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Comparative Quantifiers
, 2000
"... The main goal of the thesis is to present a novel analysis of comparative quantifiers such as more than three students. The prevalent view on such expressions advocated in Generalized Quantifier Theory is that they denoted generalized quantifiers ranging over individuals – entirely on a par with exp ..."
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Cited by 40 (2 self)
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The main goal of the thesis is to present a novel analysis of comparative quantifiers such as more than three students. The prevalent view on such expressions advocated in Generalized Quantifier Theory is that they denoted generalized quantifiers ranging over individuals – entirely on a par with expressions like every student, some student(s), etc. According to this view, more than three is a determiner (like every) that is, even though morphosyntactically complex, semantically a simplex expression that can – in terms of its interactions with the syntactic environment it appears in – be viewed as denoting simply a relation between sets of individuals. The proposal that will be developed in this thesis maintains on the other hand that expressions like more than three are also semantically complex. More specifically, an analysis of comparative quantifiers will be given that is fully compositional down to level of the formation of comparative determiners. The proposal is based on concepts that are independently needed to analyze comparative constructions.
The Semantics of Determiners
 The Handbook of Contemporary Semantic Theory
, 1996
"... The study of generalized quantifiers over the past 15 years has enriched enormously our understanding of natural language determiners (Dets). It has yielded answers to questions raised independently within generative grammar and it has provided us with new semantic generalizations, ones that were ba ..."
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Cited by 36 (1 self)
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The study of generalized quantifiers over the past 15 years has enriched enormously our understanding of natural language determiners (Dets). It has yielded answers to questions raised independently within generative grammar and it has provided us with new semantic generalizations, ones that were basically unformulable without the conceptual and technica apparatus of generalized quantifier theory. Here we overview results of both these types. historical note It was Montague (1969) who first interpreted natural language NPs as generalized quantifiers (though this term was not used by him). But it was only in the early 1980's with the publication of B&C (Barwise and Cooper, 1981) that the study of natural language Dets took on a life of its own. Also from this period are early versions of K&S (Keenan and Stavi, 1986) and Higginbotham and May (1981). The former fed into subsequent formal studies such as van Benthem (1984, 1986) and Westerstähl (1985). The latter focussed on specific linguistic applications of binary quantifiers, a topic initiated in Altham and Tennant (1974), drawing on the mathematical work of Mostowski (1957), and pursued later in a more general linguistic setting in van Benthem (1989) and Keenan (1987b, 1992). Another precursor to the mathematical study o generalized quantifiers is Lindstr_m (1969) who provides the type notation used to classif
More Algebras for Determiners
"... Abstract. Some new algebras, which are possible denotations for various determiners, are studied. One of them is the algebra of generalised cardinal quantifiers which is a subalgebra of conservative quantifiers and which contains cardinal, cocardinal and proportional quantifiers. In addition some ..."
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Abstract. Some new algebras, which are possible denotations for various determiners, are studied. One of them is the algebra of generalised cardinal quantifiers which is a subalgebra of conservative quantifiers and which contains cardinal, cocardinal and proportional quantifiers. In addition some nonconservative quantifiers are studied (symmetric, contrapositional and fixed points with respect to the postcomplement). It is shown that cointersective quantifiers are contrapositional. The analysis is extended to quantifiers of higher types. 1
Constraints on anaphoric functions
, 2012
"... Some constraints on functions from sets and relations to sets are studied. Such constraints are satisfied by anaphoric functions, that is functions denoted by anaphoric determiners. These constraints are generalisations of anaphor conditions known from the study of simpler cases of nominal anaphors. ..."
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Some constraints on functions from sets and relations to sets are studied. Such constraints are satisfied by anaphoric functions, that is functions denoted by anaphoric determiners. These constraints are generalisations of anaphor conditions known from the study of simpler cases of nominal anaphors. In addition a generalisation of the notion of conservativity as applied to anaphoric functions is proposed. Two classes of anaphoric determiners found in NLs are discussed as examples. 1
unknown title
"... A type 〈1 2, 1 〉 quantifier F is symmetric iff F (X, X)(Y) = F (Y, Y)(X). It is shown that quantifiers denoted by irreducible binary determiners in natural languages are both conservative and symmetric and not only conservative. halshs00746302, version 1 27 Nov 2012 1 ..."
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A type 〈1 2, 1 〉 quantifier F is symmetric iff F (X, X)(Y) = F (Y, Y)(X). It is shown that quantifiers denoted by irreducible binary determiners in natural languages are both conservative and symmetric and not only conservative. halshs00746302, version 1 27 Nov 2012 1
Some generalised comparative determiners
"... Abstract. Functions denoted by specific comparative expressions called generalised comparative determiners are analysed. These expressions form verb arguments when applied to common nouns. They denote functions which take sets and a binary relation as argument and give a set as result. These functi ..."
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Abstract. Functions denoted by specific comparative expressions called generalised comparative determiners are analysed. These expressions form verb arguments when applied to common nouns. They denote functions which take sets and a binary relation as argument and give a set as result. These functions are thus different from denotations of ”ordinary” determiners. However, they do obey some similar constraints, properly generalised. It is shown that verbal arguments obtained from such generalised determiners extend the expressive power of NLs since functions that they denote are not just case extensions of type 〈1 〉 quantifiers used to interpret ”ordinary ” determiner phrases. 1
In The Handbook of Contemporary Semantic Theory. 1996. Shalom Lappin (ed). Blackwell 1 The Semantics of Determiners *
"... The study of generalized quantifiers over the past 15 years has enriched enormously our understanding of natural language determiners (Dets). It has yielded answers to questions raised independently within generative grammar and it has provided us with new semantic generalizations, ones that were ba ..."
Abstract
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The study of generalized quantifiers over the past 15 years has enriched enormously our understanding of natural language determiners (Dets). It has yielded answers to questions raised independently within generative grammar and it has provided us with new semantic generalizations, ones that were basically unformulable without the conceptual and technical apparatus of generalized quantifier theory. Here we overview results of both these types. historical note It was Montague (1969) who first interpreted natural language NPs as generalized quantifiers (though this term was not used by him). But it was only in the early 1980's with the publication of B&C (Barwise and Cooper, 1981) that the study of natural language Dets took on a life of its own. Also from this period are early versions of K&S (Keenan and Stavi, 1986) and Higginbotham and May (1981). The former fed into subsequent formal studies such as van Benthem (1984, 1986) and Westerstähl (1985). The latter focussed on specific linguistic applications of binary quantifiers, a topic initiated in Altham and Tennant (1974), drawing on the mathematical work of Mostowski (1957), and pursued later in a more general linguistic setting in van Benthem (1989) and Keenan (1987b, 1992). Another precursor to the mathematical study of generalized quantifiers is LindstrÅm (1969) who provides the type notation used to classify quantifiers in many later studies. Since these beginnings work on the semantics of Dets has proliferated, both empirically and mathematically. Westerståhl (1989) provides an historical overview up to 1987. Some important collections of articles are: van