Languages & Linguistics
Quantifiers
Quantifiers are words or phrases that indicate the quantity or scope of a noun in a sentence. They can be used to express general or specific amounts, such as "some," "all," "many," or "few." In linguistics, quantifiers play a crucial role in understanding the meaning and interpretation of sentences, particularly in relation to the scope of the quantified noun.
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eBook - PDF- T. Zetenyi(Author)
- 1988(Publication Date)
- North Holland(Publisher)
Fuzzy Sets in Psychology T. ZBtBnyi (Editor) 0 Elrevier Science Publishers B.V. (North-Holland), 1988 51 Quantifiers AS FUZZY CONCEPTS Stephen E. NEWSTEAD Department of Psychology, Plymouth Polytechnic Drake Circus, Plymouth PL4 8AA, England As their name suggests, Quantifiers are used to indicate quantities along certain dimensions, whether of amount (e.g., all, some) or frequency (e.g., never, often). Such terms are among the most commonly used in English and other languages. Thorndike and Lorge (1944) in their list of the 500 most common words in English include more than a dozen such terms, including the four examples given in the previous sentence. Some writers have assumed that the quantities expressed can be precisely determined. For example, according to logic all means every single member of a set, and some means at least one and possibly all members of a set. Similarly the query languages developed by computer programmers give prectse definitions to the Quantifiers used in searching through a database. It will be argued in this chapter, however, that outside such artificial languages Quantifiers are inherently fuzzy concepts. Furthermore it will also be argued that their meaning is variable depending on the situation in which the words are used. Previous research on Quantifiers has takenplace within a variety of different 52 S. E. Newstead frameworks. Logicians and reasoning researchers have investigated the interpretation of Quantifiers as a possible explanation for errors in syllogistic reasoning; applied psychologists have studied the scale values of Quantifiers used in rating scales; and psycholinguists have investigated the representations of Quantifiers in both comprehension and memory. Each of these areas of research has its own focus of interest and its own methods of investigation. In this chapter an attempt will be made to review this work and to synthesise the findings from the disparate areas.
eBook - PDF- Paul Portner, Klaus Heusinger, Claudia Maienborn, Paul Portner, Klaus Heusinger, Claudia Maienborn(Authors)
- 2019(Publication Date)
- De Gruyter Mouton(Publisher)
A-Quantifiers, attested in all lan-guages investigated, seem syntactically less uniform than D-Quantifiers but at least as rich semantically, justifying the term quantifier in both cases. Both types now have some documentation in areally and genetically distinct languages: Bach et al. (1995), Matthewson (2001, 2008). We begin with D-Quantifiers. We are generous regarding what we count as a quantifier, but lack the space to consider the many phenomena which inter-act with quantification in revealing ways: Passive cf. article 7 [Semantics: Interfaces] (Wunderlich) Operations on argument structure ( The box was opened ( by some one ) vs John is respected ( by most relevant people )); Modal Adverbs cf. article 14 [this volume] (Hacquard) Modality ( necessarily / must = in all relevant worlds , possi-bly / can = in some relevant worlds ), Pronominal binding cf. article 1 [Semantics: Sentence and Information Structure] (Szabolcsi) Scope and binding : Most farmers who own a donkey beat it . Useful overviews are Westerståhl (1989, 1995), Keenan (1996a), van der Does & van Eijck (1996a), Keenan & Westerståhl (1997), and Peters & Westerståhl (2006). Some important collections of articles are: van Benthem & 114 Edward Keenan ter Meulen (1985), Reuland & ter Meulen (1987), Gärdenfors (1987), Lappin (1988), Kanazawa & Piñón (1994), van der Does & van Eijck (1996b), Szabolcsi (1997) and, from a mathematical perspective, Krynicki, Mostowski & Szczerba (1995). 3 Determiner Quantifiers The sentences in (1a) have the form [DP+P 1 ], where the DP ( Determiner Phrase ) is all birds , some birds , etc. and the P 1 ( one place predicate ) is the Verb Phrase can fly . In such contexts this P 1 is sometimes called the nuclear scope . It denotes a prop-erty of objects, extensionally a subset of a domain E of (possibly abstract) objects under discussion. The DP in (1a) has the form [Determiner+NP], for Determiner = all , most , etc.
- Martin Haspelmath, Ekkehard König, Wulf Oesterreicher, Wolfgang Raible, Martin Haspelmath, Ekkehard König, Wulf Oesterreicher, Wolfgang Raible(Authors)
- 2008(Publication Date)
- De Gruyter Mouton(Publisher)
92. Quantifiers 1275 Zhurinskij, Andrej Ν. 1971. O semanticheskoj strukture prostranstvennyx prilagatel'nyx [On the semantics of spatial adjectives]. In: Seman-ticheskaja struktura slova. Moscow, 96 — 124. Zubin, David A. & Choi, Soonja (1984). Orienta-tion and gestalt: Conceptual organizing principles in the lexicalization of space. CLS-20. Parasession on lexical semantics. Chicago, 333 — 345. Zubin, David A. & Svorou, Soteria (1984). Per-ceptual schemata in the spatial lexicon: A cross-linguistic study. CLS-20. Parasession on lexical se-mantics. Chicago, 346 — 358. Ewald Lang, Humboldt University (Berlin) & Centre for General Linguistics (ZAS) ( Germany ) 92. Quantifiers 1. Introduction 2. Internal typologies 3. External typologies 4. Delimitation of quantification 5. Special abbreviations 6. References 1. Introduction Quantifiers are free-standing expressions whose meanings involve the notion of quan-tity, such as English three, several, numerous, most, every, one hundred and twenty three, all but seventeen, and so forth. The basic semantic structure of quantifica-tion is bipartite, consisting of the quantifier itself plus the expression that it quantifies. For example, in a sentence such as Three boys have come, three is the quantifier, and boys the quantified expression. Quantification has traditionally been of great interest to semanticists, logicians and philosophers of language, due at least in part to the perceived 'logical' or 'mathematical' nature of the meanings involved. As such, it is striking to observe how such basic and seemingly immutable meanings may, in dif-ferent languages, be expressed with very dif-ferent morphosyntactic strategies, exhibiting a great degree of cross-linguistic variation. Typologies of quantification are of two fundamental kinds. Internal typologies are concerned with the Quantifiers themselves, their internal morphosyntactic structure and their basic semantic properties.
- Alex Barber, Robert J Stainton(Authors)
- 2010(Publication Date)
- Elsevier Science(Publisher)
Q Quantifiers: Semantics E L Keenan , University of California, Los Angles, CA, USA ß 2006 Elsevier Ltd. All rights reserved. During the past 25 years, our empirical and mathema-tical knowledge of quantification in natural language has exploded. We now have mathematically precise (if sometimes contentious) answers to questions raised independently within generative grammar, and we are able to offer many new generalizations. We review these results here. For extensive overviews, see Westersta ˚hl (1989), Keenan (1996), and Keenan and Westersta ˚hl (1997). Some important collections of articles are van Benthem and ter Meulen (1985), Reuland and ter Meulen (1987), Ga ¨ rdenfors (1987), Lappin (1988), van der Does and van Eijck (1996), Szabolcsi (1997), and from a mathematical perspective, Krynicki et al. (1995). The best understood type of quantification in natu-ral language is that exemplified by all poets in All poets daydream . We treat daydream as denoting a property of individuals, represented as a subset of the domain E of objects under discussion. Quantified Noun Phrases (NPs) such as all poets will be treated as denoting functions, called ‘generalized Quantifiers,’ which map properties to truth values, True ( T ) or False ( F ). For example, writing denotations in bold-face, all poets maps daydream to True (over a domain E) if and only if the set of poets is a subset of the set of objects that daydream. Interpreting Dets (Determi-ners) as functions from properties to generalized Quantifiers, we give denotations for many Quantifiers in simple set theoretical terms. We write X Y to say ‘‘X is a subset of Y,’’ X Y for ‘‘X intersect Y,’’ the set of objects that lie in both X and Y; X Y for the set of objects in X that are not in Y, and |X| for the number of elements in X.
eBook - PDF- Keith Allan(Author)
- 2010(Publication Date)
- Elsevier Science(Publisher)
Q Quantifiers E L Keenan , University of California, Los Angles, CA, USA ß 2006 Elsevier Ltd. All rights reserved. During the past 25 years, our empirical and mathema-tical knowledge of quantification in natural language has exploded. We now have mathematically precise (if sometimes contentious) answers to questions raised independently within generative grammar, and we are able to offer many new generalizations. We review these results here. For extensive overviews, see Westersta ˚hl (1989), Keenan (1996), and Keenan and Westersta ˚hl (1997). Some important collections of articles are van Benthem and ter Meulen (1985), Reuland and ter Meulen (1987), Ga ¨ rdenfors (1987), Lappin (1988), van der Does and van Eijck (1996), Szabolcsi (1997), and from a mathematical perspective, Krynicki et al. (1995). The best understood type of quantification in natu-ral language is that exemplified by all poets in All poets daydream . We treat daydream as denoting a property of individuals, represented as a subset of the domain E of objects under discussion. Quantified Noun Phrases (NPs) such as all poets will be treated as denoting functions, called ‘generalized Quantifiers,’ which map properties to truth values, True ( T ) or False ( F ). For example, writing denotations in bold-face, all poets maps daydream to True (over a domain E) if and only if the set of poets is a subset of the set of objects that daydream. Interpreting Dets (Determiners) as functions from properties to generalized Quantifiers, we give denotations for many Quantifiers in simple set theoretical terms. We write X Y to say ‘‘X is a subset of Y,’’ X Y for ‘‘X intersect Y,’’ the set of objects that lie in both X and Y; X Y for the set of objects in X that are not in Y, and |X| for the number of elements in X.
eBook - PDF- I. Kurcz, G.W. Shugar, J.H. Danks(Authors)
- 2009(Publication Date)
- North Holland(Publisher)
How Children Deal with Natural Language Quantification 31 tion until it creaks, in the interest of devising the sharpest possible empirical test. Suppose that the psychological seman- tics of flallT1 and lleachll actually are diametrically opposed to one another. All would represent the rule,Find a boundary and exhaustively cumulate up to it,!! with a rider that sub- totals may have to be accumulated.1f llEach'l would represent the rule.llFind entities and cumulate exhaustively over them until there are no more, when the boundary will, ips0 facto, have been reached,I1 again with the rider that accumulation may have to be carried across subboundaries. What determines a boundary, or delimits a class of tokens, is given by the determining components of the proposition. These limit the sets of denotata entered into the quantification. For example, they indicate that only toy cars are to be considered rather than cars-and-lorries or cars-and-coughsweets. People have often objected on principle to this formula-driven way of considering quantification. The argument is that just because logicians have cobbled up an agreement on the matter in the in- terests of their arcane pursuit, it does not follow that the formalism can tell us anything worth knowing about the way in which people's minds work in practice. The standard objection to applying the formalism !(&) to actual cases of natural lan- guage is that can betoo powerful in scope. As Lambek and Scott (1981) concisely point out: We feel quite comfortable with & (z(&) -c C(x)), as in 'all fleas are green' but not with - Vx (&). In fact there is no simple way of rendering the latter into idiomatic English. We are forced to say 'everything is green'or 'everybody is green' ... - x is assumed to range over all things ... all persons ... it is quite unclear whether the fol- lowing belong to the same universe: Tuesday, the number 5 ...!I (p. 102).
eBook - PDF- Shalom Lappin, Chris Fox(Authors)
- 2015(Publication Date)
- Wiley-Blackwell(Publisher)
Treatments of both interpretations are often based on the denotation of plural nouns in (61) (Carlson, 1977; Carlson and Pelletier, 1995; Chierchia, 1984, 1998b; Dayal, 2011). However, the integration of theories of generic and existential bare plurals with the formal semantics of plurality has not been researched extensively, and it is beyond the scope of this review. By contrast, deriving the referential denotation of definite plurals as in (60b) is quite straightforward with noun denotations as in (61). 21 It is the interpretation of the properly quantificational NPs, exemplified in (60c-f), that we shall focus on now. 5.2 Quantificational expressions: modifiers or determiners? Ignoring some syntactic complexities, we refer to all the pre nominal elements in (60c–e) (e.g. three, exactly ten, most of the) as quantificational expressions (QEs). 22 When analyzing NPs as in (60c–e) in simple compositional frameworks, a critical decision is whether the QE within the NP denotes a modifier or a determiner. 5.2.1 The “modifier” approach In this approach, a QE is not the compositional source of quantifi- cation. The QE is analyzed as a modifier: its denotation composes with a predicative noun deno- tation as in (61) to derive another predicate. The QE denotation is assumed to select some of the collections in the noun’s denotation according to their cardinality. For instance, in the NP “three girls,” the QE “three” selects the plural individuals with three elements from the denotation of the noun “girls.” Modificational QE denotations do not change the semantic function of the noun in the sentence, as the NP still basically denotes a predicate. Accordingly, in the modifier approach quantificational effects are analyzed as external to the denotation of the QE. 5.2.2 The “determiner” approach In this approach, the QE maps the denotation of the noun to a generalized quantifier (Peters and Westerst˚ ahl, 2006; Chapter 1 of this volume).
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