Ways of Scope Taking is concerned with syntactic, semantic and computational aspects of scope. Its starting point is the well-known but often neglected fact that different types of quantifiers interact differently with each other and other operators. The theoretical examination of significant bodies of data, both old and novel, leads to two central claims. (1) Scope is a by-product of a set of distinct Logical Form processes; each quantifier participates in those that suit its particular features. (2) Scope interaction is (...) further constrained by the semantics of the interacting operators. The arguments are developed using Minimalist syntax, Generalized Quantify theory, Discourse Representation Theory, and algebraic semantics. The contributors (Beghelli, Ben-Shalom, Doetjes, Farkas, Gutiérrez Rexach, Honcoop, Stabler, Stowell, Szabolcsi and Zwarts) make tightly related theoretical assumptions and focus on related empirical phenomena, which include the direct and inverse scope of quantifiers, distributivity, negation, modal and intensional contexts, weak islands, event-related readings, interrogatives, wh/quantifier interactions, and Hungarian syntax. An introduction to the formal semantics background is provided. Audience: Linguists, philosophers, computational and psycholinguists; advanced undergraduates, graduate students and researchers in these fields. (shrink)

This book present a unified semantic theory of expressions involving the notions of part and whole. It develops a theory of part structures which differs from traditional (extensional) mereological theories in that the notion of an integrated whole plays a central role and in that the part structure of an entity is allowed to vary across different situations, perspectives, and dimensions. The book presents a great range of empirical generalizations involving plurals, mass nouns, adnominal and adverbial modifiers such as 'whole', (...) 'together', and 'alone', nominal and adverbial quanitfiers ranging over parts, and expressions of completion such as 'completely' and 'partly'. (shrink)

Epistemology and epistemic logic At first sight, the modern agenda of epistemology has little to do with logic. Topics include different definitions of knowledge, its basic formal properties, debates between externalist and internalist positions, and above all: perennial encounters with sceptics lurking behind every street corner, especially in the US. The entry 'Epistemology' in the Routledge Encyclopedia of Philosophy (Klein 1993) and the anthology (Kim and Sosa 2000) give an up-to-date impression of the field. Now, epistemic logic started as a (...) contribution to epistemology, or at least a tool in its modus operandi, with the seminal book Knowledge and Belief (Hintikka's 1962, 2005). Formulas like Ki for "the agent i knows that " Bi for "the agent i believes that " provided logical forms for stating and analyzing philosophical propositions and arguments. And more than that, their model-theoretic semantics in terms of ranges of alternatives provided an appealing extensional way of thinking about what agents know or believe in a given situation. In particular, on Hintikka's view, an agent knows those propositions which are true in all situations compatible with what she knows about the actual world; i.e., her current range of uncertainty. (shrink)

In this article, we describe and attempt to solve a puzzle arising from the interpretation of modified numerals like less than five and between two and five. The puzzle is this: such modified numerals seem to mean different things depending on whether they combine with distributive or non-distributive predicates. When they combine with distributive predicates, they intuitively impose a kind of upper bound, whereas when they combine with non-distributive predicates, they do not. We propose and explore in detail four solutions (...) to this puzzle, each involving some notion of maximality, but differing in the type of maximality involved and in the source of maximality. While the full range of data we consider do not conclusively favor one theory over the other three, we do argue that overall the evidence goes against the view that modified numerals lexically encode a ‘standard’ maximality operator, and suggests the need for a pragmatic blocking mechanism that filters out readings of sentences that are generated by the grammar but intuitively unavailable. (shrink)

This article proposes a new logical framework for NL quantification. The framework is based on Generalized Quantifiers, Skolem-like functional dependencies, and Maximality of the involved sets of entities. Among the readings available for NL sentences, those where two or more sets of entities are independent of one another are particularly challenging. In the literature, examples of those readings are known as Collective and Cumulative readings. This article briefly analyzes previous approaches to Cumulativity and Collectivity, and indicates (Schwarzschild in Pluralities. Kluwer, (...) Dordrecht, 1996) as the best proposal so far to deal with these readings. Then, it incorporates its insights in the logical framework defined in Robaldo (J Philos Log 39(1):23–58, 2009a), leading to a scalable logical account for NL quantification. (shrink)

We give a condensed survey of recent research on generalized quantifiers in logic, linguistics and computer science, under the following headings: Logical definability and expressive power, Polyadic quantifiers and linguistic definability, Weak semantics and axiomatizability, Computational semantics, Quantifiers in dynamic settings, Quantifiers and modal logic, Proof theory of generalized quantifiers.

This article studies the monotonicity behavior of plural determinersthat quantify over collections. Following previous work, we describe thecollective interpretation of determiners such as all, some andmost using generalized quantifiers of a higher type that areobtained systematically by applying a type shifting operator to thestandard meanings of determiners in Generalized Quantifier Theory. Twoprocesses of counting and existential quantification thatappear with plural quantifiers are unified into a single determinerfitting operator, which, unlike previous proposals, both capturesexistential quantification with plural determiners and respects theirmonotonicity (...) properties. However, some previously unnoticed factsindicate that monotonicity of plural determiners is not always preservedwhen they apply to collective predicates. We show that the proposedoperator describes this behavior correctly, and characterize themonotonicity of the collective determiners it derives. It is proved thatdeterminer fitting always preserves monotonicity properties ofdeterminers in their second argument, but monotonicity in the firstargument of a determiner is preserved if and only if it is monotonic inthe same direction in the second argument. We argue that this asymmetryfollows from the conservativity of generalized quantifiers innatural language. (shrink)

We consider collective quantification in natural language. For many years the common strategy in formalizing collective quantification has been to define the meanings of collective determiners, quantifying over collections, using certain type-shifting operations. These type-shifting operations, i.e., lifts, define the collective interpretations of determiners systematically from the standard meanings of quantifiers. All the lifts considered in the literature turn out to be definable in second-order logic. We argue that second-order definable quantifiers are probably not expressive enough to formalize all collective (...) quantification in natural language. (shrink)