anaphora, especially donkey sentences and the like:

[lojbab (Bob LeChevalier)]

In response to David Elsworthy:
Nora looked David Elsworthy's postings over and helped me out with the
logical questions in his anaphora posting.  She did not see any of them
as particularly problematical in Lojban; the problems of the English
disappear in reformulating the sentences for Lojban grammar.  Here are
my attempts at each of David's examples.  Hopefully they will show
something useful.  Basically

I'm using long-form lujvo so that everyone can easily determine the
source gismu.  I'm also not explicitly using prenex constructions.  I
have given existentially quantified anaphora solutions to the problems
in most cases, and showed shorter "le" and "lo" forms for some of these
- the other ones could be similarly shortened.


>(1) Every farmer who owns a donkey beats it.

   ro da poi cangyprenu zi'e poi ponse de poi xasli cu raplydarxi de

ro   da          poi   cangyprenu   zi'e poi   ponse     de          poi   xasli
each something-x which farm-persons and  which possesses something-y which asses

   cu raplydarxi  de
      repeat-hits that-y

Or more briefly by implicit reference to the "da" of the last version:

   ro cangyprenu poi ponse de poi xasli cu raplydarxi de

ro   cangyprenu  poi   ponse     de          poi   xasli
each farm-person which possesses something-y which asses

   cu raplydarxi  de
      repeat-hits that-y

Or even more briefly using a description and no explicit existentials:

   ro cangyprenu poi ponse lo xasli cu raplydarxi ri

ro   cangyprenu  poi   ponse     lo                        xasli
each farm-person which possesses something/things that are asses

   cu raplydarxi  ri
      repeat-hits the-last-it/them.

In the last, "ri" could be replaced by "le xasli" ("the ass(es)", which
pragmatically refers back to the donkey(s) that is/are owned.  This might be
necessary/useful for more complex constructs where "ri" cannot be conveniently
used.  "le" constructions as anaphora are less logically precise than explicit
anaphora, but in situations even much more complex than this, it shouldn't
be too hard to resolve the references.

You also could assign "ko'a" to the owned donkeys (e.g. "lo xasli goi
ko'a", and use "ko'a" in the anaphora if the anaphoric reference was not
immediately following as it conveniently is in this sentence.


>The simple word copying approach gets us:
>
>(2) Every farmer who owns a donkey beats a donkey.

In Lojban, this is clearly different.  In the long existential expansion, it is:

   ro da poi cangyprenu zi'e poi ponse de poi xasli cu raplydarxi di poi xasli

ro   da          poi   cangyprenu   zi'e poi   ponse     de          poi   xasli
each something-x which farm-persons and  which possesses something-y which asses

   cu raplydarxi  di          poi   xasli
      repeat-hits something-z which asses

And I can shorten this using a tricky-by-English-standards usage to:

   ro cangyprenu poi ponse loi xasli cu raplydarxi loi xasli

ro   cangyprenu  poi   ponse     loi xasli
each farm-person which possesses of the mass of Ass-dom

   cu raplydarxi  loi xasli
      repeat-hits of the mass of Ass-dom.

or colloquially back to English.

Every farmer that owns Ass beats Ass.

(where Ass is the mass individual)

[Side explanation - since most people don't understand the Lojban masses:
When "you" are holding a pencil, it is usually true that only part of one hand
actually does the holding.  Your hand is "you" for the purpose of holding.
In the above sentence any ass meeting the x2 position in relation "ponse"
to a farmer in x1 represents the entirety of Assdom.  Similarly, any
ass (not necessarily the same as the above) which fits the x2 position
in relation "raplydarxi" to x1 - a farmer who owns an ass, also represents
all of Ass-dom.

Many English mass nouns work somewhat like this, though not completely:
"Every person is made mostly of water and drinks water."  Clearly the two
"water"s are not the >same< water.  But in "Every person who likes water
drinks water", the two masses of water overlap.  Yet the person who "likes
water" probably is not too fond of hydrochloric acid, which is mostly water.

End of digression.  Mass is a fun concept, but a different area of logic than
David asked about.]


>(3) Every farmer who owns a donkey beat a donkey which he owns.

   ro da poi cangyprenu zi'e poi ponse de poi xasli cu raplydarxi di poi
   xasli zi'e poi se ponse da

ro   da          poi   cangyprenu   zi'e poi   ponse     de          poi   xasli
each something-x which farm-persons and  which possesses something-y which asses

   cu raplydarxi  di          poi   xasli zi'e poi   se ponse        da
      repeat-hits something-z which asses and  which is-possessed-by x

This is just a restrictive clause on the latter form, and clearly be seen
to not necessarily say that "de" is being beaten.


>which is better, but still leaves a problem.  It isn't clear whether (1)
>commits each farmer to beating all the donkeys he owns, but in an
>example like
>
>(4) Every man who loves a woman likes her.
>
>(assuming "love" implies "like"), there does seem to be such a
>commitment.

   ro da poi nanmu zi'e poi prami de poi ninmu cu nelci de

ro   da          poi   nanmu zi'e poi   prami de          poi   ninmu
each something-x which mans  and  which loves something-y which womans

   cu nelci de
      likes her.


>            The paraphrase:
>
>(5) Every man who loves a woman likes a woman who he loves.
>
>does not seem to have the same reading.

   ro da poi nanmu zi'e poi prami de poi ninmu cu nelci di poi ninmu zi'e
   poi da prami

ro   da          poi   nanmu zi'e poi   prami de          poi   ninmu
each something-x which mans  and  which loves something-y which womans

   cu nelci di          poi   ninmu  zi'e poi   da prami
      likes something-z which womans and  which he loves.


>The copying problem can also be seen in another classic sentence, known
>as the Bach-Peters paradox:
>
>(6) The boy who deserves it will get the prize he wants.
>
>On the simple copying approach, we have "it" = "the prize he wants", and
>"he" = "The boy who deserves it".  It is fairly clear that this leads to
>an infinite regress if you try to expand it out.

Thinking Lojbanically offers a different insight as to what "it" means
that makes this simple even in English.  But first let me do it David's
way, in case I'm full of hot air.

The regression is lost in converting this to Lojban.  First a literal
translation that keeps the late definition of the anaphora but makes
the "copying" clear:

   le nanla goi ko'a poi jerna ko'e cu cpacu ko'e goi lo velcnemu poi ko'a
      djica

le  nanla goi           ko'a poi   jerna ko'e cu cpacu
The boy   also-known-as x1   which earns x2      gets

   ko'e goi                 lo             velcnemu    poi   ko'a djica
   x2   which-is-defined-as the-thing-that is-a-reward which x1   desires


This could also be done with a prenex-quantified variable instead of "ko'e"
which removes any qualms about using the "ko'e" without defining it first;
actually, I guess, you could put the "ko'e" in the prenex, too.

Nora prefers writing this sentence with existentials and a double-level
relative clause:

da          poi   nanla zi'e poi   jerna de          poi   velcnemu    zi'e
Something-x which boys  and  which earns something-y which is-a-reward and

   poi   da djica de cu cpacu de
   which x  wants y     gets  y

or without existentials and using a subscripted relative pronoun:

   le nanla poi [ke'a] jerna le velcnemu poi ke'axire djica ke'a cu cpacu ri

le nanla poi   [ke'a] jerna le velcnemu poi   ke'axire djica ke'a cu cpacu ri
The boy  which he     earns the-reward  which he       wants it      gets  it

Lojban allows infinitely nested relative clauses.

On later thinking, though, I think the English and Lojban versions of
David's problem resolve easily using a different interpretation of the
above.  This interpretation is natural for Lojban as a language with
explicit "abstract nouns".  In this version, "it" = "getting the prize
that he wants", expanding to:  "The boy who deserves getting the prize
he wants will get the prize he wants." which works fine in English to
eliminate the infinite regression.  (I can't say that this will work for
all such paradoxes, but I'm reasonably proud of this one - at least till
you people all tear me up on it.)

Existential:

   da poi nanla zi'e poi jerna lenu da cpacu de poi velcnemu zi'e poi
   da djica de cu cpacu de

da          poi   nanla zi'e poi   jerna lenu         da cpacu
Something-x which boys  and  which earns the-event-of x  gets

   de          poi   velcnemu    zi'e poi       da djica de cu cpacu de
   something-y which is-a-reward and  such-that x  wants y     gets  y


Non-Existential:

   le nanla goi ko'a poi jerna lenu ko'a cpacu [ko'e goi] le velcnemu poi
   ko'a djica ke'a cu cpacu [ko'e | le velcnemu poi ko'a djica]

le nanla goi           ko'a poi   jerna lenu         ko'a   cpacu
The boy  also-known-as x1   which earns the-event-of x1(he) gets

   [ko'e goi]               le  velcnemu poi   ko'a   djica ke'a cu cpacu
   [x2 which-is-defined-as] the reward   which x1(he) wants it      gets

   [ko'e   | le velcnemu poi   ko'a   djica]
   [x2(it) | the reward  which x1(he) wants]


>The conclusion from this is that the interpretation of anaphors is *not*
>the business of the parser, or of the syntactic component in any sense.
>Indeed, in English, there are very few syntactic constraints on
>anaphora:  number, gender, and a restriction on reflexivity in sentences
>like:

>(7) John talks to him. (wrong if him=John)

The paradoxes in these are dependent on English's ambiguous sex-linked
pronouns.  Lojban does both pronouns and reflexives differently than
English.

   la djan. tavla da poi nakni

la djan. tavla    da          poi   nakni
   John  talks-to something-x which males

   la djan. tavla vo'a

la djan. tavla    vo'a
   John  talks-to the-x1-of-this-bridi (himself).


>(8) John talks to himself. Jane talks to *himself. (him if we want Jane
>talking to John).

IN Lojban, the parallel construction doesn't mean the same thing:

   la djan. tavla vo'a  .i la djein. tavla vo'a

la djan. tavla    vo'a
   John  talks-to the-x1-of-this-bridi (himself)

.i     la djein. tavla    vo'a
and...    Jane   talks-to the-x1-of-this-bridi (herself).


On the other hand, I can give a good example of "ra'o" here, which shows how
repetitions of anaphoric references can be expressed:

   la djan. tavla vo'a  .i la djein. go'i

la djan. tavla    vo'a
   John  talks-to the-x1-of-this-bridi (himself)

   .i     la djein. go'i
   and...    Jane   (has the last relationship =
                    talks-to the-x1-of-THAT-bridi (himself = John).

means that the referent of "vo'a" is unchanged in the go'i sentence, so
that Jane talks to John, while:

   la djan. tavla vo'a  .i la djein. go'i ra'o

la djan. tavla    vo'a
   John  talks-to the-x1-of-this-bridi (himself)

   .i     la djein. go'i ra'o
   and...    Jane   (has the last relationship with "vo'a" re-evaluated =
                    talks-to the-x1-of-THIS-bridi (herself = Jane).

means that "vo'a" is re-evaluated in the new sentence environment, and
thus refers to Jane.

The default of non-update is because the most frequent use of "go'i" is
as a yes answer to a yes/no question, which would not work with automatic
update:

John:  "Did you talk to me?"
Jane:  "Yes (I talked to you)" - not "Yes (you talked to me)".


> Every farmer who owns a donkey beats it. ?It neighs.
>
>which is found to be unacceptable by most people, except when you
>imagine that the second sentence is somehow still within the scope of
>the "every".  (The unacceptability isn't too clear here, I know:  please
>take it for granted that the general evidence is that you can't have a
>singular anaphor in later sentences.)
>
>A problem possibly arises with this:
> Every farmer who owns a donkey beats it. They neigh.

Since Lojban does not distinguish between singular and plural, this
distinction doesn't occur in an unmarked sentence.  In a quantified sentence,
you would of course extend the scope anyway:

   ro da poi cangyprenu zi'e poi ponse de poi xasli cu raplydarxi de
   .ije de xirmybacru

ro   da          poi   cangyprenu   zi'e poi   ponse     de          poi   xasli
each something-x which farm-persons and  which possesses something-y which asses

   cu raplydarxi  de     .ije                                    de
      repeat-hits that-y logical-AND-sentence-(continuing scope) that-y

   xirmybacru
   horse-utters

It is indeed tricky to find a way to show some >other< meaning for the
plural "they" (unless "they" are the farmers, in which case ".ije roda
xirmybacru").

Incidentally, while Lojban's design is based >primarily< on 1st order
predicate logic, there are elements of higher order logics built in as
well (e.g. notably, I'm told, in quantified predicate variables, but
questions on this REALLY must go to pc).  I'm even hoping that we have
at least a partial basis for fuzzy logic built in, though no one has
really looked at Lojban closely from that perspective.

-lojbab