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Topic: Plural quantification

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	Plural quantification - Wikipedia, the free encyclopedia
		In mathematics and logic, plural quantification is the theory that an individual variable x may take on plural, as well as singular values.
		Interest revived in plurals with work in linguistics in the 1970s by Remko Scha, Godehard Link, Fred Landman, Roger Schwarzschild, Peter Lasersohn and others, who developed ideas for a semantics of plurals.
		Boolos argued that 2nd-order monadic existential quantification may be systematically intepreted in terms of plural existential quantification, and that, therefore, 2nd-order monadic existential quantification is "ontologically innocent".
	en.wikipedia.org /wiki/Plural_quantification (1039 words)

	Ontological commitment - Wikipedia, the free encyclopedia
		[The] general adoption of class variables of quantification ushers in a theory whose laws were not in general expressible in the antecedent levels of logic.
		Formally it is precisely in allowing quantification over class variables "alpha", "beta" andc, that we assume a range of values for these variables to refer [sic] to.
		There is a considerable and growing body of literature on so-called plural reference and plural quantification.
	en.wikipedia.org /wiki/Ontological_commitment (486 words)

	Notes to Plural Quantification
		Although most contemporary work on plural quantification appears to have been inspired, directly or indirectly, by the work of George Boolos, there is also a substantial pre-Boolosian literature on the topic.
		Pluralities are closely related to what the early Bertrand Russell called “classes as many,” as opposed to “classes as one”; see Russell 1903, esp. Sections 70, 74, and 104.
		For more on the complexities of plural locutions in natural languages, the reader is referred to Landman 2000, Link 1998, Lønning 1997, McKay forthcoming, and Schein 1993.
	plato.stanford.edu /entries/plural-quant/notes.html (511 words)

	Plural Quantification
		For this application of plural quantification to work, PFO must be applicable to all kinds of concrete objects, and it must be ontologically innocent, or at least not committed to any entities that share those features of abstract objects that are found to be nominalistically objectionable.
		Proponents of plural quantification claim that these theories allow plural locutions to be formalized in a way that is fundamentally different from the old set-theoretic paraphrases.
		The semantic theory regards this plurality as one entity: it is the contribution of one syntactic expression.
	www.science.uva.nl /~seop/archives/win2004/entries/plural-quant (8521 words)

	Carl Brock Sides - Mereological Nihilism and the Limits of Paraphrase - Carl Brock Sides
		For example, the plural predicate `carried a coffin' is variably multigrade: it may combine with a plural referring expression referring to four people, or six, or eight.
		The nihilist, using plural logic, may make use of the plural relation `are equinumerous with', and so she need not make use of a mereologically additive predicate, or worry about whether the simples are commensurable with respect to that predicate.
		Or, in somewhat formal plural logic: `There are some xs such that each of the xs is a statue, and for every y, if y admires one of the xs, then y is a critic and y doesn't admire any z that is not one of the xs'.
	evans-experientialism.freewebspace.com /mereology.htm (4414 words)

	Abstract of "Atom Predicates and Set Predicates: towards a general theory of plural quantification" (Site not responding. Last check: 2007-10-29)
		The interpretation of sentences with plural determiners and collective predicates is a highly complex problem that has not been sufficiently investigated, despite many advances in theories of plurality and quantification.
		This paper proposes a new typology of predicates that serves as a basis for a general treatment of singular and plural noun phrases within generalized quantifier theory.
		Section 2 substantiates the quantificational mechanism that accounts for the meaning of sentences like all the students met, where a plural determiner appears with a set predicate.
	www.cs.technion.ac.il /~winter/papers/pluQ.abs.html (378 words)

	[No title]
		The domain of quantification of the Q-adverb is read off these representations: since open propositions denote sets of events, the LF in (1') corresponds to quantification over events; since nominal predicates denote sets of individuals, the LF in (2') corresponds to quantification over individuals.
		To answer this question, we may recall that plural definites are currently analyzed as supplying a constant term that denotes the maximal group of atomic individuals that have the property denoted by the corresponding singular noun.
		Summary (i) In the unmarked case, plural indefinites are indirectly bound (they are “pseudo-generic” rather than “truly” generic): the default GEN operator (or an overt Q-adverb) quantifies over events or situations and indirectly over groups of individuals (the variable supplied by the indefinite is bound by existential closure).
	www.let.uu.nl /~Henriette.deSwart/personal/Pics/generics-PICS.doc (2720 words)

	[No title]
		The quantification of the plural nominal construction o ver the event modifies VP aspect the same way as frequency adverbs can modify them.
		This modification though is due to the event quantification form outside VP and not to the composition of nominal and verbal properties in VP.
		Achievement verbs cannot be used in progressive unless the deep object is a bare plural (the contrast between sentence 5 and 6).
	www.unige.ch /lettres/latl/chronos/toth.rtf (1162 words)

	Sebastian Löbner Negation, predication, and quantification (Site not responding. Last check: 2007-10-29)
		The talk is a contribution to the investigation of the quality of natural language polarity contrast (PC): its morphosyntactic appearance, its interplay with, and dependence on, types of predication, including quantification as a complex subtype.
		Quantification with every raises the level of macropredication by l, quantification with all by 2.
		Due to the integrativity of quantificational predication, the resulting PC is complementary.
	odur.let.rug.nl /events/96/negation/node23.htm (458 words)

	[No title]
		While we pay a lot of attention in English to singular and plural, they are not important in many circumstances; in others they are obvious from context.
		You can combine both types of quantification to express this in Lojban as: so le pano prenu [ku] cu cuxna You can use numbers and non-numeric quantifiers with pro-sumti as well, finally being able to specify, or at least imply, the 'number' of these variables.
		In general, quantification of pro-sumti should be considered the 'selective' variety of quantification: xa ti cu culno means "Six of these are-full" which implicitly says that the number of ti is su'oxa ("at least six").
	teddyb.org /www.lojban.org/publications/draft-textbook/lesson11 (1602 words)

	Institut des Sciences Cognitives Agenda (Site not responding. Last check: 2007-10-29)
		He notes that in English a bare plural which is a predicative term (type ) cannot be interpreted as a definite via covert use of IOTA, even when the context is pragmatically weighted in its favor (1).
		He points to a bare plural which does not undergo NOM because of semantic incompatibility, as in (3a).
		In episodic contexts the bare plural now interacts scopally with negation, showing that in the absence of NOM, E-type shift is available (3b).
	www.isc.cnrs.fr /dayal.htm (1126 words)

	[No title] (Site not responding. Last check: 2007-10-29)
		Saying that bare plurals in such sentences contain existential quantification as part of the meaning of the NP is purely stipulative without independent evidence.
		Heim (1982) proposed treating singular indefinite NPs may be treated like bare plurals and bound by a quantifier in another part of the sentence.
		English requires the use of a plural on nouns that refer to humans, animals and objects, i.e., count nouns.
	www.ku.edu /~pyersqr/Ling331/Kearns62.htm (2023 words)

	[No title] (Site not responding. Last check: 2007-10-29)
		The successful account of plural reference phenomena put forward in the discourse representation theory of Kamp and Reyle 1993 gave rise to a number of attempts at formulating non-representational alternatives, for instance: van den Berg 1996, Elworthy 1995 and Krifka 1996.
		Moreover, they typically differ from classic dynamic semantics in assuming that a context is a structured medium which is able to store relations between the atoms or the subgroups of two pluralities, thus accounting for examples such as (1).
		The main reason for this is that the plural pronoun in (2) has the same linguistic antecedent as the singular pronoun in (1), leading to potential variable clashes in the semantics.
	www.illc.uva.nl /dip/past-lectures/dip060603.html (281 words)

	Keywords Week 2 L322
		The stem extender disappears in the plural and in derivational forms.
		Because the feature [±Plural] may be either [-Plural] or [+Plural], the lexical entry FOOT has two lexical items: foot, feet.
		Quantification is implicit in all English noun phrases
	www.sfu.ca /person/dearmond/322/322.keywords.3.S02.htm (416 words)

	Lojban Wiki : Descriptions
		The notion of preselecting an F goes against the whole mechanics of particular quantification, where each instantiation has to be to a new term in inferences.
		Given that the problem of more than one F has been removed by plural quantification, the only problem that remains for descriptors is non-fulfillment, the case when there are no relevant Fs.
		So, in the end it was a plural (bunch) description of things that were actually called by the expression that came after the gadri, whatever its grammatical status.
	www.lojban.org /tiki/tiki-index.php?page=Descriptions (3368 words)

	Amazon.ca: Books: Plurality & Quantification (Site not responding. Last check: 2007-10-29)
		The eight papers collected in Plurality and Quantification address three central issues in the study of plurality and quantification in natural languages.
		The first major theme regards algebraic approaches to plurals and quantification that have emerged as the leading paradigm for the study of these empirical phenomena over the last decade.
		Papers collected in Plurality and Quantification address three central issues in the study of plurality and quantification in natural languages, shedding new light on how many readings have to be assigned to plural sentences & the respective consequences for syntax-semantics interface.
	www.amazon.ca /exec/obidos/ASIN/0792348419 (386 words)

	Reference and Quantification in Discourse
		This study tries to determine how reference and quantification are expressed in natural language (in particular, in English), taking into account that language does not normally come in the form of isolated sentences but in the form of discourse.
		Since this kind of quantification (one case of "A-Quantification") functions on the level of entire propositions, all the difficulties that stem from the unselectivity of implicit quantification in traditional DRT re-appear with such adverbs.
		Non-universal individual level quantification over universally quantified sets, possibly with an unexpressed universal adverb of quantification ("always"): "Most farmers beat their donkeys" is interpreted as "For any set of...
	www.ifi.unizh.ch /groups/CL/hess/hess_habil.html (4827 words)

	Plural quantification -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-29)
		Plural quantification -- Facts, Info, and Encyclopedia article
		See also (Click link for more info and facts about Gottlob Frege) Gottlob Frege 1895 for a critique of an earlier view defended by (Click link for more info and facts about Ernst Schroeder) Ernst Schroeder.
		If true, they are about individuals who are shipmates, who meet together, lift pianos &c, and nothing else (not sets, or abstract Platonic entities).
	www.absoluteastronomy.com /encyclopedia/p/pl/plural_quantification.htm (892 words)

	Thesis (Site not responding. Last check: 2007-10-29)
		This dissertation presents a formal model of plural pronominal discourse anaphora.
		A quantificational sentence has several sets associated with it, each of which is a potential antecedent for a subsequent plural pronoun.
		This study is of interest to researchers concerned with the formal semantics of quantification, plurality and anaphora, and to scholars interested in more general issues concerning the semantics and pragmatics of discourse anaphora.
	www.let.uu.nl /~Rick.Nouwen/personal/thesis (231 words)

	Øystein Linnebo, Fitzjames Research Fellow, Merton College, Oxford (Site not responding. Last check: 2007-10-29)
		Although Frege's proof is incorrect, I argue that the account of reference on which it is based is of potential philosophical value, and I analyze the class of cases to which it may successfully be applied.
		This article provides a survey of recent discussions of the logic, semantics, and metaphysics of plural quantification, as well as of its various philosophical applications.
		This paper criticizes George Boolos's famous use of plural quantification to argue that monadic second-order logic is pure logic.
	users.ox.ac.uk /~sfop0113 (1118 words)

	‘A’ plus non-count nouns (Site not responding. Last check: 2007-10-29)
		In a study of the qualification and quantification processes, we separate non-counts into 2 groups, only one of which, under certain syntactic conditions and with a certain semantic message, can operate with ‘a’.
		Again, here, we are in the plural form of the ‘a’ meaning ‘a type of’, and this will operate with the non-counts referring to material physical matter in group
		What it perhaps reflects more is the language’s desire to widely embrace today’s complex social currents, and to give a distinct existence to each one rather than house them all under the same roof with the all-embracing non-count singular.
	www.univ-pau.fr /ANGLAIS/alaes/bertrand.htm (3651 words)

	Short-answer models (with elaboration suggestions) for the exam paper "GRAMMATIK onsdag 4 (Site not responding. Last check: 2007-10-29)
		The ungrammatical plural S:g "the leafs" of the count noun "leaf" is ungrammatical and should be changed into "the leaves", as "leaf" belongs to the closed class of countable nouns with irregular plural forms in which "f" is changed to "ve".
		The the third-person singular present indicative P:v "proves" should be changed to the third-person plural form "prove" for subject-predicator concord to obtain between the finite predicator and the third-person plural S:g "the battles..assertiveness", where plural S-P concord is dictated by the plural H:n "battles".
		Hence, plural form should be changed to the singular form "hundred", as the number "hundred" is not pluralised if (part of) a dependent - as is the case here - or is H:n when preceded by a definite (cardinal) number, as in "two hundred".
	www.hum.ou.dk /institut/isk/kasch/SA-all.html (7474 words)

	ipedia.com: Second-order logic Article (Site not responding. Last check: 2007-10-29)
		When predicate logic was invented by Frege, he did use different variables to distinguish quantification over objects from quantification over properties and sets; but he did not see himself as doing two different kinds of logic.
		It was found that set theory could be formulated as an axiomatized system within the apparatus of first-order logic (at the cost of several kinds of Completeness, but nothing so bad as Russell's Paradox), and this was done (see Zermelo-Fraenkel set theory), as sets are vital for mathematics.
		In recent years second-order logic has made something of a recovery, bouyed by George Boolos' interpretaion of second-order quantification as plural quantification over the same domain of objects as first-order quantification.
	www.ipedia.com /second_order_logic.html (876 words)

	Indonesian Quantification Words - Wikibooks
		It also has no agreement rule except that if we already put some quantification words, we cannot double the noun.
		For example: It is wrong to say "banyak buku-buku" to mean lots of books, because "banyak buku" is already plural -- therefore it is redundant to repeat the noun.
		These words are essential to specify indefinite plurals:
	en.wikibooks.org /wiki/Indonesian_Quantification_Words (190 words)

	Arché TWiki . Arche . MathPlurals (Site not responding. Last check: 2007-10-29)
		The texts involve discussion of whether plural forms can be legitimately interpreted as non-first-order resources, discussion of their ontological commitments and discussion of their possible applications within the philosophy of logic and mathematics.
		Alan Berger, "A Formal Semantics for Plural Quantification.
		Nicholas Rescher, "Plurality Quantification and Quasi-Categorical Propositions", Journal of Symbolic Logic 27 (1962), pp.
	weka.ucdavis.edu /~ahwiki/bin/view/Arche/MathPlurals (826 words)

	Abstract of "Plural Type Quantification" (Site not responding. Last check: 2007-10-29)
		This paper introduces some of the main components of a novel type theoretical semantics for quantification with plural noun phrases.
		This theory, unlike previous ones, sticks to the standard generalized quantifier treatment of singular noun phrases and uses only one lifting operator per semantic category (predicate, quantifier and determiner) for quantification with plurals.
		These operators derive collectivity with plurals, keeping the analysis of singular noun phrases, where no type mismatch arises, as in Barwise and Cooper (1981).
	www.cs.technion.ac.il /~winter/papers/AC99.abs.html (189 words)

	Essays in Philosophy -- Book Review
		Boolos’ plural quantifiers: ‘some things, the U’s are such that” adds to the expressive vocabulary of logic.
		Plural quantifiers provide an alternative interpretation of second-order logic in which second-order entities are subsets of the universe.
		In his excellent introductory remarks to the various sections, John Burgess points out that plural quantification is limited by the fact that plurals provide a monadic, but not dyadic, second-order quantification.
	www.humboldt.edu /~essays/marrev.html (1585 words)

	Proceedings of SuB9
		We observe that adverbial and nominal quantification differ with respect to their ability to incorporate presuppositions into their domain restrictions, and we use that observation to motivate an account of qadverbs as quantifiers over polar alternatives.
		In this paper, I argue that the DRT Construction Rules for plural antecedents are redundant, because they are subsumed by an inference mechanism that must be made generally available for anaphora resolution.
		Furthermore, I present an argument that the general inference account correctly captures the fact that plural descriptions can be interpreted at the position of the plural pronoun, while the DRT account incorrectly requires that they be interpreted at the position of the antecedent.
	www.ru.nl /ncs/sub9/proceedings.html (4674 words)

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