xS And anaphora

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And Rosta:

XS & anaphora

On the question of PA LE as antecedent of an anaphor (symbolized as 'RI'). We need to ask both "What does this expression mean?" and "How do we express this notion?". When the lexical antecedent {PA LE}, the notions we want anaphors to express are (or include):

  1. Anaphor expresses the variable bound by PA.
  1. Anaphor expresses the constant expressed by LE.
  1. Anaphor expresses a collectivity of the individuals treated distributively by the lexical antecedent. For things like "There were four men who each shook my hand and who-jointly bought me a drink and three of whom drank my health".

Observations:

  • Note that in {PA RI}, RI can sensibly express only notion (2). So our question is: Which of (1-3) does bare RI express, and how are the other two notions expressed?
  • Notion (1) is a candidate only when the anaphor is within the scope of the PA. When the candidate is outside the scope of the PA, the notion expressed must be (2).
  • Given that {PA LE} is short for {PA da poi...}, (1-3) also pertain to {PA da}, with the difference that bare RI (i.e. tu'oRI as opposed to PA RI) cannot express (2). PA1 RI, if it expresses (2) and the antecedent is (PA2)da poi broda, would mean "PA1 da poi broda".

Hence:

  • At least sometimes, bare RI cannot express (1) or (3): in these cases, either it must express (2) or it must be gobbledygook.
  • If bare RI can take an overt da(poi) expression as antecedent, then in these cases it cannot express (2).

Some possible ways of handling this:

Approach A.

  • Disallow a da-expression as candidate antecedent of bare RI. ({da} itself is available to express (1).)
  • RI always expresses (2), whether or not the antecedent is quantified.
  • We lack a way to express (1) and (3).

Approach B.

  • PA RI always expresses (2).
  • Bare RI always expresses (2) when the antecedent is not a da-expression.
  • When the antecedent is a da-expression and bare RI is in the scope of the antecedent quantifier, RI expresses (1).
  • When the antecedent is a da-expression and bare RI is not in the scope of the antecedent quantifier, then either (i) the expression is gobbledygook, (ii) the da-expression is not a candidate antecedent for RI, or (iii) bare RI = su'oRI.
  • We lack a way to express (1) (for non-da expressions) and (3).

Approach C.

  • PA RI always expresses (2).
  • Bare RI expresses (1) when the antecedent is quantified and has scope over RI.
  • When the putative antecedent is unquantified, either (i) bare RI expresses (2), (ii) it expresses gobbledygook, (iii) bare RI = su'iRI, or (iv) the antecedent is not a licit candidate antecedent.
  • When the putative antecedent does not have scope over RI, either (i) bare RI expresses (2), (ii) it expresses gobbledygook, (iii) bare RI = su'iRI, or (iv) the antecedent is not a licit candidate antecedent.
  • We lack a way to express (2) and (3).

Approach D.

  • Treat PA LE as an antecedent exactly as overt PA da poi ME LE is treated, i.e. as a sumti within a sumti.
  • With antecedent PA1 da poi broda, PA2 RI expresses PA2 da poi broda.
  • Bare RI expresses (1) when the antecedent is quantified and has scope over RI.
  • When the putative antecedent is unquantified, bare RI expresses (2).
  • When the putative antecedent is quantified but does not have scope over RI, bare RI = su'oRI. This is analogous to the rules for {da}.
  • We lack a way to express (3).

Of these three approaches, D is the most radical but works the best. It is radical in that for the purposes of anaphora, PA LE always counts as a sumti within a sumti. It works the best because it sticks closest to the form of the underlying logical expression (deviation from which is the source of a great many of our problems).

If we go with D, the remaining problem is how to express (3). The solution has to be the usual one of using forethought and expressing the antecedent so that it contains an expression of the collective. Thus, instead of {vo broda}, we have {ro ME-member pa lo vo broda}, or, in full, {ro da poi ME-instance lo ME-member pa da poi ME-instance lo vo broda}. It would be nice if XXS could be equipped with a cmavo that abbreviates {da poi ME-instance lo ME-member pa da poi ME-instance lo} or {da poi ME-member pa da poi ME-instance lo}. An o-gadri with ro as default outer PA would do the trick. Call it {loi'o}: then instead of {vo broda} we just say {loi'o vo broda}, which for the purposes of anaphora is equivalent to {ro da poi ME-member pa da poi ME-instance lo vo broda}. As an alternative to {loi'o}, XXS could be revised so that xod-collectives are handled by lV'i, while (ro)lVi are abbreviations for {(ro) da poi ME-member pa da poi ME-instance lV}.

Recap of Approach D

  • According to XXS, only da-variables can be quantified by PA. So PA + anything else is just an abbreviation for a longer expression involving dapoi. Anaphora ignores such abbreviations and treats them as equivalent to their expanded forms with da. PA LE is equivalent to {PA da poi ME LE}, so an anaphor can point (by backcounting or whatever other method) to the sumti LE or to the sumti da.
  • The antecedent of an anaphor can be any logical sumti.
  • When the anaphor is quantified, PA RI, and the antecedent is {da poi broda}, the anaphor means {PA da poi broda}.
  • When the antecedent is quantified by a quantifier that does not have scope over RI, bare RI = su'oRI. This is analogous to the rules for {da}. So in such a case, if the antecedent is {(PA) da poi broda}, then bare RI will mean {su'o da poi broda}.

xorxes:

I would add Approach E, identical to Approach D except for the last point:

  • When the antecedent is quantified by a quantifier that does not have scope over RI, bare RI points to the sumti LE. This should be analogous to the rules for {da}. So in such a case, if the antecedent is {PA da poi broda}, then bare RI will mean {tu'o da poi broda}.

For example {da poi prenu cu prami da} and {lo prenu cu prami ri} would both mean "people love people", whereas {su'o da poi prenu cu prami da} and {su'o lo prenu cu prami ri} would both mean "someone loves themself".

And Rosta

There is a difference (in English) between:

Even George Bush despises himself.

Even George Bush despises George Bush.

Only George Bush admires himself. false

Only George Bush admires George Bush. truish

We might conclude from this that {la djan prami la djan} and {la djan prami ri} are not equivalent, and hence that {lo prenu cu prami ri} means "people love themselves".

I'm not sure whether bare da ought to mean lopoi'i, as you suggest. Maybe. I need to mull over this more.


pc:

This is going to take some working through once I figure out what these critters mean. One thing is fairly clear from the get-go: you never need -- and never should use --other anaphora for explicit bound variables. The variable rules are so much firmer and clearer than any rules about any other kind of anaphora, that to move from variable to pronoun is always to introduce unclarity. The one problem with explicit variables is, of course, scope, which is fuzzy on the left and open-ended on the right. I think it is time for some legislation here. I obviously favor the suggestion made a while back, but can live with any coherent plan. Ones that make for shorter scope, however, do sometimes require shifting to other anaphora, with the losses that entails.

On the other hand, I think that attempts to solve anaphora problems for other locutions by returning to explicit variables is -- while ultimately correct -- liable to produce very inelegant results: unclear and hard to apply at least. I suggest (as seems generally the case here) to work with the surface forms and not the ultimate logic by the side (cf. how to deal with Mr. Broda).


xorxes:

Do we need to treat {da} as a special case? I would prefer to treat bare {da} as any other bare sumti, i.e. as an unquantified constant. {da poi broda} as {lo broda}, Mr Thing which is a broda. Given that, we don't need to make distinctions in how RI deals with {da poi ...} antecedents. The rule would be:

RI repeats its antecedent minus any eventual quantifier, but bare RI within the

scope of its antecedent's quantifier is a variable bound by that quantifier.

(This is more or less Approach D, I think.) In particular, {da} works like any other RI: when under the scope of its antecedent's quantifier, it is a variable bound by that quantifier. In da's case the antecedent is identified by the name of the variable itself. RIs would differ only in how one identifies their antecedent.

  • I am pulled two ways on this. On the one hand, variables just are different from the logical point of view and I am leary of giving that up for the sake of a metaphor. On the other hand, the rule here is rather pretty in its simplicity and, when we deal with the scope issues, pretty much does what is needed. Let's see what the consquences are first. I reiterate that the scope of a short-scope quantifier is the scope of the shortest modal within whose scope it lies.

xorxes:

What, exactly, can the antecedent of anaphora be? In EBNF grammar terms, we have:

sumti = sumti-1 VUhO # relative-clauses

sumti-1 = sumti-2 ([[ek joik) [stag|stag]] KE # sumti /KEhE#/]

sumti-2 = sumti-3 joik-ek sumti-3 ...

sumti-3 = sumti-4 ([[ek joik) [stag|stag]] BO # sumti-3]

sumti-4 = sumti-5 | gek sumti gik sumti-4

sumti-5 = quantifier sumti-6 relative-clauses

| quantifier selbri /KU#/ relative-clauses

sumti-6 = (LAhE # | NAhE BO #) relative-clauses sumti /LUhU#/

| KOhA #

| lerfu-string /BOI#/

| LA # relative-clauses CMENE ... #

| (LA | LE) # sumti-tail /KU#/

| LI # mex /LOhO#/

| ZO any-word #

| LU text /LIhU#/

| LOhU any-word ... LEhU #

| ZOI any-word anything any-word #

sumti-tail = [[sumti-6 [relative-clauses|relative-clauses]] sumti-tail-1

| relative-clauses sumti-tail-1

sumti-tail-1 = quantifier selbri relative-clauses

| quantifier sumti

The obvious candidates for antecedents of anaphora are sumti-5. Can a full sumti be an antecedent? In other words, can an anaphor point to a sumti like {ko'a e ko'e}? It would seem that at least some RI will inevitably point to such things, for example the vo'a-series. The rules for those, according to approach D/E, should be that when RI is under the scope of the connective, it gets distributed accordingly. When it is outside the scope, then it must refer to the underlying group: ko'a joi ko'e (using joi as the connective corresponding to XS groups), for every variety of logical connective.

I just noticed that we can have sumti like {le ci ko'a e ko'e}, which groups as {le ci (ko'a e ko'e)}. Does that make any sense?

And Rosta:

{ko'a ce ko'e} should contain three candidate antecedents, {ko'a ce ko'e}, {ko'a} and {ko'e}. {ko'a e ko'e} should contain four, since it is short for {ro da poi cmima ko'a ce ko'e}: {da (poi cmima ko'a ce ko'e)}, {ko'a ce ko'e}, {ko'a} and {ko'e}. A vo'a-anaphor would point only to {da (poi cmima ko'a ce ko'e)}, but a ri-anaphor could point to any of them.

B e C prami vo'a

B and C love themself

B e C prami ro vo'a

B and C love themselves (i.e. love B and C)

B e C na(ku) prami vo'a

B and C don't love themself

B e C na(ku) prami ro vo'a

B and C don't love both of themselves. (Hard to express unclumsily in English.)

B e C na(ku) prami su'o vo'a

B and C don't love either of themselves.

xorxes: Sounds good. Of course, ro vo'a could also be glorked as:

B e C prami (BAhE-coordinate) ro vo'a

B and C each loves and is loved by at least one of themselves.

{ri} with candidate antecedent from {B e C} can point only to C. Are you saying that {ra} could point to {B ce C} as well as {B} or {C}?

And Rosta:

BAhE-coordinate -- yes.

ri/ra: I propose that ri (or ra?) xi can point to any sumti. Default xipa = last sumti. xire = penult, etc. xiro = first in sentence. xi da'a(pa) = second in sentence. And so on. Taking sumti to be sequenced by their starts, the linear seq is {da poi cmima B ce C} < {B ce C} < {B} < {C}. I had been waiting to write up these proposals until Nick got round to approving my long-standing request to shepherd anaphora, but with the direction things are now taking, I should write them up on a wiki page.

xorxes: So there are two steps: First we identify which sumti the anaphor points to ("the antecedent"), which can be a constant or a quantified/connected expression. Then we decide whether the anaphor repeats the constant or is a variable bound by the quantifier. For example:

no le ci lo mu broda cu brode le nu ko'a e ko'e joi ci ko'i na brodi lu'a re ko'o kei RI

The candidate antecedents for RI are:

1. no le ci lo mu broda

2. lo mu broda

3. le nu ko'a e ko'e joi ci ko'i na brodi vo lu'a ko'o

4. ko'a e ko'e joi ci ko'i

5. ko'a e ko'e

6. ko'a

7. ko'e

8. ci ko'i

9. vo lu'a ko'o

10. ko'o

Then {ri xi ci} will point to {ci ko'i} and {ri xi re} will point to {vo lu'a ko'o}, but in both cases RI is outside the scope of the quantifier, so it repeats the constant {(tu'o) ko'i} and {(tu'o) lu'a ko'o}. In the case of {ri xi ro}, which points to {no le ci lo mu broda}, RI is within the scope of {no}, so it will be bound by that quantifier.

What about sumti in previous sentences? One way could be to use a second index to identify the sentence, so for example {ri xi da'a re pi'e ci} would point to the second sumti of the third sentence back, and {pi'e no} would be the default for the current sentence.

Formally the counting scheme seems to work, but in practice it's almost certainly unusable.

And Rosta:

Unusable: yes, for more than a handful antecedents back. But Step 1 is to find a system that works formally. Step 2 is then to create something more usable (I have ideas for that, but it is premature to deliver them).

Sumti in previous sentences: I'm trying to write up a description of a system that does this (and other stuff).

Antecedents: For the sentence you give, RI has the following meaning under Scheme D (-- not to reject Scheme E, but it needs more discussion).

no le ci lo mu broda cu brode le nu ko'a e ko'e joi ci ko'i na brodi lu'a re ko'o kei RI

|ri xi pa|ko'o|

|ri xi re|su'o da poi ME ko'o|

|ri xi ci|lo BRODA be re ko'o|

|ri xi vo|ko'i|

|ri xi mu|su'o da poi ME ko'i|

|ri xi xa|ko'e|

|ri xi ze|ko'e joi su'o da poi ME ko'i (???)|

|ri xi bi|ko'a|

|ri xi so|ko'a ce ko'e joi su'o da poi ME ko'i (???)|

|ri xi dau|su'o da poi cmima ko'a ce ko'e joi su'o da poi ME ko'i (???)|

|ri xi fei|le nu ko'a e ko'e joi ci ko'i na brodi lu'a re ko'o kei|

|ri xi gai|lo mu broda|

|ri xi paci|da poi ME lo mu broda|

|ri xi pavo|le ci lo mu broda|

|ri xi pamu|da poi ME le ci lo mu broda|

I'm assuming a grouping (ko'a e (ko'e joi ci ko'i]. The items marked '???' arise from dubiety about whether it is desirable for the su'o to occur within the coordination: it's a problem that doesn't arise with Scheme E. Under scheme E, change su'o to tu'o.

xorxes: The {ci} in {no le ci lo mu broda} is not a quantifier, it can't have scope over RI so {ri xi paci} should be {su'o da poi ME lo mu broda}

The canonical grouping is {(ko'a e ko'e) joi ci ko'i}, or with ke: {ko'a e ke (ko'e joi ci ko'i) ke'e}.

And Rosta: Downside of the wiki is it makes me rush. Here's a corrected list:

no le ci lo mu broda cu brode le nu ko'a e ko'e joi ci ko'i na brodi lu'a re ko'o kei RI

|ri xi pa|ko'o

|ri xi re|su'o da poi ME ko'o

|ri xi ci|lo BRODA be re ko'o

|ri xi vo|ko'i

|ri xi mu|su'o da poi ME ko'i

|ri xi xa|ko'e

|ri xi ze|ko'a

|ri xi bi|ko'a ce ko'e

|ri xi so|su'o da poi cmima ko'a ce ko'e ku'o joi su'o da poi ME ko'i

|ri xi dau|le nu ko'a e ko'e joi ci ko'i na brodi lu'a re ko'o kei

|ri xi fei|lo mu broda

|ri xi gai|su'o da poi ME lo mu broda

|ri xi paci|le ci lo mu broda

|ri xi pavo|da poi ME le ci lo mu broda

But in On unglorkative anaphora, I state a preference for:

|ri xi pa|ko'o

|ri xi re|lo BRODA be re ko'o

|ri xi ci|ko'i

|ri xi vo|ko'e

|ri xi mu|ko'a

|ri xi xa|ko'a ce ko'e

|ri xi ze|le nu ko'a e ko'e joi ci ko'i na brodi lu'a re ko'o kei

|ri xi bi|lo mu broda

|ri xi so|le ci lo mu broda

|ri xi dau|da poi ME le ci lo mu broda