Talk:lojban Formulae
pc: > This represents an attempt to reconstruct a certain phase in the development > of Lojban, somewhere between CLL and xorlan, incorporating the practical > changes that had been worked out since CLL, without getting into the > open-ended process of change incorporated in xorlan.
Perhaps we can call it pycyban, for ease of reference.
> {ko'a broda} > aF > (a is assumed to be a group, though perhaps encompassing only a single > individual. If the collectivity of F/broda is not defined it is here assumed > to be distributive. For cases where both are possible and collective is > wanted:) > {lu'o ko'a broda} > a c-F
What happens when you have broda and brode both with undefined collectivity, but context makes it clear that distributive is intended for one and collective for the other? Is {ko'a broda gi'e brode} allowed, or do you have to necessarily expand to {ko'a broda ije lo'u ko'a brode}?
> {Q da poi broda cu brode}
> [Ix: x group & xF* & [[Az: zF*] xCz] x G & xQn/ xQf of the F*s/xQr
"There is some group of brodas x that encompasses all the brodas, such that it brodes and is Q in number/is Qf of the brodas/is Qr" but I think you don't want x to encompass all the brodas, just all the brodas that brode.
> {lo'i broda cu brode} > [Ix: x group & Fx] {y: xCy}G
You probably want a more restricted set. If x is then {y: xCy} will be {a, b, c, , , , }.
Not that I think {a, b, c} would necessarily be something more useful to talk about, but that's closer to the traditional meaning of {lo'i}.
> {Q lo broda poi brode cu brodi} > [Ix: x group & x F & x G] [Iz: z group & xCz] z d-H & z is Q of x
So {ci lo broda poi brode cu brodi} is materially equivalent to {su'o ci lo broda poi brode cu brodi}, right?
And {vo lo broda ...} entails {ci lo broda ...}?
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wrote:
> pc: > > This represents an attempt to reconstruct a > certain phase in the development > > of Lojban, somewhere between CLL and xorlan, > incorporating the practical > > changes that had been worked out since CLL, > without getting into the > > open-ended process of change incorporated in > xorlan. > > Perhaps we can call it pycyban, for ease of > reference.
Thanks, but I am just laying out what others had done. A good name escapes me (as you know, I would suggest "Lojban"). > > > {ko'a broda} > > aF > > (a is assumed to be a group, though perhaps > encompassing only a single > > individual. If the collectivity of F/broda is > not defined it is here assumed > > to be distributive. For cases where both are > possible and collective is > > wanted:) > > {lu'o ko'a broda} > > a c-F > > What happens when you have broda and brode both > with undefined > collectivity, but context makes it clear that > distributive is > intended for one and collective for the other? > Is > {ko'a broda gi'e brode} allowed, or do you have > to necessarily > expand to {ko'a broda ije lo'u ko'a brode}?
If the context really makes it clear then there is no problem; the problems come when it is not clear which is intended on each. There is also the problem of what the distributivity is for {broda} in the formula. These were problems -- though unnoticed — for the original Loglan/Lojban system and in presenting them clearly I have not yet come upon a solution (other labelling at the predicate, of course, but that is messy since there is no good place to put labels in other than first and maybe xecond place).
> > > {Q da poi broda cu brode} > > [Ix: x group & xF* & [[Az: zF*] xCz] x G & > xQn/ xQf of the F*s/xQr > > "There is some group of brodas x that > encompasses all the brodas, > such that it brodes and is Q in number/is Qf of > the brodas/is Qr" > but I think you don't want x to encompass all > the brodas, just > all the brodas that brode.
Oops, that is one of the editing glitches:
between the quantifier and "xG" should be [iy:
xCy Iy:
xCy] and then it is "yG" and "yQ". Thanks.
> > {lo'i broda cu brode} > > [Ix: x group & Fx] {y: xCy}G > > You probably want a more restricted set. If x > is > then {y: xCy} will be {a, b, c, , , > , }. > > Not that I think {a, b, c} would necessarily be > something > more useful to talk about, but that's closer to > the traditional > meaning of {lo'i}. > Yes, add "& ~y group" to the specification of the set.
> > {Q lo broda poi brode cu brodi} > > [Ix: x group & x F & x G] [Iz: z group & > xCz] z d-H & z is Q of x > > So {ci lo broda poi brode cu brodi} is > materially equivalent to > {su'o ci lo broda poi brode cu brodi}, right?
I don't follow the reasoning or the point. Your equivalence shouldn't hold and I don't yet see why it would, at least in any way that would be different from any other work with quantifiers. {ci} means "exactly three" which does imply "at least three" but why would the converse implication hold. Ahah! there might be more than three F&Gs that H, so "there is a group of three" would always be true then. Yes, but so what; this is only meant to set up A group, the one I am going to go on about, a local count not a global one (even with the group of F&Gs). I have isolated a group and note that it is a threesome: this is rather different from say "there are three things that" -- see the earlier stuff about unrestricted quantifiers.
> And {vo lo broda ...} entails {ci lo broda > ...}? No, for the same reason. There may indeed be such a group, but it is not the one I have isolated — albeit rather inspecifically. This gets clearer in the last section, but the point is the same throughout.
pc: > --- Jorge Llambías > wrote: > > Perhaps we can call it pycyban, for ease of > > reference. > > Thanks, but I am just laying out what others had > done.
I don't recall anyone but you ever proposing that outer quantifiers on sumti be dealt with as predicates. The usual understanding has been that {Q da poi broda cu brode} is the ordinary [Qx: x broda] x brode
> > What happens when you have broda and brode both > > with undefined > > collectivity, but context makes it clear that > > distributive is > > intended for one and collective for the other? > > Is > > {ko'a broda gi'e brode} allowed, or do you have > > to necessarily > > expand to {ko'a broda ije lo'u ko'a brode}? > > If the context really makes it clear then there > is no problem;
Ok, then that part works in about the same way as "xorban".
> > > {Q lo broda poi brode cu brodi} > > > [Ix: x group & x F & x G] [Iz: z group & > > xCz] z d-H & z is Q of x > > > > So {ci lo broda poi brode cu brodi} is > > materially equivalent to > > {su'o ci lo broda poi brode cu brodi}, right? > > Ahah! there might be more than three F&Gs that H, > so "there is a group of three" would always be > true then. Yes, but so what; this is only meant > to set up A group, the one I am going to go on > about, a local count not a global one (even with > the group of F&Gs).
I'm simply trying to figure out how this differs from ordinary quantification, that's all.
> > And {vo lo broda ...} entails {ci lo broda > > ...}? > No, for the same reason. There may indeed be > such a group, but it is not the one I have > isolated — albeit rather inspecifically. This > gets clearer in the last section, but the point > is the same throughout.
Then does {vo lo broda cu brode} entail {naku ci lo broda cu brode}?
(That's how it works with the normal "exact" quantifiers, isn't it?)
mu'o mi'e xorxes
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wrote:
> > pc: > > --- Jorge Llambías > > > wrote: > > > Perhaps we can call it pycyban, for > ease of > > > reference. > > > > Thanks, but I am just laying out what others > had > > done. > > I don't recall anyone but you ever proposing > that outer > quantifiers on sumti be dealt with as > predicates. The usual > understanding has been that > {Q da poi broda cu brode} is the ordinary > [Qx: x broda] x brode
True; I swiped tis from McKay because it is so
handy — no wandering long scope quantifiers
around to get in the way of other things. The
instant case does also incorporate some further
factors that were needed (unnoticed) for earlier
systems (though not necessarily in just this
way): quantifiers on variables are global — take
in all the domain, quantified descriptors are
local, just about this particular group (McKay
again).
> > > What happens when you have broda and brode > both > > > with undefined > > > collectivity, but context makes it clear > that > > > distributive is > > > intended for one and collective for the > other? > > > Is > > > {ko'a broda gi'e brode} allowed, or do you > have > > > to necessarily > > > expand to {ko'a broda ije lo'u ko'a brode}? > > > > If the context really makes it clear then > there > > is no problem; > > Ok, then that part works in about the same way > as "xorban". > > > > > {Q lo broda poi brode cu brodi} > > > > [Ix: x group & x F & x G] [Iz: z group > & > > > xCz] z d-H & z is Q of x > > > > > > So {ci lo broda poi brode cu brodi} is > > > materially equivalent to > > > {su'o ci lo broda poi brode cu brodi}, > right? > > > > Ahah! there might be more than three F&Gs > that H, > > so "there is a group of three" would always > be > > true then. Yes, but so what; this is only > meant > > to set up A group, the one I am going to go > on > > about, a local count not a global one (even > with > > the group of F&Gs). > > I'm simply trying to figure out how this > differs from > ordinary quantification, that's all.
Yes, this was a problem for you with McKay too, I recall. Note that the quantification per se is just over groups and is always (in nonnegative contexts) particular: "there is a group such that". Having found the group we can then enumerate it. This has only a remote relation to global quantification {{Q da}), which says how many of some kind of thing there are, regardless of how they are divided into groups. In Lojban terms, this is to make {lo} almost exactly parallel to {le} except for whther the quantifier is inside or outside the explicit context (and, of course, whether {broda} is taken literally or not). This amounts to separating them, as formerly required, on specificity. > > > > And {vo lo broda ...} entails {ci lo broda > > > ...}? > > No, for the same reason. There may indeed be > > such a group, but it is not the one I have > > isolated — albeit rather inspecifically. > This > > gets clearer in the last section, but the > point > > is the same throughout. > > Then does {vo lo broda cu brode} entail > {naku ci lo broda cu brode}?
No. Some times three brodas can brode, sometimes not: enough for playing cribbage but not enough for minimally surrounding a square table. What one group does has little relation to what another one — even a subgroup of the given one -- does.
> (That's how it works with the normal "exact" > quantifiers, > isn't it?) >
But the quantifiers are on different things here: the first says that there is a tetrad, drawn from the group lo broda, that brodes; the second is about a triad (obviously a different thing) drawn from lo broda. Of course, if you can draw a tetrad from a group, you can draw a triad as well, but that doesn't mean — even if the triad is drawn from the tetrad — that the new group will brode. The normal exact quantifiers cover all the domain {Q da broda} means (among other things, I would say) that in all the world there are exactly Q brodas, {Q lo broda} says that there is a subgroup of lo broda which has Q members. To be sure, that requires tha there are at least Q brodas in the whole world and it entails that there is a Q-1 (if Q > 1) membered subgroup of lo broda. But it says nothing about the properties of that subgroup — even, in fact, that it brodas (and I wonder if that is in these analyses).
pc: > Note that the quantification per se is > just over groups and is always (in nonnegative > contexts) particular: "there is a group such > that".
What happens with {su'eci}? Is that "at most three, possibly none" or "at most three and at least one"?
> Having found the group we can then > enumerate it.
But that's not how you have defined it. You have the enumeration as part of what must be satisfied by the group. For {Q lo broda cu brode} you have:
[ix: x group & xF Ix: x group & xF] [iz: z group & xCz Iz: z group & xCz] z d-G & z is Q of x
There is some group of brodas x, such that there is some subgroup z among them, such that z are brode and Q in number.
Your description above ("having found the group we can then enumerate it") would correspond more to something like
[ix: x group & xF Ix: x group & xF] [iz: z group & xCz Iz: z group & xCz] z d-G & "the brodes among the brodas are Q in number".
I didn't formalize the second part because it would take me several lines, but in any case it is outside the scope of the Ix quantifier.
In other words, is {Q lo broda cu brode}
(1) "Among the brodas, there is at least one group that is Q in number and brodes"
or
(2) "There's a group among the brodas that brodes. They, the brodas that brode, are Q in number"
Your definition corresponds to (1), but your talk points to (2).
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wrote:
> > pc: > > Note that the quantification per se is > > just over groups and is always (in > nonnegative > > contexts) particular: "there is a group such > > that". > > What happens with {su'eci}? Is that "at most > three, > possibly none" or "at most three and at least > one"?
I think it is the latter, but the other could be accomodated fairly easily (though disjunctively: "either no subgroup is brode or one of between 1 and 3 brodas is"). I think this can be eventually worked into the predicate notion of enumeration.
> > Having found the group we can then
> > enumerate it.
>
> But that's not how you have defined it. You
> have the
> enumeration as part of what must be satisfied
> by the group.
> For {Q lo broda cu brode} you have:
>
> [ix: x group & xF Ix: x group & xF] [iz: z group & xCz Iz: z group & xCz] z d-G &
> z is Q of x
>
> There is some group of brodas x, such that
> there is some
> subgroup z among them, such that z are brode
> and Q in
> number.
>
> Your description above ("having found the group
> we can
> then enumerate it") would correspond more to
> something like
>
> [ix: x group & xF Ix: x group & xF] [iz: z group & xCz Iz: z group & xCz] z d-G &
> "the brodes among the brodas are Q in number".
>
> I didn't formalize the second part because it
> would take me
> several lines, but in any case it is outside
> the scope of
> the Ix quantifier.
>
> In other words, is {Q lo broda cu brode}
>
> (1) "Among the brodas, there is at least one
> group that
> is Q in number and brodes"
>
> or
>
> (2) "There's a group among the brodas that
> brodes.
> They, the brodas that brode, are Q in
> number"
>
> Your definition corresponds to (1), but your
> talk points to (2).
Yes, this is a problem with this particular formulation — another reason to get out of groups as fast as possible. I suppose that one could go to "[iz: z group & xCz & zG Iz: z group & xCz & zG]Qz", but this seems to have some other questionable -- though so far unexplored — consequences (not the least being that I would have to agree with McKay on at least one of his problematic claims). In particular, the rhetoric seems wrong, even if the facts are OK. Again, I hope that this has been cleared up in the last section.
xorxes: > > [ix: x group & xF Ix: x group & xF] [iz: z group & xCz Iz: z group & xCz] z d-G & > z is Q of x > > There is some group of brodas x, such that > there is some > subgroup z among them, such that z are brode > and Q in > number. > > Your description above ("having found the group > we can > then enumerate it") would correspond more to > something like > > [ix: x group & xF Ix: x group & xF] [iz: z group & xCz Iz: z group & xCz] z d-G & > "the brodes among the brodas are Q in number". > > I didn't formalize the second part because it > would take me > several lines, but in any case it is outside > the scope of > the Ix quantifier. > > In other words, is {Q lo broda cu brode} > > (1) "Among the brodas, there is at least one > group that > is Q in number and brodes" > > or > > (2) "There's a group among the brodas that > brodes. > They, the brodas that brode, are Q in > number" > > Your definition corresponds to (1), but your > talk points to (2). > Of course, part of this amounts to working out when "having identified a subgroup" is realized. I would say it was in "[iz: z group & xCz Iz: z group & xCz]," you would take it as coming only at the end of the whole. The section on most likely Fs goes with the first interpretation, which also is closer to the Lojban pattern.
pc: > > [ix: x group & xF Ix: x group & xF] [iz: z group & xCz Iz: z group & xCz] z d-G & > > z is Q of x > Of course, part of this amounts to working out > when "having identified a subgroup" is realized. > I would say it was in "[iz: z group & xCz Iz: z group & xCz]," you > would take it as coming only at the end of the > whole. The section on most likely Fs goes with > the first interpretation, which also is closer to > the Lojban pattern.
I can't say I understand your section on "most likely" yet. But for ordinary quantifiers, the "Some S" part of "Some S is P" is not enough to make an identification.
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wrote:
> > pc: > > > [ix: x group & xF Ix: x group & xF] [iz: z group & xCz Iz: z group & xCz] z > d-G & > > > z is Q of x > > Of course, part of this amounts to working > out > > when "having identified a subgroup" is > realized. > > I would say it was in "[iz: z group & xCz Iz: z group & xCz]," > you > > would take it as coming only at the end of > the > > whole. The section on most likely Fs goes > with > > the first interpretation, which also is > closer to > > the Lojban pattern. > > I can't say I understand your section on "most > likely" > yet. But for ordinary quantifiers, the "Some S" > part of > "Some S is P" is not enough to make an > identification.
Remember that we aare here in inspecificity (if that is the right distinction) so that IDENTIFICATION, if that means putting a name to or pointing out or the like — outside the context --is not what is required. This is A broda, not out of context this broda or Charlie Brod or whatever. Particular quantifiers (and at the logic level we seem to need only them and universals) amount to saying whaat kind of thing we have selected but not what it does. Standard logical notation is not very good on this; restricted quantification is better but still leaves something to be desire. The "Y" notation is a bit better yet but may still fall short, though I don't see just exactly how at the moment. But, in any case, it is useful to notice that these three (standard — not group — plural quantification, restricted quantfication, and the Y language) are all equivalent to one another though they make different things "obvious." The Y notation makes the relation to Lojban at least more obvious than the other two, which shows a good intuition on JCB's part half a century ago (when most of the logic here was as yet unexplored and some not even hinted at).
pc: > [ix: x group & xF Ix: x group & xF] [iz: z group & xCz Iz: z group & xCz] z > d-G & z is Q of x > > Remember that we aare here in inspecificity (if > that is the right distinction)
Where does that show in the above formula?
> so that > IDENTIFICATION, if that means putting a name to > or pointing out or the like — outside the > context --is not what is required.
I don't think identification is ever involved when it comes to standard quantifiers. You talked of identifying first and then denumerating. My point was that the denumeration, in that formula, is done at the same time as anything we may recognize as identification.
> This is A > broda, not out of context this broda or Charlie > Brod or whatever.
That sounds good for {lo broda}.
But not what I would want for {su'o da poi broda cu brode}, which is merely [ex: x broda Ex: x broda] x brode, and where the quantifier operates on a sentence, it does not refer.
> Particular quantifiers (and at > the logic level we seem to need only them and > universals)
Given negation, either one of them will do. We can get the other in terms of it and negation.
> amount to saying whaat kind of thing > we have selected but not what it does. Standard > logical notation is not very good on this; > restricted quantification is better but still > leaves something to be desire. The "Y" notation > is a bit better yet but may still fall short, > though I don't see just exactly how at the > moment.
What would be good keywords to Google for this? I tried "most likely" and "Y notation" but it's too general and nothing related comes up. I had never heard about this before.
> But, in any case, it is useful to notice > that these three (standard — not group — plural > quantification, restricted quantfication, and the > Y language) are all equivalent to one another > though they make different things "obvious." The > Y notation makes the relation to Lojban at least > more obvious than the other two, which shows a > good intuition on JCB's part half a century ago > (when most of the logic here was as yet > unexplored and some not even hinted at).
I haven't noticed the equivalence yet, but then I still don't very well understand this Y notation.
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wrote:
> > pc: > > [ix: x group & xF Ix: x group & xF] [iz: z group & xCz Iz: z group & xCz] z > > d-G & z is Q of x > > > > Remember that we aare here in inspecificity > (if > > that is the right distinction) > > Where does that show in the above formula?
I suppose (though I am not sure I understand just whatspecificity is all about --even after Cowan's explanation, which I have lost anyhow) in the fact that there is no further identification (or whatever you want to call it) than as a grouup that Fs and as aa group subordinate to that.
> > so that > > IDENTIFICATION, if that means putting a name > to > > or pointing out or the like — outside the > > context --is not what is required. > > I don't think identification is ever involved > when it > comes to standard quantifiers. You talked of > identifying > first and then denumerating. My point was that > the > denumeration, in that formula, is done at the > same time > as anything we may recognize as identification.
Are we talking linguistically or physically here? Linguistically the "identification" is most of the sentence away from the enumeration; physically it might be hard to pick out a group without noticing at least a rough enumeration (assuming the group is not too big of course -- and even "too big" counts as an acceptable sort of enumeration). > > > This is A > > broda, not out of context this broda or > Charlie > > Brod or whatever. > > That sounds good for {lo broda}. > > But not what I would want for {su'o da poi > broda cu brode}, > which is merely [ex: x broda Ex: x broda] x brode, and > where the > quantifier operates on a sentence, it does not > refer.
Sorry, I thought we were talking about {lo broda} (well actually {Q lo broda}). The case of what are bare quantifiers in Lojban remain as bare quantifiers in the translation, except that the whole is put in terms of groups: [Ix: x group & xF & [ay: yF Ay: yF] xCy] [iz: xCz Iz: xCz] zG & z Q of x. I think that this amounts to the ordinary — though not here supported for the moment — [qx:xF Qx:xF]xG, but — the reasoning behind this analysis holds -- brings some useful but often hidden factors to light: the Fs, for example, and the sepparation of enumeration from identification (both for lack of better words at the moment).
> > Particular quantifiers (and at > > the logic level we seem to need only them and > > universals) > > Given negation, either one of them will do. We > can get > the other in terms of it and negation.
True, but not necessarily very useful. A in terms of I is messy (a conjunction of quantified sentences) I in terms of A is worse because it is hard to get the importing back in after a negation: ~A+ = O-, so ~A~ is I- rather than I+.
> > amount to saying whaat kind of thing > > we have selected but not what it does. > Standard > > logical notation is not very good on this; > > restricted quantification is better but still > > leaves something to be desire. The "Y" > notation > > is a bit better yet but may still fall short, > > though I don't see just exactly how at the > > moment. > > What would be good keywords to Google for this? > I tried "most likely" and "Y notation" but it's > too general > and nothing related comes up. I had never heard > about this > before.
I don't remember the standard terminology (this is mine, from an unfinished from long ago). Maybe "indefinite description" (though there are some large number of things that go by that name. The only thing I can remember the name of which at all related (and it is a different language altogether, though to the same point eventually)is Hans Hermes "Term Logic with Choice Operator," Lecture Notes in Mathematics 6, Springer Verlag, 1965. It is not the whole story but probably enough to get you over the rough bits. (The "most likely Fs" is, as hinted, not strictly correct but has proven pedagogically useful in the past.)
> > But, in any case, it is useful to notice > > that these three (standard — not group -- > plural > > quantification, restricted quantfication, and > the > > Y language) are all equivalent to one > another > > though they make different things "obvious." > The > > Y notation makes the relation to Lojban at > least > > more obvious than the other two, which shows > a > > good intuition on JCB's part half a century > ago > > (when most of the logic here was as yet > > unexplored and some not even hinted at). > > I haven't noticed the equivalence yet, but then > I still > don't very well understand this Y notation. > The crude equivalence is something like the following: translate among these notations Ix(xF & xG), [ix: xF Ix: xF] xG, [yx: xF Yx: xF]G. They ought to be true in exactly the same situations (there are tricky cases for each of them, but manageable and the general pattern holds). The English analogs are "There are somethings which are both F and G", "Some Fs are Gs" ("some" in phonmnetically reduced form "sm") and "Some Fs are Gs" ("some" in full form). (Or maybe the phonology goes the other way, I forget.)
John E Clifford scripsit:
> I suppose (though I am not sure I understand just > whatspecificity is all about --even after > Cowan's explanation, which I have lost anyhow)
A reference r is +specific if in order to determine its referent R we must appeal to the speaker's intention to refer to R.
A reference r is +definite if the speaker intends the listener to be able to determine R.
"The man" and "George" are +specific +definite.
"A certain man" is +specific -definite.
"A man" and "Some men" are -specific -definite.
-- "There is no real going back. Though I John Cowan may come to the Shire, it will not seem jcowan@reutershealth.com the same; for I shall not be the same. http://www.reutershealth.com I am wounded with knife, sting, and tooth, http://www.ccil.org/~cowan and a long burden. Where shall I find rest?" --Frodo
In a message dated 2004-11-17 8:43:19 PM Eastern Standard Time, jcowan@reutershealth.com writes:
> A reference r is +specific if in order to determine its referent R we must
> appeal to the speaker's intention to refer to R.
>
> A reference r is +definite if the speaker intends the listener to be able
> to determine R.
>
> "The man" and "George" are +specific +definite.
>
> "A certain man" is +specific -definite.
>
> "A man" and "Some men" are -specific -definite.
>
Does the remaining possibility of -specific +definite exist? Would you give an example?
stevo
MorphemeAddict@wmconnect.com scripsit:
> Does the remaining possibility of -specific +definite exist? Would you give > an example?
Not really, as that would imply that the speaker doesn't have a particular referent in mind, but the listener does. That pretty much only happens when the speaker is a parrot, or is repeating something he's heard parrot-fashion.
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