# XXS: Extended XS proposal

### XXS: Extended XS

XS is intended to be a minimalist proposal: it pertains only to lo/le/la, makes only one change to CLL (viz. to the interpretation of inner PA following lo), and yet makes sayable most of the key things on our list of desiderata. XXS extends XS to cover all gadri, in a way that is consistent with core-XS, yet is also as consistent as possible with CLL and CLL-intent.

For further details of XS, see the other XS pages XS gadri proposal: And's version.

#### Gadri and inner PA: Alternative A

- (tu'o)lo PA means, essentially, "Mr Group of n Broda", where n can be pa (Mr Single Broda) or tu'o (Mr Broda Stuff).
- (tu'o)loi PA means "Mr Xod-collective of n Broda". A xod-collective is a kind of group that shares none of its properties with its constituents (its members or bits or components). [[
**Correction: This hasty definition is incorrect. A better characterization of what is intended is: "If X is a xod-collective wrt property P, then X has P and the constituents of X lack P". I haven't yet thought through whether this definition is tenable within the XXS scheme.]]**

- (tu'o)lo'i PA means "Mr Mathematical Set of n Broda".
- (tu'o)lo'e PA means "Mr Typical Group of n Broda". A Typical Group is one that has a property iff the property inherits by default property to its avatars.

E-gadri counterparts follow the same pattern (Mr Group, Mr Xod-collective, Mr Mathematical Set, Mr Typical), except that the referent is specific and the description nonveridical. Following CLL-intent, a-gadri work like e-gadri, except that instead of the nonveridical description there is a name. There is a gap where the a-gadri counterpart of lo'e/le'e should be, but it is not worth filling with a new cmavo.

When inner PA is not overt, either it is glorked or, as per CLL, it is ro.

#### Gadri and inner PA: Alternative B

As Alternative A, except:

- lV'i covers both mathematical sets and xod-collectives.
- (ro)lVi is an abbreviation for {(ro) da poi ME-member pa da poi ME-instance lV}. The reasoning leading to this suggestion is given in the discussion of XS & anaphora, but in brief what it allows us to do is to first refer to the members of a group distributively and then refer back to the group by means of anaphora. (E.g. "Three policemen distrib gripped a truncheon and collective surrounded me".) {ro lVi ci broda} is equivalent to one interpretation of {ro lV ci broda} and of {ci lV pa 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 that ro does not have existential import. As a quantifier, {ro X} means "For as many X as there are, ...".

#### Outer PA

- When outer PA is not overt, it is glorked, as tu'o or some other PA.
- PA LE is equivalent to {PA da poi ke'a BRODA tu'o LE}, with BRODA glorked from {Member/cmima, Avatar, Subkind/klesi}.

- As in CLL, {PAlo broda} = {PA broda}. But these are equivalent to {PA dapoi BRODA tu'o lo broda} rather than to {PA dapoi broda}, which is equivalent to {PA da poi BRODA-avatar tu'o lo pa/tu'o broda}.
- 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})

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

- 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: {mi nenri pa lo pimu (rogai) lo pendo be mi} "I am among exactly one group of half my (dozen) friends".

#### Substantive changes to CLL

- Interpretation of inner PA after o-gadri.
- Interpretation of lVi as xod-collective rather than group (or whatever it is that CLL lVi is supposed to be).

- Change to interpretation of outer piPA. CLL interpretation is incoherent.
- Addition of glorking to interpretation of PA LE.

- Loss of strict equivalence of {PA lo broda} and {PA da poi broda}. But this was more of a theorem than an axiom.

### Some extraneous extras

#### New ME

Add to ME:

- ME-avatar/instance
- ME-subkind

- ME-member

One of these three should be equivalent to the currently ill-defined {me}. ME-member is the most consistent with CLL examples of the use of {me} ("me le ci nolraitru" = "is one of the three kings"); {me} would therefore be the ME counterpart of {lu'a}.

#### Grammar changes

- Abolish the ME + MOI construction (delete the relevant line from tanru_unit_B_152).
- Allow MOI, ROI, MAI to be preceded by any operand expression.

Some discussions arising from XXS moved from here to new page.

Discussion: Three dogs attacked four men -- moved to new page.

#### Re: Gadri and inner PA: Alternative B

*(E.g. "Three policemen distrib gripped a truncheon and collective surrounded me".)*

The logic of this is simple when dealing with specific policemen:

ro le ci pulci cu jgari lo grana ije py sruri mi

*Each of certain three policemen gripped a truncheon, *

and they surrounded me.

The non-specific case would be something like "There is some group of three policemen, such that each member of the group gripped a truncheon and the group surrounded me". We can say that as:

su'o lo ci pulci zo'u ge ro me py cu jgari lo grana gi py sruri mi

*For some three policemen: each of them gripped a truncheon *

and they surrounded me.

I'm not sure I like the idea of hiding that {su'o} (or a similar {pa}) inside a gadri so that it would have scope over the outer quantifier of that gadri. If the {pa} inside the proposed {loi} is not a quantifier like this but just part of the description, then by XS principles it can't extend its scope to include the anaphor.

And Rosta: Last para: you're quite right -- this flaw makes Alt B unworkable. However, the zo'u sentence is uncomfortably cumbersome, given the normality of the meaning. I think I'd rather revise Alt B to change what is abbreviated, so that (ro)lVi PA is short for {su'o da poi INSTANCE lo PA ... zo'u ro de poi cmima da}. Unless you can think of a better way?