TECH: AFTERTHOUGHT SCOPE

[ucleaar <ucleaar@UCL.AC.UK>]

Here is a discussion paper on afterthought scope. It discusses what
we should be able to do scopewise in afterthought, and possible ways
of doing it. I think it requires about 6 to 9 new cmavo, all in existing
selmao, plus perhaps some optional extras in UI.

                   AFTERTHOUGHT SCOPE

1. SCOPE-SENSITIVITY

SCOPE-SENSITIVE terms comprise all sumti whose innermost descriptor
is (implicitly or explicitly) {lo}.

SCOPE-INSENSITIVE terms comprise all sumti whose innermost descriptor
is {le}.

At this stage I'm ignoring {la}, {lai}, {lahi}, {loi}, {lohi}, {lei}
and {lehi}. I'm also ignoring {na} and coordinators.

Relative scope between two terms matters if at least one of them is
scope-sensitive. (An exception to this is <{suo lo},{suo lo}>
and <{ro lo},{ro lo}> pairs: the relative scope of these makes no
difference to the meaning. I shall ignore this exception.)

2. POSSIBLE SCOPES FOR A PAIR OF TERMS

2.1 SCOPE-INSENSITIVE + SCOPE-INSENSITIVE

Scope is not an issue here. {le ci nanmu cu batci le re gerku} means
that each of a certain three men bit each of a certain three dogs.

2.2 SCOPE-INSENSITIVE + SCOPE-SENSITIVE

There are two possibilities here.

2.2.1 {le ci nanmu} has scope over {re gerku}

   {le ci nanmu cu batci re gerku}
   "Ax, x in C (a certain cimei): x is man, Ey, y a remei, Az, z
    in y: z is dog, x bite z"
   There are exactly three men, and up to six dogs.
   "Ax" precedes "Ey"

2.2.2 {le ci nanmu} does not have scope over {re gerku}

   {re gerku cu se batci le ci nanmu}
   "Ey, y a remei, Az, z in y: z is dog, Ax, x in C (a certain cimei):
    x is man, x bite z"
   There are exactly three men and exactly two dogs.
   "Ey" precedes "Ax"

The relevant scope difference is whether the "Ax" precedes or follows
the "Ey".

2.3 SCOPE-SENSITIVE + SCOPE-SENSITIVE

There are three possibilities here.

2.3.1 {ci nanmu} has scope over {re gerku}

   {ci nanmu cu batci re gerku}
   "Ew, w a cimei, Ax, x in w: x is man, Ey, y a remei, Az, z in y:
    z is dog, x bite z"
   There are exactly three men and up to six dogs.
   "Ew" precedes "Az"
   "Ax" precedes "Ey"

2.3.2 {re gerku} has scope over {ci nanmu}

   {re gerku cu se batci ci nanmu}
   "Ey, y a remei, Az, z in y: z is dog, Ew, w a cimei, Ax, x in w:
    x is man, x bite z"
   There are exactly two dogs men and up to six men.
   "Ey" precedes "Ax"
   "Az" precedes "Ew"

2.3.3 {ci nanmu} and {re gerku} have coordinate scope

   {ci da poi nanmu e re de poi gerku zohu da batci de}
   "Ew, w a cimei, Ey, y a remei, Ax, x in w, Az, z in y: x is man,
    z is dog, x bite z"
   There are exactly three men and exactly two dogs.
   "Ew" precedes "Az"
   "Ey" precedes "Ax"

3 KINDS OF AFTERTHOUGHT SCOPE

I suggest that we have devices for indicating the following:

   * the scope of a scope-sensitive sumti relative to another specified
     sumti
   * the scope of a scope-insensitive sumti relative to another specified
     scope-sensitive sumti

The specified sumti can be

   * specified by an anaphor (pro-form)
   * the first term in a specified prenex
   * the last term in a specified prenex

[Where the prenex (i) contains only what has been put in it so far,
and (ii) can be implicit.]

The 5 kinds of scope (defined above) are:

   * X and Y have coordinate scope
     [X and Y are scope-sensitive]
   * X has scope over Y
     [Y is scope-sensitive]
   * Y has scope over X
     [X is scope-sensitive]
   * X doesn't have scope over Y
     [X is scope-insensitive, Y is scope-sensitive]
   * Y doesn't have scope over X
     [X is scope-sensitive, Y is scope-insensitive]

For the parsimoniously minded, the last two aren't strictly necessary.

4 SUGGESTIONS FOR IMPLEMENTATION

4.1 Scope relative to another sumti specified by an anaphor

Add 5 new cmavo in GOI, one cmavo for each of the 5 kinds of scope.
{SUMTI-X GOI SUMTI-Y} means "X is in the specified scope relationship
with Y".

4.2 Scope relative to the first/last term in a specified prenex

Define the following anaphoric possibilities:

  X is the { first | last } term in the prenex of Y

where Y, working recursively, is either

  the { outermost | localmost } bridi

or

  the bridi one level of embedding toward the middle of the bridi
  hierarchy away from Y

Thus we need the following cmavo:

  * the outermost bridi - GOhA
  * the localmost bridi - GOhA [this exists, as {nei}]
  * the bridi one level of embedding toward the middle of the bridi
    hierarchy away from ... - LAhE (1)
  * the first term in the prenex of - LAhE (2)
  * the last term in the prenex of - LAhE (2)

[i.e. in total, 3 new cmavo in LAhE, and 1 new cmavo in GOhA]

These can then be used with GOI as in 4.1.

The structure would be: SUMTI-1 GOI LAhE (2) (LAhE (1))* GOhA

5 ABBREVIATORY DEVICES

Define a set of cmavo in UI that toggle between current scope defaults.

Where X precedes Y:

   X has scope over Y / Y has scope over X / X and Y are coordinate

---
And