Le samedi 24 mai 2014 09:45:37 UTC+9, xorxes a écrit :
On Mon, May 19, 2014 at 10:04 AM, guskant <gusni...@gmail.com> wrote:I have finished English translation of my commentary on gadri from a logical point of view:Very nice. Here are some comments from me:(1)<<argument (sumti) Symbol that refers to a referent, or that another argument can be substituted for. >>Your definition of "sumti" implies that "zi'o" is not a sumti. This is fine, but perhaps it's worth pointing out in a note this odd word, which is also called a "sumti" in a wider, merely syntactic sense, Also things like "no da", "ci lo gerku", "mi .e do" and so on are called "sumti" in our formal grammars, although they only contain sumti by the semantic definition. Two other words that deserve special mention in this context are "ko" and "ma", which can arguably be said to fall under your definition, although they also are illocutionary force indicating devices, which ordinary sumti are not.
I agree. {zi'o} is difficult to deal with, because it is grammatically sumti while it is logically eraser of place for an argument. I should add a note for it, as well as the other sumti that you pointed out.
(2)<<When each of X and Y is an individual, {X jo'u Y} is called individuals.>>I think you need to add "and X is not equal to Y" if you want to be more strict.
I agree.
(3)<<A plural constant that is an individual is called singular constant.>>
I'd rephrase that as: "A plural constant that refers to a single individual is called a singular constant". I think it's worth keeping the distinction between the words or symbols, (constants and variables) and the referents of those symbols (things, people, trees, mountains, numbers, and so on). A constant can be singular or plural, and it can refer to an individual, but the constant is not the individual. The individual is the person, the tree or the house that the constant refers to. So if "X" is a singular constant, then X is an indifidual.
I agree. I should have been more attentive about that point.
(4)<<
No matter whether each of X and Y is plural or singular, {X jo'u Y} is not a singular constant.
>>
Unless X=Y and X is an individual. But linguistically that would be odd indeed. "jo'u" should not be generally used to join something with itself, although theoretically it can be.
My commentary is rather aiming at logical explanation than linguistic one. I will add "unless X=Y and X is an individual".
(5)<<
ro da ro'oi da poi ro'oi de poi ke'a xi pa me ke'a xi re zo'u ke'a xi re me de
su'o da su'oi da poi ro'oi de poi ke'a xi pa me ke'a xi re zo'u ke'a xi re me de
>>When "poi" is used to restrict the domain for da/de/di, it is not necessary to use "ke'a", and indeed it's more clear to not use "ke'a". "ke'a" is needed when there is no explicit variable bound by the quantifier, but here your definitions are much more clear as:ro da ro'oi da poi ro'oi de poi de me da zo'u da me desu'o da su'oi da poi ro'oi de poi de me da zo'u da me de
I agree.
(6)<<For example, a plural constant {A jo'u B} can be in a domain of a bound plural variable, but it cannot be in a domain of a bound singular variable because it is not an individual.>>Constants are not in the domain of variables, it's their referents that are in the domain. And plural and singular quantifiers can share the same domain. I think what you want to say is that a variable bound by a singular quantifier cannot take more than one individual value at a time.
I agree again about that point.
(7)<<lo (LE) It is prefixed to selbri, and forms a plural constant that refers to what satisfies x1, the first place of the selbri. If a quantifier follows {lo}, the quantifier represents the sum of all the referents of the plural constant. In the case that a quantifier follows {lo}, a sumti may follow it, and the quantifier represents the sum of all the referents of the sumti. >>I think "number", "count" or "quantity" would be better than "sum" there. To take an extreme example: "lo ci namcu" has three referents, three numbers. But "ci" is not (necessarily) the sum of the three numbers. The three numbers could be 1, 2 and 3. Their sum is 6, while their number is 3.
OK, this is because of my bad English. I will fix the translation.
That nitpick aside, the second part is at least unclear. In "lo ci ko'a", "ci" is the number of referents of "lo ci ko'a", but "ko'a" could have more than three referents. If you want to express that three is the number of referents of the inner sumti as well you need "lo ro ci ko'a". "lo ci lo mu gerku" has three referents, but the inner sumti has five.
I wrote about "3.1.1. Repeating inner quantification", but it would be better to add a note about {lo ci ko'a} just under the definition of {lo}.
(8)<<An empty set is {lo selcmi be no da}, and an _expression_ {lo no broda} is officially meaningless (see Section 3.1. This implies that an empty set cannot be expressed with {lo'i/le'i/la'i}.
>>Arguably, lots of things can be described as "lo selcmi be no da", not just the empty set. A spoon, for example, or anything else that is not a set, will satisfy "ke'a selcmi no da". "lo selcmi be no da" works well as a description of the empty set in a universe of discourse in which there are only sets. (But then that is really the only universe of discourse in which one should mention sets at all, in my opinion.)
{lo selcmi be no da} is a standard definition of "empty set" of set theory. In other words, {zo'e noi roda naku zo'u ke'a selcmi da}. We can think of a universe of discourse in which a spoon satisfies {ke'a selcmi no da}, but it means that the spoon is regarded as an empty set in that universe of discourse. An empty set is indeed a kind of set, {lo selcmi}. If we wanted to imply that a spoon is not a set, we could rather say that a spoon satisfies {ke'a selcmi zi'o}, in which the meaning of {selcmi} was changed by {zi'o}.
There's another problem with the "lo'i" definition. Can "lo selcmi be lo broda" be any set that has lo broda among its members, or is it the one and only set that has lo broda as its sole members? "cmima" only says that x1 is/are among the members of x2, does "selcmi" say that its x2 are all the members of its x1? Open question.mu'o mi'e xorxes
You created a Lojban entry of {selcmi} in jbovlaste:
http://jbovlaste.lojban.org/dict/selcmi
It might have been modified by someone else, and is now defined as follows:
{x1 selcmi x2} =ca'e {x1 se cmima ro lo me x2 me'u e no lo na me x2}
That is to say, the meaning of {selcmi} is different from {se cmima}, and {lo selcmi be lo broda} is the one and only set that has lo broda as its sole members.
However, I would prefer that the meaning of {selcmi} is the same as {se cmima}, and that {A cmima A ce B} is implied by {A ce B selcmi A}. In that case, {lo selcmi be lo broda} can be any set that has lo broda among its members. I am willing to add a comment on it, but I'm not sure if I should obey the definition of jbovlaste, or rather keep it as an open question.
I will release the second version of the commentary in a few days.
Le samedi 24 mai 2014 11:53:33 UTC+9, Pierre Abbat a écrit :
On Friday, May 23, 2014 21:45:35 Jorge Llambías wrote:
> (8)<<
> An empty set is {lo selcmi be no da}, and an _expression_ {lo no broda} is
> officially meaningless (see Section
> 3.1<http://www.lojban.org/tiki/gadri%3A+an+unofficial+ commentary+from+a+logi
> cal+point+of+view&bl#Inner_quantification>[image: Edit Plugin:alink]. This
> implies that an empty set cannot be expressed with {lo'i/le'i/la'i}.
>
>
> Arguably, lots of things can be described as "lo selcmi be no da", not just
> the empty set. A spoon, for example, or anything else that is not a set,
> will satisfy "ke'a selcmi no da". "lo selcmi be no da" works well as a
> description of the empty set in a universe of discourse in which there are
> only sets. (But then that is really the only universe of discourse in which
> one should mention sets at all, in my opinion.)
That's why I entered "zilcmi". lo kunti zilcmi cu na selcmi .iva'i lo kunti
zilcmi cu selcmi noda
mu'omi'e .pier.
--
ve ka'a ro klaji la .romas. se jmaji
i ja'aku zo'u lo smuci cu ka'e selcmi zi'o ije lo kunti selcmi be zi'o cu na selcmi zo'e iku'i ma'i lo selcmi saske naku zo'u lo kunti selcmi be zi'o cu selcmi noda iki'ubo lo nu pilno lo fe zei sumti po zo selcmi cu sarcu lo nu skicu lo smuni be zoi gy empty set gy
Le dimanche 25 mai 2014 01:23:16 UTC+9, clifford a écrit :
While it is important to point out the word/object distinction, it is probably a lost cause in Lojban (as it is in English and logic textbooks). Every time any systematic attempt is made to fix this distinction, the new expressions are collapsed together again: term, predicate, function,. argument, and so on. One is tempted (for more reasons than just this) to go back to "noun" and "verb" for the words.
I will fix the confusing parts. If la xorxes approves the whole commentary, it will become indeed the important theoretical basis of gadri, and it should be included in the next version of CLL, because the current gadri page of BPFK lacks explanation on the relation between gadri and logic.