Quantifiers (all, some, many, none, every, etc.) play an essential role in semantics. In Chomskyan Universal Grammar theory quantifiers are considered archetypical language elements the notion of which is hard-wired into the brain and thus the according concepts must be present in any language; the Chomskyan Generative Grammar builds upon the Universal Grammar theory (Chomsky 1965). Mainstream semantics theory today, as developed by Chomsky and his followers among other at the MIT employs methodical elements like Deep Structure, Surface Structure, quantifier raising and Logical Form to model the semantic structure of a natural speech utterance and represent its meaning in an abstract, logical meta language. On the basis of the assumption that due to universality of the concept of quantification, Chomskyan semantics is entirely based on English.

A semantic meta language as employed in semantics theory (first order / predicate logic), lexical decomposition (Dowty 1979) and in Role and Reference Grammar (Logical Structure, Van Valin 2005) interprets language as a code of symbols with a fixed, unequivocal meaning for every of its symbols. Meta language represents only the primary element of meaning and ignores all potential secondary meanings, as well as connotations and possible associations the word may generate in a listener's mind. But these are essential to natural language and a semantics theory shouldn't ignore them. Highly grammaticized morphemes / language elements are indeed better suited for abstract representation, while other, rather lexically (as opposed to morphosyntactic) determined language elements are under circumstances very difficult to represent in an abstract manner; some semantic aspects will always be lost. There are languages, like many North American languages, which feature rich and complex locative, possessive, relative, collective, quantifying, evidential, classifying, etc. marker systems which differ significantly from most European languages, but there is also common ground.

Lakhota

eyá
takú eyá
DET
PRON
'some, certain ones'
'some particular things'
refers to plural or uncountable objects/facts existing in reality (not hypothetical ones) and with waŋ, (singular, existing in reality); older form: k'eyá
etáŋ DET 'some, any' refers to plural objects/facts that are hypothetically, those usually in questions, demands, or sentences which contain ktÁ; marks plural or uncountable nouns
waŋžígži NUM 'one each, one apiece, one after another, one by one' / 'some, one here and one there, certain, particular ones, some picked from a number'  of plural existing objects or facts as individuals
húŋȟ ~unǧé ~ huŋǧé
QNT 'some, some of, a number of, part of an undifferentiated mass or number' Santee speakers prefer uŋǧé and apá; REDUP húŋȟhuŋȟ, húŋhuŋȟ, huŋǧéǧe
haŋké QNT 'part or portion of a unit, piece of a unit' REDUP haŋkéke
takúku ~ takúkuka ~ takúkušni PRON 'some things, various things, all sort of things' fast speech: takú
otóhaŋl ~ otóhaŋn ADV 'for some time, for some distance, for a short time or distance' otóhaŋyaŋ synonym
owátohaŋyaŋ ~ owátohaŋyaŋkel ~ owátohaŋyela
ADV 'for a short time, for a little while, for some time'
otóhaŋyaŋ
ADV 'for a while, within some time; for some time or distance, for a short distance'
waŋží ȟčiŋ
NUM+ENCL 'something/someone, at least one' waŋží (in this use) 'one'; ȟčiŋ is the subordinate form of ȟčA 'very, very much, really, real, particularly, in particular'
tuwá PRON 'who, whom' (interrogative); 'someone, an individual, a person' REDUP tuwáwa 'certain individuals, certain persons, various persons'

(Ullrich, ed. 2008: 1091)

Rood and Taylor (1996: 457) specify that "when used alone or before an article or a demonstrative, the quantifiers specify the size of the group. Used after the determiner, they indicate that the predicate refers to a specified part of the subject." According to them, the way 'some' (which means 'part of') is expressed in Lakhota depends on "the nature of the whole, the nature of the part, and whether the part is positive, negative, or interrogative." The specification for what 'a whole' may be, is that it can consist of several individual elements (like a bundle of sticks, or persons in a group), a single individual element (like a single fruit), or an undifferentiated mass (like water, or sugar) and it may be specific or generic. Analogous, a part may be individual elements (less then the number which form the whole), a part or portion of the single object (or even of an animate being), or a portion of a mass.

Affirmative Negative* Interrogative Meaning
1 húŋȟ waŋžíni tóna or tónakeča Some individuals from a group of individuals
2 haŋké haŋkéni tóháŋya Some of a single individual
3 húŋȟ or etáŋ etáŋni tóháŋya or tónakeča Some of an undifferentiated mass
* The notions generic and negative are incompatible. The negative partitive can thus be used only with specific reference.
(after Rood & Taylor 1996: 457)

Rood & Taylor specify that "the complete set of possible slots in the nominal composed of a noun and its determiners is as follows: (demonstrative) noun (quantifier) (article) (demonstrative) (quantifier)". The three example groups below (1), (2), (3) correspond to the rows 1-2-3 in the table.

(1) a.  oyáte húŋȟ wichášiče.
        'Some people are evil.'
    b.  lakhota tóna waŋwíčhalaka he?
        'How many indians do you see?'
    c.   ȟʔokhá kiŋ húnŋ hí pi.
         'Some of the singers have come.'
    d.   ȟʔokhá kiŋ tóna hí pi he?
         'How many of the singers have come?'
    e.   ȟ?okha kiŋ wãzíni hí (pi) šni.
         'None of the singers has come.'

(2) a.   špáŋ-šni-yútapi haŋké uŋyúta pi sʔa.
         'We (habitually) eat some watermelon.'
    b.   špáŋ-šni-yútapi toháŋyaŋ yáta pi sʔa he?
         'How much watermelon do you eat (habitually)?'
    c.   aǧúyapi-skúyela kiŋ haŋké uŋyúta pi.
         'We ate some of the cake.'
    d.   aǧúyapi-skúyela kiŋ haŋkéni uŋyúta pi.
         'We didn't eat any of the cake.'
    e.   aǧúyapi-skúyela kiŋ toháŋya yáta pi he?
         'How much of the cake did you eat?'

(3) a.   phežúta húŋȟ phá.
         'Some medicine is bitter.'
    b.   phežúta toháŋyaŋ ničʔú he?
         'How much medicine did he give you?'
    c.   aǧúyapi-blú kiŋ etáŋ úŋ we.
         'Use some of the flour.'
    d.   aǧúyapi-blú kiŋ etáŋni úŋ šni.
         'She didn't use any of the flour.'
    e.   aǧúyapi-blú kiŋ toháŋya nú he?
         'How much of the flour did you use?'

(Rood & Taylor 1996: 457-458)

Cf. 'Some'-related indefinite quantifying elements in Osage.