So, to the question of that {gu} and {go} mean with more than 2 arguments, we kind of find ourselves with tradeoff between logic and ease of use.
First I get nervous extending them to >2-ary at all, since it becomes harder to reason about the negations ({gonai X gi Y} is XOR, but {gonai X gi Y gi Z} is not, it's something strange instead -- and nobody can do truth tables in their head, even fluent speakers).
The interpretations you list are undoubtedly useful (particularly the "which one out of these X alternatives"-connective is often asked for, though there is a workable solution using {moi}). But they do not correspond to the mathematical interpretation. For example, n-ary XOR is supposed to be true when an odd number of the arguments are true, which is not obvious (or often useful in speech). Changing this can cause difficulties with composition, for example logical transformations like De Morgans' laws will not work. And {go ko'a gi ko'e gi ko'e [gi'i]} would be different from {go go ko'a gi ko'e gi'i gi ko'i [gi'i]}, which is kind of annoying. Basically we would want to stop defining {go} as iff and {gonai} as xor, because people coming from a math/logic background would have the wrong expectations.
mu'o mi'e la durkavore
On July 16, 2015 at 6:23:19 AM, guskant (gusni.kantu@gmail.com) wrote:
Le mercredi 15 juillet 2015 21:29:50 UTC, xorxes a écrit :
On Wed, Jul 15, 2015 at 4:29 AM, guskant
<gusni...@gmail.com>
wrote:
3. sentences connected with forethought connective:
{nu ju'e gi broda gi brode gi brodi gi brodo gi brodu}
(CU [nu {CU <(¹ju'e gi¹) broda (¹[gi brode] [gi brodi] [gi
brodo] [gi brodu]¹) GIhI> VAU} KEI] VAU)
(Forethought connectives of la zantufa-0.2 can connect more
than three "statements (not only sentences)", and {gi'i} is used as
the elidible terminator GIhI, not as GIhA. See
for more info.)
I like this use of "gi" because connected lists are by far
more common than embedded binary connectives. The meanings of "ge
... gi ... gi ..." and "ga ... gi ... gi ..." are fairly obvious,
but what are the proposed generalizations for "go" and "gu"? Is
"go" all true or all false? What are "gu", "se gu", "te gu",
etc?
mu'o mi'e xorxes
La zantufa gives only syntactic structure, and I have not yet
suggested the semantic structure. From any approach, it is
reasonable to interpret that {gu A gi B gi C} has the same truth
value as A.
As for {se gu}, one of possible interpretations is grouping of
binary transitive connective: that is, {segu A gi B gi C} = {segu
(segu A gi B gi'i) gi C} = {segu A gi (segu B gi C)}, and then the
truth value of {segu A gi B gi C} is the same as C. However, as you
suggested, we may give another interpretation that {se gu} draws
the truth value of B, {te gu} draws the truth value of C, and so
on. I like the latter interpretation, because it cannot be easily
represented by grouping system of binary connectives, and therefore
profits from the n-ary forethought connective system.
For the same reason, I prefer the interpretation of "all true
or all false" for {go} and "one and only one of them is true" for
{gonai} to the interpretation of grouping of binary
connectives.
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