The main claim of this book is that the very same distinction between semantic singularity and plurality that is fundamental to the semantics of nouns in the nominal domain is operative and fundamental in the verbal domain as well, applying ...

Structures for Semantics offers an advanced course in logical and mathematical techniques and structures that are used in semantics, in relation to their semantic applications. The book helps students with a background in semantics to develop their skills of formalization and it makes research in semantics accessible. Workers in other disciplines will use it to discover more about the role of formal modelling in current semantic research, and about semantics itself. Following a chapter on logic and set theory there are (...) three parts of chapters: two pairs of chapters on partial order and equivalence relations in relation to semantic analyses of tense, partial information and vagueness; two chapters on methods for creating ordered structures in relation to intervals, events, and the semantics of change; two chapters on lattices and Boolean algebras in relation to types for noun phrases and verbs, and the semantics of plurals and mass nouns. For upper-level undergraduate students and graduate students in semantics: theoretical linguists, logicians, philosophers of language, computer scientists interested in natural language semantics. (shrink)

In this paper, we argue that there are more kinds of relative clause constructions between the linguistic heaven and earth than are dreamed of in the classical lore, which distinguishes just restrictive relative clauses and appositives. We start with degree relatives. Degree, or amount, relatives show restrictions in the relativizers they allow, in the determiners that can combine with them, and in their stacking possibilities. To account for these facts, we propose an analysis with two central, and novel, features: First, (...) we argue that the standard notion of degree (a number on a measuring scale) needs to be replaced by a notion of structured degree, which keeps track of the object measured. Second, we argue that at the CP-level of degree relatives an operation of (degree) maximalization takes place. We show that the observed facts concerning degree relatives follow from these assumptions. We then broaden the discussion to other relative clause constructions. We propose that the operation of maximalization takes place in relative clauses when the head noun is semantically interpreted CP-internally, while syntactically the CP is part of a DP that also contains CP-external material. Based on this, we argue that degree relatives form part of a linguistically coherent class of relative clause constructions -- we call them maximalizing relatives -- which all show restrictions similar to those observed for degree relatives, and which differ semantically (and often also syntactically) both from restrictive relative clauses and from appositives. We discuss free relatives, internally-headed relatives, and correlatives. (shrink)

This paper gives an analysis of the Chinese distributivity marker dou 'all', which can occur not only with definite plural NPs but also with NPs whose determiner is a quantifier word such as mei 'every' or dabufen-de 'most'. Besides normal distributive predicates, it can also occur with certain types of collective predicates. The difficulties of giving a compositional interpretation to constructions of these kinds are discussed in detail. I show that we can solve those difficulties if we treat dou as (...) a generalized distributivity marker in the sense of Schwarzschild (1991, 1996), which distributes over the members of a plurality cover. Apart from the above topic, which is more narrowly a semantics topic, this paper also discusses some syntax-semantics interface issues related to the distribution of dou's associates. (shrink)

In this paper I propose and formalize a theory of the mass-count distinction in which the denotations of count nouns are built from non-overlapping generators, while the denotations of mass nouns are built from overlapping generators. Counting is counting of generators, and it will follow that counting is only correct on count denotations.I will show that the theory allows two kinds of mass nouns: mess mass nouns with denotations built from overlapping minimal generators, and neat mass nouns with denotations built (...) from overlapping generators, where the overlap is not located in the minimal generators. Prototypical mass nouns like meat and mud are of the first kind. I will argue that mass nouns like furniture and kitchenware are of the second type.I will discuss several phenomena—all involving one way or the other explicitly or implicitly individual classifiers like stuks in Dutch—that show that both distinctions mass/count and mess/neat are linguistically robust. I will show in particular that nouns like kitchenware pattern in various ways like count nouns, and not like mess mass nouns, and that these ways naturally involve the neat structure of their denotation. I will also show that they are real mass nouns: they can involve measures in the way mess mass nouns can and count nouns cannot.I will discuss grinding interpretations of count nouns, here rebaptized fission interpretations, and argue that these interpretations differ in crucial ways from the interpretations of lexical mass nouns. The paper will end with a foundational problem raised by fission interpretations, and in the course of this, atomless interpretation domains will re-enter the scene through the back door. (shrink)

The background for this paper is the framework of Boolean semantics for mass and count nouns, and singular and plural count nouns, as developed from the work of Godehard Link in Link 1983. Link-style Boolean semantics for nouns analyzes the oppositions mass-count and singular-plural in terms of the notion of atomicity: counting is in terms of singular objects, which are taken to be atoms. Consequently, Link bases his semantics on two separate Boolean domains: a non-atomic mass domain and an atomic (...) count domain. Singular count nouns are interpreted as sets of atoms, and semantic plurality is closure under sum, so plural objects are sums of atoms. In this, sorted setup portions - like two portions of soup - are a puzzle: they are mass stuff - soup -, but count - two. But in order to be count they must be atoms. But they are not, because they are just soup. Mountain semantics can deal with portions, but at a cost. In the first part of this paper I outline Iceberg semantics, an alternative to Mountain semantics within the general framework of Boolean semantics. Iceberg semantics specifies a compositional mechanism which associates with the standard denotation of any noun phrase a base set, a set that generates the body under the sum operation ⊔. For count nouns, the base is the set in terms of which the members of the body are counted and to which distribution takes place. In Iceberg semantics, what allows counting to be correct is the requirement on the interpretations of count nouns that the base of their interpretation is disjoint. Already at this level we see two salient properties of Iceberg semantics: -Atoms and atomicity play no role in the theory, so we can assume an unsorted interpretation domain for mass nouns and count nouns. In Iceberg semantics, mass and count can be seen as different perspectives on the same stuff. This means that we can do away with the extreme body-sorting and body-gridding that atomicity entails. With this we allow a simpler and more elegant analysis of mass-count interactions. For instance, portions can just be 'mass' stuff, evaluated relative to a count base. -The mass-count distinction is formulated in terms of disjointness of the base. Iceberg semantics associates bases not just with the interpretations of lexical nouns, but with NPs in general and with DPs. This means that Iceberg semantics provides a compositional semantic theory of the mass-count distinction, and hence it provides a framework in which the mass-count nature of complex NPs and of DPs can be fruitfully studied. It is the analysis of complex NPs and their mass-count properties that is the focus of the second part of this paper. There I develop an analysis of English and Dutch pseudo- partitives, in particular, measure phrases like three liters of wine and classifier phrases like three glasses of wine. We will study measure interpretations and classifier interpretations of measures and classifiers, and different types of classifier interpretations: container interpretations, contents interpretations, and - indeed - portion interpretations. Rothstein 2011 argues that classifier interpretations of pseudo partitives pattern with count nouns, but that measure interpretations pattern with mass nouns. I will show that this distinction follows from the very basic architecture of Iceberg semantics. (shrink)

Some Generalizations of Categorical Grammars Emmon Bach 0. INTRODUCTION The last decade of work in syntax has seen a marked demotion in the importance of ...