Providing a compositional interpretation procedure for discourses in which descriptions of complex dependencies between interrelated objects are incrementally built is a key challenge for formal theories of natural language interpretation. This paper examines several quantificational phenomena and argues that to account for these phenomena, we need richly structured contexts of interpretation that are passed on between different parts of the same sentence and also across sentential boundaries. The main contribution of the paper is showing how we can add structure to (...) contexts in an incremental way, starting with the basic notion of context in classical first-order logic, i.e., interpretation contexts formalized as single total variable assignments. (shrink)

The paper proposes a novel solution to the problem of scope posed by natural language indefinites that captures both the difference in scopal freedom between indefinites and bona fide quantifiers and the syntactic sensitivity that the scope of indefinites does nevertheless exhibit. Following the main insight of choice functional approaches, we connect the special scopal properties of indefinites to the fact that their semantics can be stated in terms of choosing a suitable witness. This is in contrast to bona fide (...) quantifiers, the semantics of which crucially involves relations between sets of entities. We provide empirical arguments that this insight should not be captured by adding choice/Skolem functions to classical first-order logic, but in a semantics that follows Independence-Friendly Logic, in which scopal relations involving existentials are part of the recursive definition of truth and satisfaction. These scopal relations are resolved automatically as part of the interpretation of existentials. Additional support for this approach is provided by dependent indefinites, a cross-linguistically common class of special indefinites that can be straightforwardly analyzed in our semantic framework. (shrink)

What licenses the use of a definite description? The formal and philosophical literature has approached this question in two ways. The uniqueness approach (Frege, 1892; Russell, 1905; Strawson, 1950) holds that we may use a definite determiner only if the property denoted by its complement holds of exactly one individual in some domain: Sentence (1) and (2) can only be true if there is exactly one king of France, and exactly one American governor, respectively. Since this is not the case (...) in the actual world, the sentences are either false or (on most modern accounts) fall prey to a presupposition failure. (shrink)

The paper proposes an account of the contrast (noticed in Karttunen 1976) between the interpretations of the following two discourses: Harvey courts a girl at every convention. {She is very pretty. vs. She always comes to the banquet with him.}. The initial sentence is ambiguous between two quantifier scopings, but the first discourse as a whole allows only for the wide-scope indefinite reading, while the second allows for both. This cross-sentential interaction between quantifier scope and anaphora is captured by means (...) of a new dynamic system couched in classical type logic, which extends Compositional DRT (Muskens 1996) with plural information states (modeled, following van den Berg 1996, as sets of variable assignments). Given the underlying type logic, compositionality at sub-clausal level follows automatically and standard techniques from Montague semantics become available. The paper also shows that modal subordination (A wolf might come in. It would eat Harvey first) can be analyzed in a parallel way, i.e. the system captures the anaphoric and quantificational parallels between the individual and modal domains argued for in Stone (1999) (among others). In the process, we see that modal / individual-level quantifiers enter anaphoric connections as a matter of course, usually functioning simultaneously as both indefinites and pronouns. (shrink)

The paper proposes a novel analysis of quantificational subordination, e.g. Harvey courts a woman at every convention. {She is very pretty. vs. She always comes to the banquet with him.} (Karttunen 1976), in particular of the fact that the indefinite in the initial sentence can have wide or narrow scope, but the first discourse as a whole allows only for the wide scope reading, while the second discourse allows for both readings. The cross-sentential interaction between scope and anaphora is captured (...) in terms of structured anaphora to quantifier domains, formalized in a new dynamic system couched in classical type logic; given the underlying type logic, Montague-style compositionality at sub-clausal level follows automatically. Modal subordination (Roberts 1987) is analyzed in a parallel way, thereby capturing the parallels between the individual and modal domains argued for in Stone (1999). Several other phenomena are analyzed in terms of structured anaphora: exceptional wide scope, weak / strong donkey readings, anaphoric / uniqueness-implying definite descriptions and interactions between same / different and quantifier scope. (shrink)