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)

We show in rather informal terms how witness sets can be useful in both explicating some basic intuitions about scope and understanding how particular denotational semantic differences between noun phrases affect their abilities to bear out certain scopal patterns. More generally we suggest that the usual notion of scope needs to be factored into variation distributivity and maximality. This part lays some groundwork for several of the subsequent chapters and is thus of interest to all readers. The second part shows (...) that already in this initial raw form the above insights can be applied to make a novel claim concerning the availability of so-called branching readings. In logical terms a branching reading can be defined for any sentence with a subject and a direct object. However speakers of English accept only a fraction of these readings, so the question arises how the data can be predicted from the meanings of the participating quantifiers and the syntactic structure of the sentence. We propose that thinking about the behavior of quantifiers along the lines introduced in the first part leads to a simple answer to this question. (shrink)