Scopes and quantifiers

From the @guyemerson’s paper Linguists Who Use Probabilistic Models Love Them: Quantification in Functional Distributional Semantics - ACL Anthology, I thought that all scopes with quantifiers should have only one EP, the quantifier itself. But exploring the profiles under erg/tsdb/gold/ I found many cases a quantifier EP shares the same label with another non-quantifier EP.

Nearly every dog barked.

[ TOP: h0
  INDEX: e2
  RELS: < [ _nearly_x_deg<0:6> LBL: h4 ARG0: e5 ARG1: u6 ]
          [ _every_q<7:12> LBL: h4 ARG0: x3 RSTR: h7 BODY: h8 ]
          [ _dog_n_1<13:16> LBL: h9 ARG0: x3 ]
          [ _bark_v_1<17:23> LBL: h1 ARG0: e2 ARG1: x3 ] >
  HCONS: < h0 qeq h1 h7 qeq h9 > ]

[<EP object (h4:_nearly_x_deg(ARG0 e5, ARG1 u6)) at 4895099392>, 
 <EP object (h4:_every_q(ARG0 x3, RSTR h7, BODY h8)) at 4895099584>]

or

Not all those who wrote oppose the changes.

[ TOP: h0
  INDEX: e2
  RELS: < [ part_of<0:7> LBL: h4 ARG0: x3 ARG1: x5 ]
          [ _all_q<0:7> LBL: h6 ARG0: x3 RSTR: h7 BODY: h8 ]
          [ not_x_deg<0:7> LBL: h6 ARG0: e9 ARG1: u10 ]
          [ generic_entity<8:13> LBL: h11 ARG0: x5 ]
          [ _those_q_dem<8:13> LBL: h12 ARG0: x5 RSTR: h13 BODY: h14 ]
          [ _write_v_to<18:23> LBL: h11 ARG0: e15 ARG1: x5 ARG2: i16 ]
          [ _oppose_v_1<24:30> LBL: h1 ARG0: e2 ARG1: x3 ARG2: x17 ]
          [ _the_q<31:34> LBL: h18 ARG0: x17 RSTR: h19 BODY: h20 ]
          [ _change_n_of<35:42> LBL: h21 ARG0: x17 ARG1: i22 ] >
  HCONS: < h0 qeq h1 h7 qeq h4 h13 qeq h11 h19 qeq h21 > ]

[<EP object (h6:_all_q(ARG0 x3, RSTR h7, BODY h8)) at 4895059680>, 
 <EP object (h6:not_x_deg(ARG0 e9, ARG1 u10)) at 4895059488>]

Are these MRS valid? If that is the case, the definition of scope tree given by @guyemerson does not apply to scope trees produced from MRS in general.

Each non-terminal node is a quantifier, with its bound variable in brackets. Its left child is its restriction, and its right child its body.

In both cases, the EP that shares the label with a quantifier is completely disconnected from the predicate-argument structure of the sentence. In my tentative to write an MRS to first-order logic translator, it seems that those cases need case-by-case analysis:

  1. not all = some
  2. nearly every = some
  3. about N = ?
  4. about a X = ?
  5. especially X = ?

I know… I know… we already hit the wall trying that in http://svn.delph-in.net/lkb/branches/fos/src/tproving/gq-to-fol.lisp! This is my first step towards a tentative of MRS to dependent types. Comments are welcome! From @AnnC I already expect the suggestion “forget logic… use DMRS…” :wink: