TECH: Quantifiers; Confusing prenexes

[Logical Language Group <lojbab@ACCESS.DIGEX.NET>]

Cowan (even numbers of ">"s) and Iain (odd numbers of ">"s):
>>It does and it doesn't, because in the context "da poi ... da" the second
>>use of "da" has been restricted by the "poi".  So "poi" really sets a
>>domain, rather than selecting a subset. "ro da poi" = "all-of those-things
>>in-domain".
>
>I'm not sure I understand the distinction you're making between setting
>a domain and selecting a subset - "all-of those-things in-domain" is a
>subset of "all-of those-things".
>
>>>>        ro da poi broda de vau ro de poi brode de zo'u da brodi de
>...
>>But if forward reference is not possible, then the first occurrence of "de"
>>has scope forward from just after the first "poi", leading to the reading:
>
>>      All X's which foogle some Ys snorgle all of >those same< Y's which
>>              zarkify the X in question.
>
>>In order words, the "ro de" selects all of the {su'o} referents implicit
>>in the first appearance of "de".
>
>Exactly.

Maybe %^)

I still haven't read where this problem started and/or how it got here,
but I've looked at this in conjunction with what I responded to last
time, and talked briefly with Nora to confirm my suspicions.  So lets
see if the following muddies waters, or clears them up.

In

ro da poi broda de vau ro de poi brode da zo'u ...

the question of the scope of the first "de" must be resolved; as stated
it is confusedly stated although logic and hence Lojban has a way to
resolve it.  Nora and I believe that there is no question that the "da"
subordinate to "ro de" is within the scope of "ro da" as well.

"de" has two possible scopes within this prenex, because THERE ARE TWO
RELEVANT PRENEX EXPRESSIONS LEFT UNSTATED as the text is currently
stated.  Making these explicit, we have for:

(1) [ro da poi broda de vau] [ro de poi brode da] zo'u ...

either

(1a) [ro da poi {de zo'u (da) broda de vau}] [ro de poi brode da] zo'u ...

in which case the expression is grammatical but logically ill-formed
because "de" is being requntified in the second half of the prenex;
i.e., it should really be a separate variable "di".

or, to get a non-ill-formed prenex, you must re-prenex "de" so that both
occurances lie within its scope by explicitly adding another prenex in
front:

(1b) {de zo'u [ro da poi (da) broda de vau] [ro de poi brode da]} zo'u ...

Since the assumptions are that all Lojbanists make only logically
well-formed expressions %^), we must assume that (1a) is not indtendeed
and that the latter (1b) is the correct expansion of (1).

Nora says that if you want in any way to have the variable subordinate
to "de" to be quantified any OTHER way than under the "roda" scope
previously expressed, it also must be expressed as a separate variable,
newly quantified (presumably) within the subordinate clause prenex.

Does this help???

lojbab