XS gadri proposal: And's version

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'XS' gadri proposal (And's version -- 'XS&')

Note: in the following, a 'change' to CLL is defined as something that conflicts with CLL, and is distinguished from an 'addition' to CLL.

The proposal covers only lo and le (and la, which is assumed to continue to function like le, as in CLL). None of the remaining gadri are expressively necessary, and they can be defined according to whatever compromise between usefulness, logical coherence and CLL-conformity the BF deems best.

Default outer quantifiers

The CLL rules can be interpreted as (a) xor (b):

(a) When there is no overt outer quantifier, su'o is inserted before lo and ro is inserted before le and la.

(b) When there is no overt outer quantifier, the outer quantifier is glorked. (CLL *predicts* -- but does not *stipulate* -- that in usage the most frequently intended implicit quantifiers will be (su'o)lo and (ro)le and (ro)la.)

XS& prefers rule (c):

(c) When there is no overt outer quantifier, no quantifier is inserted into the logical expression derived from it. This would be equivalent to inserting a zi'o-like tu'o as implicit outer quantifier.

As a second-choice fallback compromise option, XS& prefers (b). Even (a) is not outright incompatible with the rest of the proposal, though it would mar its elegance and economy.

Interpretatiion of PA+LE

1a. tu'ole, with null quantification, refers to the whole group of one or more in-mind things. This is not a change from CLL, because tu'ole has no meaning there.

1b. tu'olo, with null quantification, refers to the Kind ('Mister'). This is not a change from CLL, because tu'ole has no meaning there.

2a. PAle, with nonnull quantification, quantifies over the members of the whole group of one or more in-mind things. This is as in CLL.

2b. PAlo, with nonnull quantification, quantifies over members of the category Broda, as in CLL. Whereas lo in CLL has no independent meaning (apart from being not-le), PAlo in XS can be seen to have a compositional meaning with lo referring to Kind, and PA quantifying over avatars of the Kind.

As in CLL, {PAlo broda} = {PA broda} = {PA dapoi broda}.

Meaning of ro

{ro} is defined as whatever number is the cardinality of the set it is applied to. There was a massive debate over this last year, and everybody supported it except John. The only substantive change from CLL that it entails is that CLL ro does not have existential import when (and only when) functioning as an external quantifier. CLL ro as inner quantifier lacks existential import, so the XS proposal brings consistency to CLL.


As in CLL, {le re plise} is a specific group of two apples. {le pimu plise} is a specific one half of an apple (I'm not sure whether this counts as an addition to CLL). {le PA broda}, then, is a specific group consisting of PA times a single broda. When the reference is to uncountable Substance, the inner PA is tu'o.

The CLL rule for default inner PA for le is either (a) or (b):

(a) Default inner PA for le is le(su'o).

(b) Default inner PA for le is glorked.

Because XS allows inner tu'o for Substance, XS prefers (b), or else (c), which is not substantively different from (b).

(c) Default inner PA for le is ro.


In CLL, PA in {lo PA broda} is the cardinality of the set of all things that are broda. But in XS -- and this is the only substantive change in the whole of XS -- loPA expresses instead the category of things that are PA broda. {ci lo re plise} = "three pairs of apples", {ci lo pimu plise} = "three apple halves". As with lePA, tu'o gives Substance: {su'o lo pa plise} = "at least one apple", {su'o lo tu'o plise} = "at least one amount of apple".

In other words, inner PA is not the cardinality of the set being referred to or quantified over (as in CLL) but rather the the cardinality of each member of the set being referred to or quantified over.

The default inner PA for lo can remain lo(ro), as in CLL.


"A specific trio of broda" = {le ci broda}

"A nonspecific trio of broda" = {pa lo ci broda}

"Two nonspecific trios of broda" = {re lo ci broda}


{PA lu'a (tu'o)lo (za'u) broda} quantifies over members of a Kind (such as Mr Two Snakes).

A new LAhE would be useful for quantifying over subkinds of Kinds ("Each of us has *a favourite meal*"). So XS proposes a LAhE-subkind as an addition.

Quantifier expressions

XS& proposes that, at least for the outer quantifier of lo and le, quantifier expressions are underlyingly fractional/rational (i.e. expressing fractions/ratios), as follows (brackets mark elidable defaults):

PA (fi'u ro)

"PA (out of all)"

PA1 fi'u PA2 = piPA

"PA1 out of every PA2, PA1 per PA2"

(ro fi'u) ro(PA) = ro(PA) (fi'u ro)

"each of all PA"

Because ot the "(pa) fi'u" convention:

(pa) fi'u PA2

"one out of every PA2, one per PA2"

(pa) fi'u roPA2

"one out of all PA2"

As a new abbreviatory convention, fi'u could be elidable between PA and ro:

PA1 (fi'u) roPA2

"PA1 out of all PA2" (= CLL {PA1 lo PA2})

Finally, the more complex expressions

PA1 fi'u PA2 ro PA3

(pa) fi'u PA2 ro PA3

piPA ro PA3

could be used for things like "three quarters of all 200". "75% of the over five hundred graduates from our college find jobs in the first 3 months after graduation": {pi ze mu ro za'u mu no no -graduates from our college ...".

These fractional quantifiers can be collectivized:

"I am among exactly one group of half my (dozen) friends"

mi nenri pa lo pimu (rogai) lo pendo be mi


(1) piPA LE. This should have been noted above as a quasi-change to CLL. Although {piPA lo/le} are undefined in CLL (unless, by extrapolation, {pimu (lo) plise} is taken to mean "(there is) half an apple"), piPA is used as some kind of outer quantifier before lei/loi. The CLL meaning is unclear and debatable, but the most coherent interpretation is something like "something consisting of x out of every y bits of".

(2a) Add a LAhE for "is an instance/avatar of".

(2b) Make PA LE be always an abbreviation of PA LAhE (tu'o) LE, with the appropriate LAhE glorked. Since LAhE-subkind, LAhE-instance and LAhE-member (lu'a) all make sense when applied to (tu'o)le and (tu'o)lo, this revision does not priviiege any of the three by exclusively assigning it to PAle and PAlo. This is a change from CLL, in that it makes the CLL interpretations of PAle and PAlo the product of glorking.

(3) Part of the intent of XS is to leave loi, lei, lai, lo'i, le'i and la'i alone, so that they can be defined by the BF solely on the basis of consistency and CLL-conformity, uncomplicated by criteria of expressiveness. However, it is still worth pointing out that these redundant gadri could be given a useful abbreviatory function by matching PA(lo)/le/la, (PA)loi/lei/lai and (PA)lo'i/le'i/la'i one-to-one with PA LAhE-instance, PA LAhE-member (= PAlu'a) and PA LAhE-subkind.

Further addendum on lVi & lV'i

In XS, (tu'o)lV means, essentially, "Mr Group of su'o/tu'o Broda". I suggest the following extension.

(i) Let (tu'o)lV'i mean "Mr Mathematical Set of", so as to be consistent with both CLL and XS.

(ii) Let (tu'o)lVi mean "Mr Xod-collective of", where a xod-collective is a kind of group that shares none of its properties with its constituents; there are no other cmavo-based ways of expressing xod-collectives. Outer and inner PA would mean the same for all gadri.

Re: Addenda

(2b) I agree. If LAhEs are defined as {lo broda be}, this will generate some recursiveness though. This is like the recursiveness we get if we try to define CLL-lo in terms of CLL-lo'i: {PA lo broda} = {PA lo cmima be lo'i broda} = {PA lo cmima be lo'i cmima be lo'i broda}, etc. We never manage to get rid of {lo}. A broda is a member of the set of brodas, which is a member of the set of members of the set of brodas, and so on. Similarly an avatar of Mr Broda is an avatar of Mr Avatar of Mr Broda, and so on. --xorxes


Default outer quantifiers:

choice (c) is just choice (b) gussied up: we are talking about some fraction of the set and, if not told which fraction it is, we are left to guess -- how we are not told doesn't matter.

  • The idea is that a sumti quantified neither overtly nor covertly is a constant and that Kind is the constant corresponding to the category. IOW (c) is not talking about some fraction of the set.
    • As noted on the xorxes page, being a constant (unaffected by negation passage) has nothing to do with quantification. And as long as we are talking about about something with members or masses, we have quantification in some way or other.
      • There's nothing special about having members that entails quantification.
        • Unfortunetely, there is something about having members that entails quantification. A constant may be a singular term, but it does not represent a single object and so we need to know what is the relation between the referent of the constant and the objects that comprise it. The archetype of a constant is not {la djan} but {lo'e broda}.
          • Fleetwood Mac has members. The Garrick Club has members. A wall has members. I am a group whose only member is me. All sorts of individuals can have members. The relation 'member of' relates individuals to other individuals and has no privileged status among other types of relation.
            • I'd shift to saying "object" rather than "individual" if I thought it would help. Fleetwood Mack is not an individual nor is The Garrick Club, for all that they are referred to by singular terms; those terms are just convenient ways of talking about what a bunch of individuals do on occasions. You are not a group, though you can be referred to in group term, either distributively or collectively (it doesn't matter which). You have parts, Fleetwood Mack does not. You do not have members -- though the singleton of you, which acts d&c just like you, does. Membership is a relation that applies only to things that are sets. Part-whole applies only to objects (spatio-temporally continuous, etc.)
              • Ah, I see where you're coming from now. You're of that school of thought that thinks you can look around and classify the things you find as individuals and nonindividuals -- i.e. that there are definable criteria for individualhood. Whereas, I am of that school of thought that thinks that everything is an individual: anything that can be the value of a variable is an individual. On this latter view, you can talk about individuals either by linguistically pointing directly to them, or by grouping them into categories and quantifying over members of the categories. So when xorxes & I are talking of 'constant' and 'individual', we are talking of this 'direct pointing' method in contrast to the quantification method.
                • Yes, I suppose I am sane -- in this one respect at least. To be sure, what is an individual is relative to context to a certain extent. The current context is Lojban, however, not set theory or mass theory or what not. So, variables range over individuals in the simplest sense -- spatio-temporally continuous and delimited objects. To be sure, we can talk using set or mass terminology, and even have predicates for it, but these are all just ways of talking about objects. If we allow quantification over these things we will get into serious problems from time to time, as we would obviously for quantifying over "the average man", say. For the most part, however, taking these things as individuals makes very little difference, since we can usually figure out how to unpack them. In some technical operations, however (substitution in lambda, for example) it can give wrong -- or at least misleading -- results. And, at the moment I at least am in the midst of such a technical context.
  • xorxes: If only spatio-temporally continuous and delimited objects are individuals (xu ro da dacti?) then it is hard to tell what you make of things like {su'o namcu}, {su'o selkai}, {su'o selcmi}, (some number, some property, some set) for example. Or are these outside of the Lojban context? If you say {lo'i broda cu selcmi}, can you later refer to lo'i broda with {le selcmi}? Is that an individual? In any case, are we just getting bogged down on terminology?

{PA le}:

(1a) If {tu'o le} means {ro le}, why not use {ro le}?

  • {ro le} isn't the whole group; it's each of the members.
    • And what does "the whole group" mean? Either all of its members distributively or collectively or cumulatively. So, if not {ro} then {piro}.
      • "The whole group" means a certain single thing. Without quantification, it is to be treated as a reference to that certain single thing. With quantification, quantification is over members of this certain single thing.
        • A group is not an individual, it is just a mess of things considered in a certain way.

(1b)Which meaning of "Kind" is involved here? This looks like {loi}, but it is not clear.

  • We haven't articulated any list of alternate meanings of Kind, so I can't say. I'm taking it for granted that the Explainer in Chief (Nick, probably) will eventually be explaining terms.
    • Meanwhile, how does what you have in mind (if at all precise) differ from {loi broda} or, perhaps, {piro loi broda}?
      • Since we lack a clear articulation of what these mean, I can't answer that question yet.
        • These are out of CLL.

(2b)Why doesn't {lo broda} mean "some subset of the set of broda, considered distributively" in CLL, as it does here?

  • I'm not sure I understand the question. That's not what {(tu'o)lo broda} means in XS. The word {lo} in CLL means something like "nonspecific", "not-le", but nothing else AFAICS.
    • I know it is not what it means in XSA and am trying to figure what it does mean there (if anything). It is what it means in CLL; the difference from {le} takes place within that context "of broda" being replaced for "le" by "of designated items called 'broda'" and "some subset" by "all".

The equation works in simple cases, but it would be useful to separate these out in more complex contexts (see Logic Language Draft 3.1

{ro}: What is accomplished by going against 2500 years of logical (and language) tradition escapes me still, nor is the reason for comlicating matters at the definitional level obvious.

  • Here's not the page to reprise those discussions. Here I will just note that CLL-Lojban uses ro as a cardinal (lo ro broda) -- and one that doesn't entail su'o.
    • The internal {ro} in CLL entails {su'o}.
      • I believe not.
        • This has been established roughly a dozen times in as many years. You may not like it, but I don't like a lot of real things either.
          • I am equally certain that the general consensus has always been the opposite. So all we can be certain about is that this is not a point that is universally agreed on, and hence must be decided by the BF.
            • This is presumably not a popularity contest but an attempt to make a reasonably coherent and efficient language "based on formal logic." Since the last clause is definite for importing and it is the more efficient of the possibilities, that should settle the matter even if the clear implications of CLL did not.
              • It ends up being a popularity contest partly because political considerations supervene and partly because sometimes there remain legitimate differences of opinion about what the logical solution is. (Illegitimate differences usally get ironed out in debate, until people forget & reargue it all.)

{le PA}

I think internal quantifiers should be done away with as an obligatory category.

  • I agree. But we still have to decide what they mean when they're present.
    • They give the cardinality of the set involved, in case someone cares.

I wonder which definition of "Substance" is involved here. It looks like a complex {loi}-- so complex that having a different gadri for it makes sense. But not some futzing with existent forms to break up the underlying unity of the forms.

  • Substance = 'Mass' (in Linguistics, not Lojban terminology). Uncountable stuff.
    • But sliceable, and fractionally quantifiable. As I said, it sounds like the collective group of the constitutive parts of broda, which is complex enough to recommend a new gadri -- if there is any significant use for the notion.

{lo PA}

We have a perfectly transparent way to talk about n-ads. Why break up the parallelism between desriptions and predications? That is not logical.

  • I take your point about breaking the parallelism, though I wouldn't call it clearcut breakage.
    • {ti re broda} does not mean "that is a couple of broda." I'm not sure what it does mean, though.
      • xorxes: It's two terms in succesion: {ti} and {re broda}. {mi dunda ti re prenu}, "I give this to two people".
        • So not "That is a pair of broda." That is all I needed.
          • xorxes: The same applies to the canonical interpretation of inner PA, of course. It breaks the parallelism as much as XS. Also, from {lo mi broda} I can't go to {ti mi broda} either.
            • Regardless of what the parser says, the numbers and the other modifiers at the beginning of descriptions go with the gadri, not the selbri -- logically, that is.
              • xorxes: Hmmm... {lo mi broda} can be paraphrased as {lo broda poi srana mi}, which in turn is {da poi broda gi'e srana mi}, so I would put {mi} with the description rather than with the gadri. The inner number I agree is not really part of the description when it is the cardinality. I think there was an argument that it was a part of the non-veridical description when considering the e-series though.
  • As for the alternative transparent ways to talk about n-ads, I'd like to see full examples of what they are.
    • {ti broda remei}or {ti remei le'i broda} etc.
      • One is a tanru, so inherently vague. The other brings in spurious specificity.
        • I'm not sure either the the vagueness is undesireable or the specificity spurious (but I'll use {lo'i} if you prefer it to {le'i}).
          • xorxes: {lo'i} doesn't work with the canonical place structure of mei. The x2 of PAmei has to be a set with cardinality PA. {ti remei lo'i plise} would say that the set of all apples is a two-some. You can say {ti remei fi re plise}, but the forced repetition of the number sounds redunant. You could also say {ti remei re lo'i plise} with your proposed interpretation of {PA lo'i}, but again you redundantly repeat the number.
            • OK, I'll stick with the first version then or fall back on {pisu'o lo'i broda} which is about what wanted anyhow. But the tanru will do for descriptions.
              • And: Given that tanru are by intent and definition vague, I don't think it satisfactory that a notion that is precise should be expressible only by means of a tanru. That said, perhaps {romei befi re plise} (or with 'gunma' instead of 'romei') is free from both vagueness and redundancy, but it is hardly free from necessary longwindedness.
  • Also, as a general principle, if we can use gadri complexes to talk about two things distributively, one would expect to be able to use gadri complexes to talk about two things collectively, too.
    • Difference between lV and lVi in CLL
      • xorxes: Yes, but CLL loi won't let you talk about a nonspecific group of two broda.
        • True, whence the conservative extension proposed to get the external quantifiers in balance.


The example of subkinds is covered already by quantifier rules. The rest of this passage is unclear.

  • The example means "a favourite kind of meal". Or consider: "We drank the same (kind of) wine". Sure there's quantification, but over subkinds.
    • Subkinds are just kinds with added predicates, "my favorite kind of meal" is just a selected kind from "kind of meal" so nothing new is needed.

Quantifier expressions

Having gotten rid of internal quantifiers, I see no reason to smuggle them back into external quantifiers, as this proposal does. It also breaks the parallelism between quantifiers on descriptions and those on variables, which again seems illogical and unjustified (so far at least).

  • We haven't got rid of internal quantifiers, though. The rationale for the smuggling back is the expressive power -- how else to say the stuff, if not this way. And the parallelism with descriptions is still there: the quantifier expressions apply to le as well as to lo.
    • Context! I have done it in my mind and thus am not in a mood to listen to it coming back. What is it that these quantifiers (which we already have) can say that others cannot? Instead of saying "three broda" about a set that in fact has 50 members, we now say "3/50 of the broda." And this adds exactly the (usually unneeded and irrelevant) cardinality of the set or at least its proportionality. The latter is occasionally useful admittedly, but can bve done now without mucking with normal quantifiers. Can these "new" quantifers be used, in the same sense with {da} -- that they are the same with {lo} and {le} is acknowledged and beside the point.
      • You choose whether to say "3 broda" or "3/50 broda".
        • I have come to agree with this point, at least, when I say oddness of fractional quantifiers on lV and the lack of cardinal ones on lV[')i). I wish you had pointed this out.

pc (added from other places)

If Kind includes also all unreal avatars (yuck!), does Substance include all their constitutive parts? I actually like have everything (every permutationally possible combination of properties taken as an object) in the domain but restricting quantification to the real things. If that is the game afoot, then -- provided all the safeguards and all the other mechanisms needed are in place -- I will sign on. I suspect this will involve some rewriting up and down CLL and the corpus (but it would bring {sisku} into line).

  • xorxes: Great!

It does create some problems for using Kind for things like "I like chocolate" however, for even a person who likes no real chocolate likes the bit of chocolate that everyone likes out there in Nephelococcygia.

  • xorxes: But similarly, a person who doesn't like John may like two-month-old John. It's a matter of context. We are probably talking about the present John, in the appearances that are known by the person. Similarly we'd be talking of the most representative instances of Mr Chocolate, which might vary with context.
    • Ahah! If you are going to move to representative avatars (which probably aren't avatars at all: see "the average"), then Mr. Chocolate no longer does it. Rather this goes off on totally different problem, related to {lo'e}(the CLL one). And, of course,even if the representative chocolate is an avatar, some people who like chocolate by any normal standard will not by this one, since they have tried the representative (in fact almost all of them, since the representative bits can't get passed around). And oppositely a person we would normally say does not like chocolate, may happen to like (exactly) this bit and so end up being called a chocolate lover by this definition.
      • In absence of context, when someone says something about John I assume a general setting. In {la djan cu xabju la paris} I will assume it is the current John that lives there, though context may prove me wrong. Similarly for Mr Chocolate.
        • I don't see how this helps. No avatar of Mr. Chocolate nor any combination of them is decisive for liking chocolate -- even liking it now. But the the current slice of the John worm is decisive for liking John now. To be sure, liking John in general is in as bad shape as liking chocolate in general. And neither problem is solved; the analogies hold no clues.
          • xorxes: Liking the current slice of John is analogous to liking a particular avatar of Mr Chocolate, say the one I had last night. Liking John in general is analogous to liking Mr Chocolate in general.
            • Overnight flash. The solution, since no one item nor group of items is either sufficient or necessary to determine liking a generality, seems to be {rau} on either CLL or your {lo} (or my forthcoming {loi}). This is close to ignotum per ignotiusbut it has enough usage in Lojban and is clearly close enough to English to be a real solution (the "whafor" is covered by the context: {mi nelci rau lo cakla}.
              • xorxes: That says that there are enough avatars of chocolate that I like. It is a valid claim, no doubt, but much more detailed than "I like chocolate". (A possible dialogue: "Do you like John?" "Well, let me see, there are enough particular times when I have liked John-at-that-time, so yes, I can say that I do like John." "Do you like chocolate?" "Well, let me see, there are enough particular instances of chocolate such that I have liked that-instance-of-chocolate, so yes, I can say that I do like chocolate.") {mi nelci rau cakla} can be a good justification for the more general and vague {mi nelci lo cakla}.
  • (multiply the indent the appropriate number of times)As often noted, liking one bit of chocolate is technically a sufficent reason to say that one likes loi -- your {lo} -- cakla. But we don't want that. Nor do we want to allow some nonexistent 'chocolate everyone likes' to do it. Nor do we want to insist that it is all existing chocolate. I would now insist on using a distributive set (my {lo}), not a collective (your {lo}), not that it makes much difference with chocolate. It does with temporal slices of John, I think, since collectives of those slices usually aren't parts of him. I suspect that the only safe generality (for which {mi nelci rau cakla} is perfect evidence) is {mi cakla nelci} or a compound based on it.
    • Well, we now know that {lo} is under a modality, probably "generally," which is a quantification on occasions (here for doing something appropriate with chocolate). The quantifier is probably "enough" if we are to avoid other kinds of problems.