# Discussion: Three dogs attacked four men

moved from XXS: Extended XS proposal

pc:

Further sorting: Three dogs attacked four men

lo ci gerku cu gunta lo vo nanmu : three dogs, four men, one attack

ci gerku cu gunta lo vo nanmu: three dogs, up to 12 men, three attacks

lo ci gerku cu gunta vo nanmu: three dogs, four men, four attacks

ci gerku cu gunta vo nanmu: three dogs, up to 12 men, 12 attacks

(I think MCLL is the same with {loi} for {lo}) Right so far?

• Not sure about {lo ci gerku cu gunta vo nanmu}. I'd say "up to 12 dogs, four men, four attacks". It doesn't have to be the same avatar of Mr Three Dogs that attacks each of the four men. {pa lo ci gerku cu gunta vo nanmu} would give three dogs, four men, four attacks. --xorxes
• Damn. Now I don't understand this at all again. I would think that {lo ci gerku} was outside the scope of {vo}, as the order says, that your reading would require {vo nanmu cu se gunta lo ci gerku}. Aha! Not your point (I think), but (lo ci gerku} is not restricted to real dog packs, so this has to be taken as modal. But even so, it still seems to be about three dogs, four men and four attacks.
• In your terms, {lo ci gerku} has a su'o with minimal scope, so always inside the scope of whatever else has scope, in this case vo nanmu. In my terms, {lo ci gerku} is a constant, "Mr Three Dogs", which on each occasion it shows up can show up as a different avatar. We have four attacks here, so "Mr Three Dogs" will show up on four different occasions. If I say {la djan cu gunta vo nanmu} I am not saying that it was the same stage of John that participated in each attack, he may have attacked them one at a time.
• I rather think that you are letting this weird Mr. analogy to a real individual get the better of you, but since it is your mishugash, I'll play along and use {pa}. So far as I can tell, the short scope quantifiers are coextensive with the modals they occur under and so, since the modal here ("last night," say, is sentential, the {vo} would be in the scope of the {su'o}. But a glance show that I never made that point anywhere else that I can find readily, so let em say it now:to enable coherent references in anaphora, the scope of a short-scope quantifier has to be coincident with the shortest modal within whose scope it lies. I suspect this will need some fine tuning, but it works so far.
• That way it stops being a constant. I want it to be a constant. For example, I want {lo remna cu xabju ro braplu} to mean that humans inhabit every continent, not that there is some human that lives in every continent.
• On further thought, sentences with more than one number quantifier are more complex than it appears at first sight. {ci gerku cu gunta vo nanmu} is not really about 12 attacks, anymore than {ci gerku cu gunta no nanmu} is about zero attacks. Both sentences are in fact about all attacks of dogs to men. The first one says that if we look at all the instances where a dog attacks a man, we will find exactly three dogs such that each connects with exactly four men. The second one says that we will find exactly three dogs that connect with no men. But {ci gerku cu gunta vo nanmu} says nothing about, for example, how many dogs attack only two men. So it doesn't say that there are only 12 attacks. It doesn't exclude the possibility of there being more attacks. {ci gerku cu gunta no nanmu} doesn't say that there are no attacks, it only says that exactly three dogs attack no man (which must mean that every other dog attacks at least one man). --xorxes
• Is this again about generality, that is that this is not about one incident (broadly speaking) but about dogs and men generally? How then do we say ths particular case -- headline for one day, say? In CLL at least this one is pretty clearly as I give it (maybe throw in a {pu} to be sure?). {ci gerku cu gunta no namu} is just odd, with the implication that every other dog attacked at least one man on this occasion -- or even, admittedly, ever. I can see that examples neeed not only be full sentences -- which has been a probolem with much discussion in the past -- but a complete context. My examples can mean what you say, but they can also mean what I say, I think. Context needed though (for both cases, not just mine, by the way). Or we need generality modals (which we do anyway).
• Are you saying that {ci gerku cu gunta vo nanmu} entails in some contexts {naku mu gerku cu gunta re nanmu}? Doesn't it always entail, rather, that {da'aci gerku cu gunta me'ivo ja za'uvo nanmu} "all but three dogs attack other than four men"? (In a context where there are only three dogs, both entailments would be correct.)
• I wouldn't think either entailment held in the intended intrerpretation. It just says that some three dogs each attacked some four men (there are three dogs such that for each of them there are four men that dog attacked). Nothing is said about any other dogs or men. I suppose it follows that all the other dogs each attacked some or no men, but that is hardly worth mentioning.
• OK, we agree then. It is just a very odd thing to say, not very informative. Suppose someone asks {xo gerku cu gunta xo nanmu}, "how many dogs attacked how many men?" Saying {ci gerku cu gunta vo nanmu} is nowhere near a complete answer. I'd still have to ask, and how many attacked none, how many attacked one, how many attacked two, how many attacked three, how many attacked five, and so on. You only say how many attacked four. The meaning is clear. The context in which one would want to give such a limited information is not clear. Unless there is some presupposition that there were only three dogs in all, given that no info is given about more than three dogs.
• Context: morning paper, local section. Presupposition: it happened last night in this vicinity. Same for all of these by the way. I can't imagine how else it would appear as a headline.
• With that context I would expect {lo ci gerku cu gunta lo vo nanmu}, the total number of dogs involved and the total number of men. I don't see why it would be interesting to know how many dogs attacked four men without being told how many dogs attacked three men and how many attacked five. Unless I'm supposed to assume none. And presumably it would be more interesting to know how many men were attacked in all, which {ci gerku cu gunta vo nanmu} does not say.
• What we do not have is the case of three dogs, four men and four attacks but without the pack: each dog attacks one man and one also attacks another, say. Maybe that has to be spelled out just like that and cannot be collapsed.
• Something like: {lo ci gerku lo vo nanmu zo'u vo da nu pa lu'a gy gunta pa lu'a ny} "three dogs, four men: there are four occasions in which one of the dogs attacks one of the men". But that doesn't really say that everyone was involved at least once.
• Nice to see you using {lu'a}, but, yes, this could be true if one of the dogs attacked the same man four times. No short form suggests itself.
• {lu'a} is retained in XS, and it would be nice to have accompanying LAhEs for avatars and for subkinds.
• Subkinds I agree, avatars seem to be all there really is, so we get them all the time.
• Right, it wouldn't be used much. But if {PA lo} is to be glorkable among {PA lu'a lo}, {PA LAhE-subkind lo} and {PA LAhE-avatar lo}, there should be a way to disambiguate when needed.
• It's orthogonal to XS, but I favour moving these putative LAhE to ME. And Rosta

lo ci gerku cu gunta lo vo nanmu : three dogs, four men, one attack

• one trio of dogs, one quartet of men, one attacker/attackee pairing

ci gerku cu gunta lo vo nanmu: three dogs, up to 12 men, three attacks

• three dogs, one quartet of men, three pairings
• ci gerku cu gunta pa lo vo nanmu: three dogs, up to three quartets of men, three pairings

lo ci gerku cu gunta vo nanmu: three dogs, four men, four attacks

• one trio of dogs, four men, four pairings

ci gerku cu gunta vo nanmu: three dogs, up to 12 men, 12 attacks

• three dogs, up to 12 men, 12 pairings

lo ci gerku cu gunta lo vo nanmu ze'a le crisa

Trios of dogs have been attacking quartets of men all summer.

• Well, {ze'a le crisa} make a single event unlike and points toward plurals in both cases. It also points to real dogs and men. But, of course, it could equally well be There was an incident ofa three-dog pack attacking a four-man band this summer." The joys of unmarked number.
• {ze'a} indicates the duration of the relationship, so in this case there was attacking all summer long. For an incident at some point in the summer it would be better to say {ca le crisa}.

ci gerku cu gunta lo vo nanmu i reboi cy gunta lo reboi ny i noboi cy gunta lo paboi ny

Three dogs attack quartets of men, two dogs attack pairs of men, no dog attacks single men.

• In this case, the {noboi cy} tends toward a general look, but again, it could just be the report of last night (the night before three solo men got attacked, so tonight is different).

lo ci gerku cu gunta vo nanmu ze'a le ca crisa

Trios of dogs have attacked four men this summer.

Four men have been attacked by trios of dogs this summer.

• Or, ... see the first one.

ci gerku cu gunta vo nanmu i pa gerku cu gunta mu nanmu i no gerku cu gunta za'umu nanmu

Three dogs attacked four men, one dog attacked five, no dog attacked more than five.

• Yeah, there are nights like that in Dogtown. I have lost your point here. They can all have a variety of readings, courtesy of lack of number and modals, and we glork from (in this case nonexistent) contexts. You have warned me that you always take the unmarked as general. I should say that I always take the unmarked as something I could imagine saying, namely about some particular event, if possible (CLL seems to follow this except to make weird points).
• I'm just trying to figure out in what contexts one would want to use two number quantifiers together. Number quantifiers in Lojban are weird in that they are "exact", so that not only do they claim existence, but they also give an upper boundary. That means they all include hidden negations. {ci gerku cu gunta vo nanmu} is a very specific thing to say. It does not answer the question "how many dogs attacked men last night?" nor the question "how many men were attacked by dogs last night?". Those seem to be the questions one would expect to have answered by this sort of claim. It only answers the question "How many dogs attacked exactly four men last night?". It says nothing about how many dogs attacked any other number of men. It answers a very specific question that would not normally be interesting to ask.
• And Rosta: It's not really due to the exactitude of Lojban numbers, because {su'o ci gerku cu gunta su'o vo nanmu} still doesn't get the more normal meaning you're after. Rather, the problem is that more normal reading is logically rather tricky to formulate: "there is a group of dogs and a group of men such that for each of the dogs there is at least one man it attacks and for each of the men there is at least one dog he is attacked by, and the cardinalities of dogs and men are three and four respectively". Can that be simplified, logically? I don't see a way. And it's far too cumbersome to say, so the question is how to lexicalize in abbreviated form something that expresses that logical formula? Some sort of selbri that takes a relation (ka/du'u with multiple ce'u) as one sumti and whose remaining sumti, which refer to groups, are somehow mapped to the ce'u? But that's both clunky and hard to get to work.

xorxes: Right. We want to make the two claims:

ci gerku cu gunta lo nanmu ije lo gerku cu gunta vo nanmu

Three dogs attacked men, and dogs attacked four men.

We could say that as:

ci gerku kufa'u lo gerku cu gunta lo nanmu kufa'u vo nanmu

cifa'utu'o gerku cu gunta tu'ofa'uvo nanmu

but that wouldn't make for a nice headline.

The alternative is to define multiple quantifiers such that they act in parallel rather than one in the scope of the other. So {ci gerku cu gunta vo nanmu} would by definition expand to {ci gerku cu gunta lo nanmu ije lo gerku cu gunta vo nanmu}. I don't know how much havoc that would wreck elsewhere.

I suggest this:

lo ci gerku lo vo nanmu NU ce'u gunka ce'u

Underlying x1, x2 order corresponds to linear order of ce'u.

The NU means that for each of its sumti, every member of the sumti is in the specified relation with some member of each of the other sumti.

To capture the notion that exactly 3 dogs were involved in attacks on men, and exactly four men were involved in attacks by dogs:

pa lo ci gerku pa lo vo nanmu NU ce'u gunka ce'u

To capture the notion that at least 3 dogs were involved in attacks on men, and at least four men were involved in attacks by dogs:

su'o lo ci gerku su'o lo vo nanmu NU ce'u gunka ce'u

or

pa lo su'o ci gerku pa lo su'o vo nanmu NU ce'u gunka ce'u

xorxes: {pa lo ci gerku pa lo vo nanmu cu NU ce'u gunta ce'u} seems to run into the same problem as the original {ci gerku vo nanmu cu gunta}. There is only one dog-trio NU-related to one man-quartet, but how many dog-trios are NU-related to more than one man-quartet? You'd have to apply the same method again:

lo pa lo ci gerku lo pa lo vo nanmu cu NU ce'u ce'u NU ce'u gunta ce'u

(I think)

we could do something similar by defining a lujvo, cmiti'i: "x1 and x2 are related so that each member of one is in relationship x3 with at least one member of the other, in the appropriate order". Then we'd have:

lo ci gerku lo vo nanmu cu cmiti'i le ka ce'u gunta ce'u

Your NU would be a generalization of {cmiti'i fi le ka}, because cmiti'i could only take binary relationships.

And Rosta: {pa lo ci gerku pa lo vo nanmu cu NU ce'u gunta ce'u} -- hmm. There is exactly one dog trio and exactly one man quartet such that each member of the trio attacks a member of the quartet and each member of the quartet is attacked by a member of the trio. I haven't spotted how this fails to say what we want. There can't be more than three dogs attacking men, because that then would allow there to be more than one dog trio. What am I missing? In asking how many dog-trios are NU-related to more than one man-quartet, you seem to be suggesting that {pa lo ci gerku pa lo vo nanmu} doesn't exclude {za'u lo ci gerku za'u lo vo nanmu}, right? Doh! Yes of course. (Sorry for thinking aloud.) So the problem lies in using numbers as quantifiers. Instead we need something more like this:

li (su'o)ci li (su'o)vo NU ce'u poi gerku gunka ce'u poi nanmu

where the external sumti give the cardinalities of the sets of things that satisfy the relation. Is there any way to express this more simply, supposing that logic must be respected but Lojban grammar can, for the sake of discussion, be thrown out the window?

xorxes:I think we wouldn't need to throw the grammar out the window, but just reinterpret things differently. We throw out the window the left to right scope rule for multiple quantifiers. Instead, we say that one quantifier is under the scope of another only if it appears explicitly in an inner prenex. So:

ci da poi gerku zo'u vo de poi nanmu zo'u da gunta de

gives the odd reading that we now assign to {ci gerku cu gunta vo nanmu}. When two quantifiers appear in the same prenex, they are no longer taken to be one under the other. Instead, each is taken to head its own claim, and both claims are conjoined:

ci da poi gerku ku'o vo de poi nanmu zo'u da gunta de

expands to:

ci da poi gerku zo'u su'o de poi nanmu zo'u da gunta de

ije

vo de poi nanmu zo'u su'o da poi gerku zo'u da gunta de

which gives the natural reading of {ci gerku cu gunta vo nanmu}.

In general, the rule is that {PA1 broda PA2 brode cu brodi} expands to {PA1 da poi broda zo'u su'o de poi brode zo'u da de brodi ije PA2 de poi brode zo'u su'o da poi broda zo'u da de se brodi}. This rule requires double negatives to negate things: {no gerku cu gunta no nanmu} to say that no dog attacked no man, i.e. that no dog attacked any man and no man was attacked by any dog. I'm starting to like it... If one of the quantifiers is su'o and the other is not {no}, then one of the two claims adds nothing, su'o is just as if under the scope of the other quantifier. So su'o always has minimum scope (unless scope is forced with a prenex). The order of equal level terms is irrelevant. {ro le nanla cu cinba ci le nixli} says that all the boys kissed only three of the girls, i.e. every boy kissed at least one girl, and only three girls were kissed by at least one boy.

And Rosta: I take it that you're not proposing branching quantifiers in the underlying logic. That would blow my mind, let alone the rest of Lojbanistan's. Instead, you're proposing some complex rules for how unprenexed quantifiers translate into (still first order) logical forms. I'll have to think about it -- whether the complexity of the translation to logical form is justified by the utility.

Okay, I've gone away & thought about it. Here are my thoughts:

• Under current Lojban principles, my li/ce'u proposal is the best way to go.
• Your novel readings are good, but (a) the novel reading is a little counterintuitive (or at least unfamiliar) when ro is involved, (b) I don't think we should have to resort to prenexing to get what are fairly natural readings ("for each boy there are three girls he kissed"), (c) I don't think the logically simpler should be drastically more marked than the logically more complex. Perhaps a better solution is to have new metalinguistic UI that mark which scope rule is being applied in a bridi with multiple quantifiers. Either one such UI could be the default, or there could be no default, with unmarked scope being resolved by glorking. With this qualification, I think your proposal excellent.

Something I haven't thought through:

1. "Every boy knows you kissed two girls"
1. "There are two girls that every body knows you kissed"
1. "Every boy knows you kissed a girl, and there are only two girls that a boy knows you kissed".

In current Lojban (1) requires no overt prenexing, but (2) does -- "two girls" exports to a prenex higher than "every boy". In your system, (2-3), but not (1), require exporting both "every" and "two", right? In (3) you have to export "every" and "two" to the same prenex, else you get reading (1).

xorxes: (a) I find the novel reading fairly intuitive in lots of cases, starting with {ci gerku cu gunta vo nanmu}. It is possibly also the logic behind double negatives in languages like Spanish and some varieties of English. (b) I agree. (c) I like the idea of glorking + optional disambiguation very much. There is in fact some precedent for some kind of "parallel" scope of quantifiers in CLL:

The solution is to use a termset, which is a group of terms either joined by ce'e

(of selma'o CEhE) between each term, or else surrounded by nu'i (of selma'o NUhI)

on the front and nu'u (of selma'o NUhU) on the rear. Terms (which are either

sumti or sumti prefixed by tense or modal tags) that are grouped into a termset are

understood to have equal scope:

7.5) ci gerku ce'e re nanmu cu batci

nu'i ci gerku re nanmu nu'u cu batci

Three dogs plus two men, bite.

which picks out two groups, one of three dogs and the other of two men, and says

that every one of the dogs bites each of the men. The second Lojban version uses

forethought; note that ``nu'u is an elidable terminator, and in this case can be

freely elided.

But that is not quite what I propose, since it requires each member of each set to be related to each member of the other, not just that every member participates in at least one relationship. It also has the problem of using termsets for something different than their original function, so in some cases it creates ambiguity, and also of being cumbersome in forcing the two terms to be together. A UI indicator makes more sense.

1. "Every boy knows you kissed two girls"
• CL ro nanla cu djuno le du'u do cinba re nixli
• NL ro nanla cu djuno le du'u do cinba re nixli
1. "There are two girls that every body knows you kissed"
• CL re da poi nixli zo'u ro nanla cu djuno le du'u do cinba da
• NL re da poi nixli zo'u ro nanla cu djuno le du'u do cinba da
1. "Every boy knows you kissed a girl, and there are only two girls that a boy knows you kissed".
• CL ???
• NL ro da poi nanla ku'o re de poi nixli zo'u da djuno le du'u do cinba de

I think it would make sense that explicit prenex is above the implicit prenex of the terms in the body, so that (2) in the novel interpretation would be the same as in the current one.

Now I've slept on this, I like it even more than I did last night. The great virtue of the left-to-right scope rule was its straightforwardness, but its downside was (i) the way it forces fixed linear order onto structures that would otherwise have free order and (ii) the way an essentially hierarchical phenomenon (i.e. scope) is represented nonhierarchically bridi-internally. So the idea that same-level quantifiers translate to a same-level prenex, with linear order not mattering, is very good. The logic of cohabited prenexes is not compositional, but is justified by its expressive power. (Or maybe it is compositional, to somebody who can get their head round branching quantifiers...)

But this opens the way to a whole new programme of enquiry. With the left-to-right rule gone, the meanings of lots of bridi will have to be reexamined and new rules decided or deduced. For example, can naku cohabit a prenex? Probably not. In that case, in {ci da naku vo de}, do ci & vo cohabit a prenex, or does the linear position of naku somehow force them into different prenexes? And so on and so on. There needs to be a balance among (a) the need for simple rules, (b) the attraction of linear order not having logical import, and (c) the need for expressiveness and convenience.

xorxes:I can't make any sense of naku at the same level of the quantifiers, so I see three options:

1. naku forces a new prenex
1. naku has scope over the branching structure at its level.
1. naku is within the scope of each quantifier at its level.

(1) is nice in that {ja'aku} is available to do the same thing without the negation.

(2) is nice in that the order of terms at the same level, including naku, remains free.

(3) seems totally unintuitive and I mentioned it just for completeness.

I like (2).

And Rosta: I meant that as just an example of the host of unresolved issues that are newly created by the direction we're taking. As for your answer, I don't know which I prefer. If linear order becomes insignificant, then it has to be (2) or (3), and I don't know how we'd decide which. If the answer is (1), then linear order remains significant: and then we have to seek some principle to determine and justify when linear order is and isn't significant. I'm not saying that it is beyond our powers to do this: I'm just pointing out what has to be done.

xorxes: Another issue would be logical connectives. In principle, connected sumti should behave like quantified ones, so that {ko'a e ko'e broda ko'i e ko'o} should expand to {ko'a broda ko'i a ko'o ije ko'e broda ko'i a ko'o ije ko'a a ko'e broda ko'i ije ko'a a ko'e broda ko'o}. In other words, {e} should behave like {ro} and {a} should behave like {su'o}. Symmetric connectives present no problem of interpretation in this scheme because they can all be expressed in terms of quantifiers. Asymmetric connectives... I have to think some more about it.

And Rosta: It would be very bad if connectives weren't symmetrical with quantifiers. But how to express the CLL contrast

ko'a su'oda ge broda gi brode

ko'a ge broda gi brode vau su'oda

You can't readily prenex nonsumti connectives.

xorxes: The particular example you give doesn't present a problem. {su'oda zo'u ko'a da ge broda gi brode} gives the first meaning and either of your forms gives the other meaning. However, with any quantifier other than su'o it will be a problem. One possibility could be to have some way of marking a prenex as base-level, so that following prenexes will be under the scope of the connectives that appear in the body of the bridi. Anything in the base-level prenex would have the same scope level as things in the body. Something to indicate sub-base level would be needed too, as one may want to start with a sub-base prenex. So:

CLL: ko'a roda ge broda gi brode

NI: roda zo'u ko'a da ge broda gi brode

CLL: ko'a ge broda gi brode vau roda

NI: roda zo'u-SUB-BASE ko'a da ge broda gi brode

CLL: ko'a roda ga broda gi brode ije ko'a ge broda gi brode vau su'o da

NI: ko'a roda ge broda gi brode

Another possibility is to use postnexes for sub-levels. That's different than what we introduced postnexes for in the first place, though. That would give:

CLL: ko'a ge broda gi brode vau roda

NI: ko'a da ge broda gi brode vau zo'au roda

This could get horribly complicated, & I'm getting cold feet! To some extent the complexity arises from Lojban syntax's failure to base itself primarily on logical structures, so the blame lies at the feet of loglanists of old, but still, there's nothing we can do about that now. So anyway, I'm thinking that maybe we should switch to the following:

• Any scope-sensitive bridi-internal element is preceded by an implicit or explicit scope-BAhE.
• There are two scope-BAhE: one means "scope subordinate to previous element"; the other means "scope coordinate with previous element". Coordinate scope is as per your definition.

This is like a simple add-on to current Lojban, rather than any sort of radical innovation.

xorxes: Glorkable scope-BAhE sounds excellent.

And Rosta: Good. So linear order continues to have semantic import -- it was a nice thought that that could be done away with, but it would work only if we could reengineer the syntax wholesale.

The scope-BAhE allow us to state, for example, that {na} is always {(BAhE-subordinate) na} -- it should be quite straightforward, given the scope BAhE mechanism, to formulate rules for which elements can and can't have coordinate scope.

xorxes: Actually, I changed my mind about {na}. {na} can have coordinate scope, but only with negative terms. {no gerku naku gunta no nanmu} "no dog didn't attack no man" with coordinate scope should exapand as {no gerku cu gunta lo nanmu ije lo gerku cu gunta no nanmu ije lo gerku na gunta lo nanmu}. {na} can't have coordinate scope with afirmative quantifiers, but then neither can {no}. Afirmative and negative can't mix coordinately, because obviously they give a contradiction. It would also be contradictory to say coordinately {no gerku ja'aku gunta no nanmu}: "no dog does attack no man". It is clear that if we have {naku} mixed with affirmative quantifiers, the only reasonable glorking is subordinate scoping.