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Discussion of "kancusu'oi"
[parent] [root]
Comment #1: Why have two sumti slots?
Curtis W Franks (Fri Jan 29 07:01:58 2021)

We need only one with "gi'e" (or any other desired connective) internal
to the abstraction (id est: between "ka" and implicit/explicit "kei")
for an, I think, equivalent result. The flexibility with the connective,
if it present at all, is a strengthening of the definition, I think.

Comment #2: Re: Why have two sumti slots?
la du kooi noi zo zei zei zei zei fao ku ne vou biu pei (Fri Jan 29 07:43:26 2021)

kancusu'oi and the others are meant to cover the meanings of quantifiers
when given two predicates. As in:

> su'o mlatu cu barda
> ro mlatu cu barda

where the first implies ∧ between mlatu and barda and the second
implies →.

You can find predicates for su'oi and ro'oi with one argument, without
the implied connective, at suzdza and roldza.

Comment #3: Re: Why have two sumti slots?
Curtis W Franks (Sat Jan 30 21:12:50 2021)

zozeizeizeizeifaho wrote:
> kancusu'oi and the others are meant to cover the meanings of
quantifiers
> when given two predicates. As in:
>
> > su'o mlatu cu barda
> > ro mlatu cu barda
>
> where the first implies ∧ between mlatu and barda and the second
> implies →.
>
> You can find predicates for su'oi and ro'oi with one argument,
without
> the implied connective, at suzdza and roldza.

Okay, but why not make it arbitrarily many (including possibly infinitely
many)?

Comment #4: Re: Why have two sumti slots?
la du kooi noi zo zei zei zei zei fao ku ne vou biu pei (Sun Jan 31 09:28:57 2021)

krtisfranks wrote:
> Okay, but why not make it arbitrarily many (including possibly
infinitely
> many)?

Since the quantifier grammar allows at most two predicates as arguments, I
hadn't thought about how they might generalize! Now that I do, I'm
confused.

su'oi's expansion uses the associative ∧, and
> su'oi gi [ke'a] broda gi brode gi brodi [gi'i]
(forgive the grammar) would make sense as
> ∃x (broda(x) ∧ brode(x) ∧ brodi(x))

but what would
> ro'oi gi broda gi brode gi brodi
best mean?
> ?? ∀x ((broda(x) → brode(x)) → brodi(x))
> ?? ∀x (broda(x) → (brode(x) → brodi(x)))
> ?? ∀x (broda(x) → (brode(x) ∧ brodi(x)))

Comment #5: Re: Why have two sumti slots?
Curtis W Franks (Mon Feb 1 07:36:24 2021)

zozeizeizeizeifaho wrote:
> krtisfranks wrote:
> > Okay, but why not make it arbitrarily many (including possibly
> infinitely
> > many)?
>
> Since the quantifier grammar allows at most two predicates as arguments,
I
> hadn't thought about how they might generalize! Now that I do, I'm
> confused.
>
> su'oi's expansion uses the associative ∧, and
> > su'oi gi [ke'a] broda gi brode gi brodi [gi'i]
> (forgive the grammar) would make sense as
> > ∃x (broda(x) ∧ brode(x) ∧ brodi(x))
>
> but what would
> > ro'oi gi broda gi brode gi brodi
> best mean?
> > ?? ∀x ((broda(x) → brode(x)) → brodi(x))
> > ?? ∀x (broda(x) → (brode(x) → brodi(x)))
> > ?? ∀x (broda(x) → (brode(x) ∧ brodi(x)))

I actually think that "ro'oi" should not require and implication like
that at all. It might require implication, but it is not necessarily
structured in any of those ways. "∀x ∈ A, (P(x))" just means "x ∈ A ⇒
P(x)"; if "A" is omitted, then the universal set/set of discourse is meant
(where "set" can be replaced by "category", "object", or some other
structure, depending on context). The universal quantification is just the
first portion of this clause. But, if we are to include both pieces, then
I guess that I would say that "ro'oi(x, A, (P_1, P_2, P_3, ...))" would
mean "x ∈ A ⇒ (P_1 (x), & P_2 (x), & P_3 (x), ..."; we can, again, omit A.
A phrase "all cats" implicitly means "∀x ∈ A" where A is the set of only
and all cats, too.

Alternatively, we can take P_0 to be the proposition representing
membership in A, which would immediately narrow the range of relevant x
values from the universal set to A. This would introduce an asymmetry in
the the (now-ordered) list of propositions (because it would mean "∀x,
(P_0 (x) ⇒ (P_1 (x), & P_2 (x), & P_3 (x)))"), where "∀x" means "all x in
our discourse space". This would be, I think, the last option which you
outlined.

I am going off how I use it and have seen it be used. We can, of course,
define it in any manner which we want.

 Comment #6: Re: Why have two sumti slots? la du kooi noi zo zei zei zei zei fao ku ne vou biu pei (Thu Feb 4 22:14:12 2021) krtisfranks wrote:> I actually think that "ro'oi" should not require and implication like> that at all. It might require implication, but it is not necessarily> structured in any of those ways. "∀x ∈ A, (P(x))" just means "x ∈ A ⇒> P(x)"; if "A" is omitted, then the universal set/set of discourse ismeant> (where "set" can be replaced by "category", "object", or some other> structure, depending on context). > This is where one of xorlo's weirdnesses shows itself. Single-predicatero'oi is supposed to mean that in a domain of individuals, allcombinations of them satisfy the predicate. Treating two-predicate ro'oithe same, just with the domain stated explicitly, would result inunexpected meanings when both of the predicates are non-distributive.Take:> ro'oi tavlysi'u cu nelcysi'u ja xebnysi'uSay the domain contains the individuals A, B, C, D, E, of which A and Btalk to each other, and C and D do too. Under the reading with twopredicates and implication, this sentence would mean that:- A and B like or hate each other, and- C and D like or hate each other.Taking the tavlysi'u to specify a domain for a simple> ro'oi da nelcysi'u ja xebnysi'uon the other hand, would give a meaning of:- A likes or hates each other (sic), and- A and B like or hate each other, and- A, B and C like or hate each other, and so on for every combination ofA, B, C and D.So I think only the all-predicate version (your second option) would makesense here.
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