would they be i or p?

And finally, to clarify, I want to distinguish what we can consider core principles of DELPH-IN MRSs (e.g., as we’ve adopted the intrinsic-variable-property), and what is ERG MRS conventions.

Thanks

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It’s been about a month but I’m still hoping to get some feedback about this so we can have a more directed conversation about it in Cambridge.

Also a small correction:

And if dropped e arguments are possible (all my examples insert ellipses or unknowns), would they be i or p ?

That should have been i or u (p is not a supertype of e). But maybe we’d actually want a variable underspecified over e and h?