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"Grammar, Comparative and general Quantifiers."
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Eliminating the universe : logical properties of natural language
\"This book synthesizes the author's work (1980s-2015) on the logical expressive power of natural language. It extends the tools and concepts of model theory as used in (higher order) predicate logic to the study of natural language semantics. It focuses on boolean structure, generalized quantification (separated from variable binding), covering some cases of anaphora. Different categories -- predicates, adjective, quantifiers -- are modeled by non-isomorphic boolean lattices. Of empirical linguistic interest is the expressibility of many natural classes of quantifiers defined in terms of their logical (automorphism invariant) properties. Some of these correlate with classes used syntactically in generative grammar. In other cases we find general (possibly universal) constraints on possible quantifier denotations in natural language. Also of novel logical interest are entailment paradigms that depend on relations between pairs or triples of generalized quantifier denoting expressions, ones that are in some cases inherently vague. In addition we note novel binary quantifiers that lie beyond the \"Frege boundary\" in that they are provably not identical to any iterated application of unary quantifiers. Of philosophical interest is the existence of models which make the same sentences true as standard models but which lack a universe and hence, seemingly, a notion of \"reference\". Moreover, these models generalize to ones in which we can represent (some) intensional expressions without the use of novel ontological objects, such as \"possible worlds\" or \"propositions\"-- Provided by publisher.
Book
Handbook of Quantifiers in Natural Language
Covering a strikingly diverse range of languages from 12 linguistic families, this handbook explores 17 languages, including German, Italian, Russian, Mandarin Chinese, Malagasy, Hebrew, Pima, Basque, and more. The language data sets enable detailed crosslinguistic comparison of numerous features.
eBook
Quantifiers in Language and Logic
Quantification is a topic which brings together linguistics, logic, and philosophy. Quantifiers are the essential tools with which, in language or logic, we refer to quantity of things or amount of stuff. In English they include such expressions as no, some, all, both, or many. This book presents the definitive interdisciplinary exploration of how they work — their syntax, semantics, and inferential role.
eBook
Q-Adverbs as Selective Binders
This book deals with the interpretation of adverbially quantified sentences containing definite DPs and Free Relatives (FR) Thereby, it concentrates on the origins of Quantificational Variability Effects (QVEs), i.e. readings according to which the respective quantificational adverb seems to quantify over the individuals denoted by the respective DP/FR.
QVEs are usually discussed only in connection with singular indefinites and bare plurals. This book therefore provides the first comprehensive account of QVEs with definite DPs and Free Relatives (while also discussing singular indefinites and bare plurals). Presenting new empirical observations and arguments for the assumption that Q-adverbs quantify over situations exclusively, it is also an important contribution to the theoretical debate concerning the quantificational domain of Q-adverbs..
It is of interest to linguists working in formal semantics and the syntax-semantics interface as well as to philosophers of language who are interested in adverbial quantification and situation semantics. Furthermore, it offers an introduction to the core issues of situation semantics and adverbial quantification and is therefore accessible to graduate students interested in these topics.
eBook
Taking Scope
A novel view of the syntax and semantics of quantifier scope that argues for a “combinatory” theory of natural language syntax.
In Taking Scope, Mark Steedman considers the syntax and semantics of quantifier scope in interaction with negation, polarity, coordination, and pronominal binding, among other constructions. The semantics is “surface compositional,” in that there is a direct correspondence between syntactic types and operations of composition and types and compositions at the level of logical form. In that sense, the semantics is in the “natural logic” tradition of Aristotle, Leibniz, Frege, Russell, and others who sought to define a psychologically real logic directly reflecting natural language grammar.
The book reunites the generative-transformational tradition initiated by Chomsky—which views the formal syntactic component as entirely autonomous—-with the older, strongly lexicalist, construction-based tradition, which has sought to define a more lingistically transparent theory of meaning representation. Steedman offers a logical formalism that relates directly to the surface form of language and to the process of inference and proof that it must support. Such a natural logic, although formal by definition, should be allowed to grow organically from attested language phenomena rather than be axiomatized a priori in terms of any standard logic. Steedman also considers the application of natural semantic interpretations to practical natural language processing tasks, emphasizing throughout the elimination of traditional quantifiers from semantic formalism in favor of devices such as Skolem terms and structure-sharing among representations in processing.
eBook
Plurality and Classifiers across Languages in China
Plural marking, numeral classifiers and reduplication constitute the main means of quantification marking in the domain of grammar. The contributions in this book focus on the typological correlation between the three different strategies for quantification, as well as on some general issues. A better understanding of the quantification strategies in the languages of China will enrich our comprehension of human language and thought. The book is expected to have an impact on the study of linguistic typology, language contact, and patterns of the evolution.
eBook
Something Out of Nothing
In this book, Ariel Cohen makes the novel proposal that an implicit quantifier isn't simply an empty category, but is generated by well-defined reinterpretation mechanisms. He demonstrates how this theory naturally accounts for puzzling properties of implicit quantification.
eBook
Adverbs of Degree in Dutch and Related Languages
Adverbs of degree form an intriguing part of the lexicon: numerous, multiform and everchanging. They also show a great variety in distribution. In this study, the characteristics of adverbs of degree are investigated from a semantic point of view. The main focus is on Dutch, but previous studies about English and German adverbs of degree are used to compare with and to build on.The book starts with an introduction on grading and gradability, and a classification of the adverbs according to the degree they express. Next, the different lexical sources from which the adverbs emerge and the process of grammaticalization are discussed. The main part of the book is devoted to semantic restrictions on the use of adverbs of degree, on the one hand restrictions concerning the modified elements, on the other hand those concerning the environment. Topics include absoluteness versus gradability, positive versus negative evaluation, the strengthening of negation, polarity sensitivity, the logical properties of the adverbs themselves, and restrictions to reduplication and stacking.Besides the main text, three case studies are presented in which the pecularities of some of the adverbs are investigated in depth, to show more in detail to complexities of their distribution. The appendix gives an overview of Dutch adverbs of degree.
eBook
Quantification, definiteness, and nominalization
This book addresses recent developments in the study of quantifier phrases, nominalizations, and the linking definite determiner. It reflects the intense reconsideration of the nature of quantification, and of fundamental aspects of the syntax and semantics of quantifier phrases. Leading international scholars explore novel and challenging ideas at the interfaces between syntax and morphology, syntax and semantics, morphology and the lexicon. They examine core issues in the field, such as kind reference, number marking, partitivity, context dependence and the way presuppositions are built into the meanings of quantifiers. They also consider how in this context definiteness and the definite determiner D play a central role, and the way in which D is also instrumental in nominalizations. With nominalization, the lexical semantic contribution of verbs and their arguments becomes central, and within the perspective of this book the question is asked whether syntactic nominalizations share with noun phrases the same external layer, namely the functional projection DP. If so, what exactly is the contribution of D in this case, and how much of the lexical correspondence between nouns and verbs is preserved? This book presents the latest thinking on cross-paradigm and cross-linguistic approaches in three of the most vibrant and productive research areas in linguistics. It paves the way towards a more comprehensive understanding of how quantification, definiteness, and nominalizations are encoded in the grammar.
eBook
Scope and Specificity
Scope and Specificity is an investigation of quantifier scope interaction in natural language, with special reference to English and Chinese. In particular, it is concerned with semantic properties of NPs. Quantifier scope plays an important role in current theories of syntax and semantics. However, most studies of quantifier scope are only concerned with the behavior of a small number of quantifiers, e.g. 'every', 'some', 'all'. As a result, the generalizations made on the basis of these quantifiers often do not hold when a wider range of quantifiers is considered. In this study a wide variety of NP types are examined with respect to how they interact with other NPs. The key concept explored is that of semantic scope dependency/independence. NPs are considered according to two properties: whether they can induce scope-dependency and whether they can be scope-dependent. By observing how in basic sentences NPs behave with respect to the two properties, the author presents a picture of quantifier scope much different from what has been assumed in the literature.
eBook