Rigid and flexible quantification in plural predicate logic

Noun phrases with overt determiners, such as \u3ci\u3esome apples\u3c/i\u3e or \u3ci\u3ea quantity of milk\u3c/i\u3e, differ from bare noun phrases like \u3ci\u3eapples\u3c/i\u3e or \u3ci\u3emilk\u3c/i\u3e in their contribution to aspectual composition. While this has been attributed to syntactic or algebraic properties of these noun phrases, such accounts have explanatory shortcomings. We suggest instead that the relevant property that distinguishes between the two classes of noun phrases derives from two modes of existential quantification, one of which holds the values of a variable fixed throughout a quantificational context while the other allows them to vary. Inspired by Dynamic Plural Logic and Dependence Logic, we propose Plural Predicate Logic as an extension of Predicate Logic to formalize this difference. We suggest that temporal \u3ci\u3efor\u3c/i\u3e-adverbials are sensitive to aspect because of the way they manipulate quantificational contexts, and that analogous manipulations occur with spatial \u3ci\u3efor\u3c/i\u3e-adverbials, habituals, and the quantifier \u3ci\u3eall\u3c/i\u3e

Specificity distinction

This paper is concerned with semantic noun phrase typology, focusing on the question of how to draw fine-grained distinctions necessary for an accurate account of natural language phenomena. In the extensive literature on this topic, the most commonly encountered parameters of classification concern the semantic type of the denotation of the noun phrase, the familiarity or novelty of its referent, the quantificational/nonquantificational distinction (connected to the weak/strong dichotomy), as well as, more recently, the question of whether the noun phrase is choice-functional or not (see Reinhart 1997, Winter 1997, Kratzer 1998, Matthewson 1999). In the discussion that follows I will attempt to make the following general points: (i) phenomena involving the behavior of noun phrases both within and across languages point to the need of establishing further distinctions that are too fine-grained to be caught in the net of these typologies; (ii) some of the relevant distinctions can be captured in terms of conditions on assignment functions; (iii) distribution and scopal peculiarities of noun phrases may result from constraints they impose on the way variables they introduce are to be assigned values. Section 2 reviews the typology of definite noun phrases introduced in Farkas 2000 and the way it provides support for the general points above. Section 3 examines some of the problems raised by recognizing the rich variety of 'indefinite' noun phrases found in natural language and by attempting to capture their distribution and interpretation. Common to the typologies discussed in the two sections is the issue of marking different types of variation in the interpretation of a noun phrase. In the light of this discussion, specificity turns out to be an epiphenomenon connected to a family of distinctions that are marked differently in different languages

Focus structure and the referential status of indefinite quantificational expressions

Many authors who subscribe to some version of generative syntax account for the two readings of [...] sentences [...] in terms of LF-ambiguity. There is assumed to be covert quantifier raising (QR), which results in two distinct possibilities for the indefinite quantificational expressions involved to take scope over each other [...] In this paper, an alternative account is proposed which dispenses with the idea that there are different scope relations involved in the readings of […] sentences [...] and, consequently, with QR as the syntactic operation to be assumed for generating the respective LFs. I argue that it is rather focus structure in connection with type semantic issues pertaining to the indefinite quantificational expressions involved which result in the different readings associated with [...] sentences

Could have done otherwise, action sentences and anaphora

What does it mean to say of a certain agent, S, that he or she could have done otherwise? Clearly, it means nothing at all, unless the anaphoric devices within the sentence have been anchored to definite antecedents. In this paper, I shall argue that there may be more ways of effecting this anchoring than is commonly supposed, and hence more questions potentially available to be asked by means of the formulation ‘Could S have done otherwise?’ than is generally assumed to be the case in most of the relevant literature

The Modal Future Hypothesis Debugged

This note identifies and corrects some problems in developments of the thesis that predictive expressions, such as English "will", are modals. I contribute a new argument supporting Cariani and Santorio's recent claim that predictive expressions are non-quantificational modals. At the same time, I improve on their selectional semantics by fixing an important bug. Finally, I show that there are benefits to be reaped by integrating the selection semantics framework with standard ideas about the future orientation of modals

Tense and the Logic of Change

In this paper it is shown how the DRT (Discourse Representation Theory) treatment of temporal anaphora can be formalized within a version of Montague Semantics that is based on classical type logic

Against the iterative conception of set

According to the iterative conception of set, each set is a collection of sets formed prior to it. The notion of priority here plays an essential role in explanations of why contradiction-inducing sets, such as the Russell set, do not exist. Consequently, these explanations are successful only to the extent that a satisfactory priority relation is made out. I argue that attempts to do this have fallen short: understanding priority in a straightforwardly constructivist sense threatens the coherence of the empty set and raises serious epistemological concerns; but the leading realist interpretations---ontological and modal interpretations of priority---are deeply problematic as well. I conclude that the purported explanatory virtues of the iterative conception are, at present, unfounded

Quantification and polarity: negative adverbial intensifiers ('never ever', 'not at all', etc.) in Hausa

Hausa has a typologically interesting but poorly understood set of quantifying time and degree adverbs—equivalent to English 'never ever', 'not at all', etc.—which behave as negative polarity items and enhance the pragmatic impact of a negative utterance (both verbal and non-verbal). The functional distribution of these adverbial intensifiers is unusual, however, in that some are "bipolar", i.e., they can express opposite (minimal/maximal) values according to whether they occur in negative or positive syntactic environments, with the minimal intensifiers operating at the negative pole. An intensifier such as dàɗai, for example, can mean either 'never' (negative) or 'always' (positive), and other modifiers, e.g., atàbau, can express these same temporal meanings in addition to 'absolutely'. This paper provides a unified account of this natural functional class of adverbs, and is seen as a contribution to cross-linguistic research into polarity items and their licensing contexts