Random Conlang Grammar Ideas Thread

[TomHChappell]

[spoiler]

Using Case-Endings and Postpositions and Prepositions to Mark Case-Like Stuff
Imagine a language with a few case-endings and a few postpositions and a few prepositions.
Imagine the following are true:
* any noun-phrase can be used with no case-ending and no postposition and no preposition.
* any noun-phrase can be used with any case-ending and no postposition and no preposition.
* any noun-phrase can be used with any postposition and no case-ending and no preposition.
* any noun-phrase can be used with any preposition and no case-ending and no postposition.

Assume all of those marking possibilities indicate different syntactic roles and/or different semantic roles; ad-verbal or ad-nominal.

More assumptions:
* any noun-phrase can be used with any case-ending and nearly any postposition and no preposition.
* any noun-phrase can be used with any case-ending and nearly any preposition and no postposition.
* any noun-phrase can be used with any postposition and nearly any case-ending and no preposition.
* any NP can be used with any postposition and nearly any preposition and no case-ending.
* any NP can be used with any preposition and nearly any case-ending and no postposition.
* any NP can be used with any preposition and nearly any postposition and no case-ending.

Assume all of the marking possibilities mentioned so far indicate either different syntactic roles or different semantic roles, whether ad-verbal or ad-nominal.

One more assumption:
* For any case-ending and any postposition and any preposition, if that case-ending can be used with each of the adpositions separately, and those adpositions can be used together with no case-ending, then any NP can be used with that case-ending and that postposition and that preposition all together at once.

And, with different semantic or syntactic implications than any other of the markings mentioned so far.

. . . . .. . . . . . . . . .. . . . . . . . . . . .. .. .. .. . .

I’m about to get ready to figure out how many different marking combinations there are.

. . .. . . . . . . . . . . . . . . . . .

If for each postposition there is one and only one case-ending with which it is incompatible (ie they can’t be used together), then there aren’t more postpositions than case-endings.
If for each preposition there is one and only one case-ending it is incompatible with, there aren’t more prepositions than case-endings.
If for each case-ending there’s one and only one postposition it’s incompatible with, there aren’t more case-endings than postpositions.
If for each case-ending there’s exactly one preposition it’s incompatible with, there aren’t more case-endings than prepositions.
If for each preposition there’s just one postposition it can’t be used with, there aren’t more prepositions than postpositions.
If for every postposition there’s just one preposition it can’t be used with, there aren’t more postpositions than prepositions.

I’m going to assume all six of the above hypotheses. That will mean the number of case-endings and the number of postpositions and the number of prepositions are all equal. And that will make the following algebra a lot simpler.

. . . . .. .. .. .. . . . . . . . . . . . . . . . .. . . . .

Let n be the number of case-endings and the number of postpositions and the number of prepositions.
Then, there are
1 way to “mark” a NP with no case-ending and no adposition,
n ways to mark a NP with a case-marking but no adposition,
n ways to mark a NP with a postposition but no case-ending and no preposition,
n ways to mark a NP with a preposition but no case-ending and no postposition,
n(n-1) ways to mark a NP with a case-ending and a postposition but no preposition,
n(n-1) ways to mark a NP with a case-ending and a preposition but no postposition,
n(n-1) ways to mark a NP with a postposition and a preposition but no case-ending.

So far that’s 1+3n+3n(n-1) = 1 + 3n + 3(n^2) - 3n = 1 + 3(n^2) ways to mark a NP with none ore one or two, but not all three, of a case-ending and/or a postposition and/or a preposition.

. . . . .. . . . . . . . . . . . . . .

How many marking-combinations there are, when all three types — a case-ending, a postposition, and a preposition — are used, depends on how the incompatibilities line up with each other.
I’m going to calculate under two assumptions, which I’m guessing are the extremes. I doubt they’re the only possibilities unless n is small.

—————

First; assume:
* if a case-ending is incompatible with both a postposition and a preposition, then that postposition and that preposition are incompatible with each other.
* if a postposition is incompatible with both a case-ending and a preposition, then that case-ending and that preposition are incompatible with each other.
* if a preposition is incompatible with both a case-ending and a postposition, then that case-ending and that postposition are incompatible with each other.

If we assume those, then the number of ways to mark a noun-phrase with all three of a case-ending and a postposition and a preposition, each compatible with each of the others, is n(n-1)(n-2) = (n^3) - 3(n^2) + 2n.
So the total number of grammatical ways to mark up a NP in this language is
(n^3) - 3(n^2) + 2n + 3(n^2) + 1 = (n^3) + 2n + 1

If n is 0 this is 1. Boring.
If n is 1 this is 4, because you can’t use the case-ending with either adposition, and you can’t use both adpositions together. Still kinda boring.
If n is 2 this is 13. Now maybe we’re getting somewhere.
If n is 3 this is 34. That is at least as many as in Stanley Starosta’s “The Case for Lexicase”, unless my memory is completely misleading me, which gets ever likelier year by year.
If n is 4 this is 73. Four is my favorite value for n.
If n is 5 this is 136. Nearly as many as Tsez’s cases.
If n is 6 this is 229. More than Tsez has cases. I think that’s enough and I’m not going for bigger n under this assumption.

—————

The other assumption I plan to check out, about how the incompatibilities line up with each other, is the following threefold statement:
If a case-ending is incompatible with each of a postposition and a preposition, then that postposition and that preposition can be used together with any other case-ending, and also with no case-ending.
If a postposition is incompatible with each of a case-ending and a preposition, then that case-ending and that preposition can be used together with any other postposition, and also with no postposition.
If a preposition is incompatible with each of a case-ending and a postposition, then that case-ending and that postpositions can be used together with any other preposition, and also with no preposition.

Under this assumption, the number of grammatical ways this language has to markup case-wise and adposition-wise a NP with each of a case-ending and a postposition and a preposition all together at once, is
n(((n-1)^2) - 2) = n((n^2) - 2n + 1 - 2) = n((n^2) - 2n - 1) = (n^3) -2(n^2) - n .

So the total number of grammatical marking possibilities is
(n^3) - 2(n^2) - n + 3(n^2) + 1 = (n^3) + (n^2) - n + 1.

(This will usually exceed (n^3) + 2n + 1, as long as n-1 > 2.)

So for each value of n from 0 to 6, how many is (n^3) + (n^2) - n + 1 ?
If n is 0, this is 1. Of course. Boring.
If n is 1, this is 2. That doesn’t make sense. I don’t think all my other assumptions are consistent together with n=2.
If n is 2, this is 11. Not as many, yet, as the previous assumption.
If n is 3, this is 34. Same number as the previous assumption.
If n is 4, this is 77. A few more than under the previous assumption.
If n is 5, this is 146. Several more than the previous assumption.
If n is 6, this is 247. 28 more than under the previous assumption.

—————

So what does anyone think?

[/spoiler]

I have had a re-think; and I think the number of ways to mark a NP with all three of a case and a postposition and a preposition, might be something like the following.
If there are n cases and n postpositions and n prepositions, I hypothesize there’ll be
n(n-1)(n-2) + 3n(n-1) + 3n + 1
ways to mark up a NP like we were talking about below.

If n is 0 this is 1
If n is 1 this is 3+1 = 4
If n is 2 this is 6+6+1 = 13
If n is 3 this is 6+18+9+1 = 34
If n is 4 this is 24+36+12+1 = 73
If n is 5 this is 60+60+15+1 = 136
If n is 6 this is 120+90+18+1 = 229 .

[bradrn]

[spoiler]

The tag is actually called [more]:

More: show

Like this.

[ophois]

Okay, so here's one idea I think is pretty neat but will require multiple steps to fully explain.

First, the proto-lang is strongly head-initial. Second, there is no real distinction between prepositions and conjunctions. The same word can be used to mean both 'and' and 'with', for example. There's also a basic case system based solely on alignment and consisting of Nominative/Accusative/Dative.

The first step in the evolution of agreement in prepositional phrases. PPs as a whole agree in case, number, and person with the NPs they modify. So, lumuk tak samak 'The book on the table' where -k indicates accusative case, singular number, and third person. If there's no NP to modify on account of the PP modifying a VP, it agrees with the subject of the VP instead. Dasan kipidan tan saman 'They danced on the table'

Due to being redundant, the affix on the noun is frequently omitted and eventually lost, leading to a language where prepositions agree not with the complement, but with the head of the NP they modify. Prepositions as a whole eventually cliticise onto the noun, creating a neat set of not-quite-case prefixes which also encode grammatical information of, again, the NPs they modify.

So, in the end, tan- would not only be the prefix for the superessive case (kinda...), but also indicate that the thing the noun's on top is third-person plural nominative. Thanks to the lang being pro-drop, tansama on its own can also mean 'they, which are on top of a table'. And the fact that conunctions are rolled into this too means that another affix could mean 'me and (X)', for instance.

It might be a bit confusing, but the end would be so cool. I can imagine an essive clitic being used for politeness, like 'I, as an officer, command you to give me a drink'.

[bradrn]

The first step in the evolution of agreement in prepositional phrases. PPs as a whole agree in case, number, and person with the NPs they modify. So, lumuk tak samak 'The book on the table' where -k indicates accusative case, singular number, and third person. If there's no NP to modify on account of the PP modifying a VP, it agrees with the subject of the VP instead. Dasan kipidan tan saman 'They danced on the table'

Two issues:

• PPs typically act as complements to verbs, not nouns. Only in some languages are they allowed to modify NPs directly (e.g. French generally disallows it).
• The head of a PP is generally considered to be the preposition, not the noun. The term ‘prepositional agreement’ is more often used for a preposition agreeing with its own complement (as in e.g. Irish), which is head-marking rather than dependent-marking.

That said, the outcome you describe is actually attested, in NE Caucasian languages. In Tsakhur, some postpositions agree with the absolutive argument. In Lak, the allative case has an agreement slot, again agreeing with the absolutive argument. In Dargi the essive is signalled only by agreement with the absolutive, with no case-marker of its own at all. And even stranger things have happened: in Archi, for instance, some pronouns show agreement with the absolutive argument. (When the pronoun is itself in the absolutive, we get the astonishing phenomenon of a pronoun agreeing with itself.)

(For more on such things I recommend Corbett’s book on Agreement, which is where I got those examples from.)

EDIT: Apparently Iwaidja also has adpositions which agree with the nominative argument. Evans speculates that they came from serial verb constructions.

[ophois]

EDIT: Apparently Iwaidja also has adpositions which agree with the nominative argument. Evans speculates that they came from serial verb constructions.

Serial verb constructions are probably another thing worth looking into, as it means coverbs can be introduced into the mix, which in turn means that the clitics can be applied to verbs as well. This system of 'pre-forms' would fit well in a polysynthetic language, methinks.