An expression's presuppositions must be satisfied by its local context, that is, by the utterance context updated with the content of expressions that have already been evaluated. Traditional dynamic approaches track local context by remaking clause denotations into context update functions. This requires crafting for each semantic operator an update recipe that is not fully determined by its truth conditions, failing to capture how local contexts depend only on truth conditions and order of evaluation. In other theories, computing local contexts involves reasoning about the set of all possible grammatical syntactic completions, which relocates local contexts outside of the semantics. I show how to build local contexts systematically and uniformly as part of the composition of ordinary truth conditions. The result is a minimalist dynamic semantics in which the only thing that is dynamically tracked is the semantic content of what has already been said.

Relative clauses and tensed clauses are standardly assumed to be scope islands. However, naturally occurring counterexamples are abundant and easy to find. Therefore, we should revisit analyses that reject Quantifier Raising on the assumption that QR is clause-bounded. The data show that scope islands are sensitive to the identity of both the scope-taker and the predicate embedding the island. I propose the Scope Island Subset Constraint: given two scope islands, the scope-takers trapped by one will be a subset of the scope-takers trapped by the other. A simple refinement of semantic types allows encoding and enforcing of scope islands.

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Displaced scope is a hallmark of natural language, and Quantifier Raising (QR) has long been the standard tool for analyzing scope. Yet despite the foundational importance of QR to theoretical linguistics, as far as I know, there has never been a study of its formal properties. For instance, consider the decidability problem: given an initial syntactic structure, is there an algorithm that will determine whether a semantically coherent QR derivation exists? If at least one such derivation exists, is the number of semantically different analyses always finite? How do we know when we have found them all? Do the answers to these questions depend on imposing scope islands or other constraints on QR, such as forbidding vacuous movement, re-raising, remnant raising, raising of names, repeated type lifting, and so on? I settle these issues by defining QRT (Quantifier Raising with Types), a substructural logic that is a faithful model of QR in the following respect: every semantically coherent QR derivation corresponds to a semantically equivalent proof in QRT, and vice-versa. Since QRT is decidable and has the finite readings property, it follows that a broad class of theories that rely on QR also have these properties, without needing to place any formal constraints on QR. I go on to study the special relationship between type lifting and QR, drawing an analogy with eta reduction in the lambda calculus. Allowing unrestricted type lifting does not compromise decidability. In addition, it turns out that QR with type lifting validates the core type shifting principles of Flexible Montague Grammar, a paradigm example of an in-situ type-shifting approach to scope taking. This suggests that QR is compatible with a local, directly compositional view of scope taking. These results put Quantifier Raising on a reassuringly firm formal footing. EARLY ACCESS

This article concentrates on nominal possessives (John’s friend) rather than on verbal possessives (John has a friend). In John’s friend, John is the possessor, and friend describes the entity possessed (the possessee). Nominal possessives constitute a major construction type in the languages of the world. In contrast with a sortal noun (e.g., person), friend is a (two-place) relational noun: a person counts as a friend only in virtue of standing in a particular relationship with another individual. Relational nouns are an important element in the study of possessives because the content of a possessive typically, perhaps characteristically, depends on the content of a relational nominal. Possessives provide particularly compelling support for type shifting as a general principle of syntactic and semantic composition. Possessives also inform debates involving definiteness, binding, and a wide variety of other semantic phenomena.

Lambek elegantly characterized part of natural language. As is well-known, his substructural logic L, and its non-associative version NL, handle basic function/argument composition well, but not scope taking and syntactic displacement—at least, not in their full generality. In previous work, I propose $$\text {NL}_\lambda $$ , which is NL supplemented with a single structural inference rule (“abstraction”). Abstraction closely resembles the traditional linguistic rule of quantifier raising, and characterizes both semantic scope taking and syntactic displacement. Due to the unconventional form of the abstraction inference, there has been some doubt that $$\text {NL}_\lambda $$ should count at a legitimate substructural logic. This paper argues that $$\text {NL}_\lambda $$ is perfectly well-behaved. In particular, it enjoys cut elimination and an interpolation result. In addition, perhaps surprisingly, it is decidable. Finally, I prove that it is sound and complete with respect to the usual class of relational frames.

What is the communicative value of negative polarity? That is, why do so many languages maintain a stock of special indefinites (weak Negative Polarity Items) that occur only in a proper subset of the contexts in which ordinary indefinites can appear? Previous answers include: marking the validity of downward inferences; marking the invalidity of veridical inferences; or triggering strengthening implications. My starting point for exploring a new answer is the fact that an NPI must always take narrow scope with respect to its licensing context. In contrast, ordinary indefinites are notorious for taking wide scope. So whatever other functions NPIs may have, they at least serve as an utterly reliable signal that an indefinite is taking narrow scope. As also proposed in recent work of Kusumoto and Tancredi, I will show that NPIs are only licensed in contexts in which the wide scope construal of an indefinite fails to entail the narrow scope. In other words, weak NPIs occur only in contexts in which taking narrow scope matters for interpretation. Thus one part of the explanation for the ubiquity and robust stability of negative polarity is that it signals scope relations.

Concealed questions are determiner phrases that are interpreted as if they were questions. For instance, I found out Bills age can be paraphrased as / found out what Bill's age is.It has long been observed by Labner and others that DPs headed by inherently relational nouns such as age make excellent concealed questions, but simple DPs headed by sortal nouns such as brick do not: it is difficult or impossible to interpret ??/ found out the brick as meaning anything, let alone as containing a concealed question.I argue that this systematic restriction on concealed questions follows from the nature of questions in natural language. Questions generally contain two parts: a foreground, which identifies a set of alternatives, and a background, which distinguishes among those alternatives. For instance, the question Who left? identifies a set of relevant people (the foreground) and asks which of those objects have the property of leaving (the background).My main claim is that in order to qualify as a concealed question, a DP must provide both a foreground and a background, For a DP headed by a relational noun, such as Bills age, this is natural: the set of ages serves as the alternatives (the foreground), and the property of standing in the appropriate relation to the possessor (Bill) serves as the distinguishing property (the background). In contrast, simple sortal DPs provide only a set of objects (e.g., the set of bricks), without providing any property for distinguishing one brick from another. It is this lack of foreground/background structure that makes DPs headed by sortal nouns defective as concealed questions. (C) 2016 Elsevier B.V. All rights reserved.

What is the logic of scope? By “scope”, I mean scope-taking in natural languages such as English, as illustrated by the sentence Ann saw everyone. In this example, the quantifier denoted by everyone takes scope over the rest of the sentence, that is, it takes the denotation of the rest of the sentence as its semantic argument: 𝐞𝐯𝐞𝐫𝐲𝐨𝐧𝐞 (λ x . 𝐬𝐚𝐰 (x)(𝐚𝐧𝐧 )) . The answer I will give here will be to provide a substructural logic whose two modes are related by a single structural postulate. This postulate can be interpreted as constituting a kind of lambda-abstraction over structures, where the abstracted structures are interpreted as delimited continuations. I discuss soundness and completeness results, as well as cut elimination. I also compare the logic to a number of alternative approaches, including the standard technique of Quantifier Raising, and mention applications to scope ambiguity and parasitic scope.

AbstractChapter 9 develops an account of donkey anaphora on which the binding scope of an indefinite is a subdomain of its logical (LF) scope. This requires analyzing the conditional using split scope, in such a way that the conditional contributes an instance of negation that is able to take scope independently from the rest of the contribution of the conditional. This enables the indefinite to take scope over the antecedent and the consequent without taking scope over the detached negation. This leads to good predictions concerning the problem of indistinguishable participants (the bishop problem). It also leads to good predictions for conjoined and disjoined antecedents. Crucially, the continuation‐based evaluation order account correctly predicts donkey crossover: that the indefinite antecedent must be evaluated (processed) earlier than the donkey pronoun.

Abstract Chapter 6 explains how the tower grammar handles reconstruction. Reconstruction examples show that a simple linear‐order constraint would not be adequate, since in reconstruction a quantifier can bind a pronoun that linearly precedes it. We show that, given the independently‐motivated account of wh‐fronting and relative clause formation in the previous chapter, reconstruction examples fall out without additional stipulation. Unlike accounts in which reconstruction involves syntactic movement, Principle C effects are not expected on the account developed here. The analysis is extended to reconstruction into relative clauses, as well as to examples involving idiom chunks, reflexives, and other anaphors. Crucially, even in reconstruction examples, crossover constraints remain in effect: roughly, a quantifier can only bind a pronoun if the quantifier precedes the reconstruction gap site.

Abstract Chapter 15 develops further applications of parasitic scope. There is a discussion of parasitic scope from a conceptual point of view, including a schematic diagram. NL‐lambda is compared with Morill et al.’s Discontinuous Lambek Grammar, a formal system that allows expressions to contain arbitrarily many points of discontinuity. In contrast, NL‐lambda achieves similar results while assuming that all expressions are contiguous constituents. Adapting an analysis from Morrill et al., we provide a parasitic scope analysis of pronoun binding and of verb phrase ellipsis. Derivations are given that show the interaction of pronoun binding with verb phrase ellipsis to provide an account of simple strict versus sloppy interpretations of VPE. A number of other parasitic scope analyses from the literature are briefly mentioned.

Abstract Chapter 18 discusses three other continuation‐based analyses of natural language: de Groote’s application of the lambda‐mu calculus to scope‐taking; Moortgat and Bernardi’s application of the Lambek‐Grishin calculus to scope‐taking; and de Groote’s continuation‐based grammar for dynamic anaphora. The main issue addressed throughout concerns the differences between undelimited continuations and delimited continuations. We argue that these approaches either do not allow sufficient variation in the result category of the expression over which a scope‐taker takes scope, or else require additional semantic mechanisms beyond the basic scope‐taking mechanism. We conclude that the expressive power of delimited continuations is essential for an adequate description of natural language. We also briefly discuss monads, a technique from functional programming related to continuations that has applications to natural language.

Abstract Chapter 17 explores the formal properties of NL‐lambda. This is done indirectly, by first studying NL‐CL, a type‐logical grammar with standard structural postulates. We prove that NL‐CL is sound and complete with respect to the usual class of relational models. We then prove that NL‐CL is conservative over NL (the non‐associative Lambek grammar). That is, a sequent in NL is a theorem in NL iff it is a theorem of NL‐CL. We then prove that NL‐CL is equivalent to a restricted version of NL‐lambda. We prove cut elimination for NL‐lambda. This clears the way for showing that NL‐lambda is decidable. In addition, we extend NL‐lambda to a still‐decidable version that handles syntactic displacement (which was handled in Part I by postulating silent expressions called gaps). We briefly mention a variant of NL‐CL that corresponds to unrestricted NL‐lambda.

Abstract Chapter 12 discusses two computational topics. The first topic is one of the key inspirations for our approach, namely, Plotkin’s treatment of the call‐by‐name evaluation discipline versus the call‐by‐value evaluation discipline for a formal language (the untyped lambda calculus). Plotkin’s Continuation Passing Style technique allows explicit control over the evaluation order of an expression within a larger system that is order‐independent. We show the family resemblance between Plotkin’s CPS transforms and our combination schema. The second main topic of the chapter is of a more practical nature, and concerns the computational implementation of the tower system. We show how a refactoring of the type‐shifters into a slightly larger set of combinators guarantees that it is possible to build an efficient (decidable) implementation.

AbstractChapter 3 argues that Montague’s conception of DP meanings as generalized quantifiers is a (limited) form of continuation passing. Likewise, the dynamic semantics conception of sentence meaning as an update function on surrounding context is also seen to be a form of continuation passing. There is a brief comparison of the continuation‐based tower approach to Dynamic Montague Grammar. Montague’s insight follows from making continuations available to expressions in category DP; the dynamic conception of meaning follows from making continuations available to expressions in the category S. Since the continuation‐based approach makes continuations available systematically and uniformly to expressions not only in categories DP and S, but to expressions in any syntactic category, generalized quantifier theory and dynamic semantics turn out to be two special cases of a single general strategy of making continuations available throughout the grammar.

AbstractChapter 7 argues that Partee and Rooth’s theory of generalized coordination implicitly involves a limited form of continuation‐capture. On a continuation account, coordination can be analyzed as reuse of a continuation: first, the continuation of the coordinated expression is combined with one coordinand, then with the other one. Continuations are implicit also in Hendriks’ Flexible Montague Grammar, a conceptually related type‐shifting system. Like the continuation‐based tower fragment, Flexible Montague Grammar is a simple type‐shifting system that provides a robust account of scope relations. However, it is not well‐suited to reasoning about order, and therefore is not able to explain crossover contrasts. This claim is explored by extending Flexible Montague Grammar with a binding type‐shifter, and noting that the type‐shifter generates crossover violations.