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http://loglang.wordpress.com/2012/09/20/xorban-termset-solution-1/
So…
je (la mlta le ldre) pnxake (la xrma le djce) pnxake
je Ba1 Ra1 Be1 Re1 F Ba2 Ra2 Be2 Re2 F
“The cat milk drinks, and the horse water drinks.”
=>
lake gake (je mlta ldre) (je xrma djce) pnxake
Bake gake je Ra1 Re1 je Ra2 Re2 F
=Ba sma Be gake je Ra1 Re1 je Ra2 Re2 F
“The cat milk, and the horse water, drinks.”
The lV[kV]* gV[kV]* _expression_ binds each free variable in F. The bigger that gets, the more the overall sentence starts to resemble prenex normal form. It feels kludgy to convert termsets into multivar-restrictions complementing gV[kV]*, pulling lV[kV]* binders out along the way.
Problems:
1. All binders have to be of one type for each variable.
2. Only handles sentential “je”. No workaound for “ja”, etc.
3. Logical modifiers and other unary operators esp. “na” within termsets are not handled.
How about the more straightforward approach of treating termsets like termsets? Observation: Long stretches of Xorban sentences can be analyzed as sequences of modifiers, including both BR-expressions and unary operators, that are followed by a formula. Without suggesting that a “termset” is part of the grammar, because it isn’t, why don’t we try to take advantage of the formal interchangeability of modifers by creating a simple syntax to coordinate termsets directly?
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Mike’s termset solution #1
This is a proposed syntax for termset structures (TSSs) i.e. the arbitrary coordination of termsets (TSs). The syntax allows sequential TSSs, but disallows TSSs inside TSs. Variant syntaxes with TSSs inside TSs are possible if something that insane is desired.
TSS modifiers are all formally unary operators:
ne’e: and
ne’a: or
ne’o: iff
ne: separator / trailing formula place holder.
“na” and the like are not in this syntax; those are terms.
Xform Rules
Def
A termset is a sequence of zero or more terms, i.e. non-TSS modifiers: M1, M2, M3, …
TSsi, TSsm: unstructured termsets, sentence-initial & sentence-medial
TS1, TS2, etc. : structured termsets
F: a trailing formula
Basic xforms:
TSsi ne’e TS1 ne TS2 ne F => TSsi je TS1 F TS2 F
TSsi ne’a TS1 ne TS2 ne F => TSsi ja TS1 F TS2 F
TSsi ne’o TS1 ne TS2 ne F => TSsi jo TS1 F TS2 F
Notice that after xform, all “ne” place holders become F, and all ne’e/ne’a/ne’o coordinators become je/ja/jo. A nested xform:
TSsi ne’o TS1 [ne] ne’e TS2 ne TS3 ne F => TSsi jo TS1 F je TS2 F TS3 F
We could probably allow “ne” to be elided whenever followed by a TSS coordinator inside the same TSS. I am not sure if we should though, as that would complicate the formalism. But it might make things easier for the speaker. A sequential xform:
TSsi ne’e TS1 ne TS2 ne [TSsm] ne’a TS3 ne TS4 ne F
=> TSsi ne’e TS1 ne TS2 ne ( [TSsm] ja TS3 F TS4 F )
=> TSsi je TS1 ( [TSsm] ja TS3 F TS4 F ) TS2 ( [TSsm] ja TS3 F TS4 F )
Sequential TSSs are most efficiently processed right to left, but any order works. Note that the “ne” after “S2 must NOT be elided even if TSsm is empty.
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Examples
je la mlta le ldre pnxake la xrma le djce pnxake
=> ne’e la mlta le ldre ne la xrma le djce ne pnxake
“The cat milk, and the horse water, drinks.”
je ra mlta se ldre pnxake sa xrma re djce pnxake
=> ne’e ra mlta se ldre ne sa xrma re djce ne pnxake
“Every cat some milk, and some horse all the water, drinks.”
la ma djna jo (le nnle li crdi) dndakike (le nxle li ckti) dndakike
=> la ma djna ne’o (le nnle li crdi ne) (le nxle li ckti ne) dndakike
“John (to the boy a radio) if and only if (to the girl a book) gives.”
la ma djna ja je (le nnle li crdi) dndakike (le nxle li ckti) dndakike je (le nnle li ckti) dndakike (le nxle li crdi) dndakike
=> la ma djna ne’a ne’e (le nnle li crdi ne) (le nxle li ckti ne) ne’e (le nnle li ckti ne) (le nxle li crdi ne) dndakike
“John either both (to the boy a radio) and (to the girl a book) or both (to the boy a book) and (to the girl a radio) gives.”
je (la nnla ni) le ckte nclake (la nxla na) le ckte nclake
=> ne’e (la nnla ni ne) (la nxla na ne) le ckte nclake
“The boy does and the girl doesn’t like the book.”
It is also possible to say:
je (la nnla ju li djci pnxaki) le ckte tcdake (la nxla ju li plsi ctkaki) le ckte tcdake
=> ne’e (la nnla ju li djci pnxaki ne) (la nxla ju li plsi ctkaki ne) le ckte tcdake
“The boy, drinking water, and the girl, eating an apple, read books.”