All the basics of Gua\spi grammar have been covered, but of course there are several important details that are worth exploring. One reader asked about mathematical expressions in Gua\spi, and indeed the author of Gua\spi considers MEX to be the core of Gua\pi. Being a huge fan of mekso in Lojban, I can only be excited about this. And from what I can see, Gua\spi does it a bit less awkwardly.
So let's see what Gua\spi does with numbers. First of all, here are the digits from 0 to 9:


You will note that the pattern of the vowels is the same as in the case link prefixes (FA) and the predicate conversion prefixes (SE).
I already hinted in previous articles at the fact that numbers in Gua\spi are predicates, and that's entirely true. Every number has the place structure: x1 is a set of n members x2, in extension" (where n is the number/digit) If we apply a conversion with zu, it will be "x1 is a member of set x2 which has n members".
So the word cu would mean "x1 is a set of 2 members x2, in extension".
Let's see how we could use such a number in a sentence (1) and (2).
(1) ^:i \kmau /zu jiau \zu ce
"The cat has four legs."
lit. "the four members of some set are the legs of the cat"
(2) ^:i \ji /vyi \xgom zu ka
"I see eight dogs." ("I see dogs which are eight in number")
Sentence (2) uses a relative clause to attach a number to an argument, this is very common in Gua\spi.
We can also ask about numbers, like {xo} in Lojban. The word pa has the place structure: "x1 is a set of how many members x2 ?". Here's an example sentence (3):
(3) ^:i \ju /crw \qkao zu pa
"How many cakes did you eat?"
Okay, but how do we talk about the number itself. How do we say "1 + 1 = 2" ? Gua\spi thinks about numbers as sets, and the set of all the numbers in a set is the number itself. The article xu gets the entire referent set of an argument, as a set (or class). Let's look at an example (4).
plw = x1 is the sum of x2 (xu), x3 (xu), x4 (xu)... (things in brackets always indicate a default article)
(4) ^:i \xu cu /plw \co ^co
"2 is the sum of 1 and 1."
As you can see, we don't need to place xu before the numbers because this article is there by default in plw2n, but not in plw1. Here's one with subtraction, using the same predicate:
(5) ^:i \ca /zu plw \xu ka ^ci
"3 is the difference 8 minus 5"
Ordinals are constucted using the word tr, whose place structure is: x1 is nth in list (xy) x2 starting at x3:
(6) ^:i \tr cu \dwu /fi kmau
"The second animal is a cat." (maybe several animals are standing in a line)
(7) ^:i \ji /tr cu \sty kqa \diu sui
"I am the second smallest in my class."
sty = List (xy) x1 is a list of set (xy) x2 in order (vo) x3
kqa = x1 is big
diu = (xy) x1 is a team for activity (vo) x2+1
sui = x1 learns to do skill (xovo) x2 from teacher x3
It's like 40 degrees today, so I don't feel like writing more. Sentence (7) might be too difficult...
These are the basics of how Gua\spi treats numbers. "[The] syntax for mathematical expressions is neat, compact and unambiguous. No special syntax needs to be added to gua\spi beyond that already in use for ordinary arguments and sentences." — from the reference grammar.
If you have any questions, leave a comment below.
End of part 9
I already hinted in previous articles at the fact that numbers in Gua\spi are predicates, and that's entirely true. Every number has the place structure: x1 is a set of n members x2, in extension" (where n is the number/digit) If we apply a conversion with zu, it will be "x1 is a member of set x2 which has n members".
So the word cu would mean "x1 is a set of 2 members x2, in extension".
Let's see how we could use such a number in a sentence (1) and (2).
(1) ^:i \kmau /zu jiau \zu ce
"The cat has four legs."
lit. "the four members of some set are the legs of the cat"
(2) ^:i \ji /vyi \xgom zu ka
"I see eight dogs." ("I see dogs which are eight in number")
Sentence (2) uses a relative clause to attach a number to an argument, this is very common in Gua\spi.
We can also ask about numbers, like {xo} in Lojban. The word pa has the place structure: "x1 is a set of how many members x2 ?". Here's an example sentence (3):
(3) ^:i \ju /crw \qkao zu pa
"How many cakes did you eat?"
Okay, but how do we talk about the number itself. How do we say "1 + 1 = 2" ? Gua\spi thinks about numbers as sets, and the set of all the numbers in a set is the number itself. The article xu gets the entire referent set of an argument, as a set (or class). Let's look at an example (4).
plw = x1 is the sum of x2 (xu), x3 (xu), x4 (xu)... (things in brackets always indicate a default article)
(4) ^:i \xu cu /plw \co ^co
"2 is the sum of 1 and 1."
As you can see, we don't need to place xu before the numbers because this article is there by default in plw2n, but not in plw1. Here's one with subtraction, using the same predicate:
(5) ^:i \ca /zu plw \xu ka ^ci
"3 is the difference 8 minus 5"
Ordinals are constucted using the word tr, whose place structure is: x1 is nth in list (xy) x2 starting at x3:
(6) ^:i \tr cu \dwu /fi kmau
"The second animal is a cat." (maybe several animals are standing in a line)
(7) ^:i \ji /tr cu \sty kqa \diu sui
"I am the second smallest in my class."
sty = List (xy) x1 is a list of set (xy) x2 in order (vo) x3
kqa = x1 is big
diu = (xy) x1 is a team for activity (vo) x2+1
sui = x1 learns to do skill (xovo) x2 from teacher x3
It's like 40 degrees today, so I don't feel like writing more. Sentence (7) might be too difficult...
These are the basics of how Gua\spi treats numbers. "[The] syntax for mathematical expressions is neat, compact and unambiguous. No special syntax needs to be added to gua\spi beyond that already in use for ordinary arguments and sentences." — from the reference grammar.
If you have any questions, leave a comment below.
End of part 9