A study of the contribution semantics makes to the syntactic patterns of English: an intepretive theory of grammar.

Plurality, Conjunction and Events presents a novel theory of plural and conjoined phrases, in an event-based semantic framework. It begins by reviewing options for treating the alternation between `collective' and `distributive' readings of sentences containing plural or conjoined noun phrases, including analyses from both the modern and the premodern literature. It is argued that plural and conjoined noun phrases are unambiguously group-denoting, and that the collective/distributive distinction therefore must be located in the predicates with which these noun phrases combine. More (...) specifically, predicates must have a hidden argument place for events; the collective/distributive distinction may then be represented in the part/whole structure of these events. This allows a natural treatment of `collectivizing' adverbial expressions, and of `pluractional' affixes; it also allows a unified semantics for conjunction, in which conjoined sentences and predicates denote groups of events, much like conjoined noun phrases denote groups of individuals. (shrink)

The Montagovian hypothesis of direct model-theoretic interpretation of syntactic surface structures is supported by an account of the semantics of binding that makes no use of variables, syntactic indices, or assignment functions & shows that the interpretation of a large portion of so-called variable-binding phenomena can dispense with the level of logical form without incurring equivalent complexity elsewhere in the system. Variable-free semantics hypothesizes local interpretation of each surface constituent; binding is formalized as a type-shifting operation on expressions that denote (...) functions, & sentences containing a free pronoun are analyzed as a function from individuals to propositions having a meaning of type (e,t). Standard weak crossover effects & binding patterns in sentences with multiple pronouns are shown to submit to straightforward type-theoretic treatments that do not rely on indexation. The variable-free semantics smoothly implements full surface compositionality & requires less machinery than standard accounts to handle functional questions, their answers, sloppy inferences, & across-the-board binding. 73 References. J. Hitchcock. (shrink)

This book uses mathematical models of language to explain why there are certain gaps in language: things that we might expect to be able to say but can't. For instance, why can we say I ran for five minutes but not *I ran to the store for five minutes? Why is five pounds of books acceptable, but *five pounds of book not acceptable? What prevents us from saying *sixty degrees of water to express the temperature of the water in a (...) swimming pool when sixty inches of water can express its depth? And why can we not say *all the ants in my kitchen are numerous? The constraints on these constructions involve concepts that are generally studied separately: aspect, plural and mass reference, measurement, and distributivity. In this book, Lucas Champollion provides a unified perspective on these domains, connects them formally within the framework of algebraic semantics and mereology, and uses this connection to transfer insights across unrelated bodies of literature and formulate a single constraint that explains each of the judgments above. (shrink)

Rooth & Partee (1982) and Rooth (1985) have shown that the English-specific rule-by-rule system of PTQ can be factored out into function application plus two transformations for resolving type mismatch (type lifting and variable binding). Building on these insights, this article proposes a universal system for type-driven translation, by adding two more innovations: local type determination for gaps (generalizing Montague 1973) and a set of semantic filters (extending Cooper 1983). This system, dubbed Cross-Linguistic Semantics (XLS), is shown to account for (...) various phenomena — including scope relations in English and Greenlandic Eskimo, internally headed relative clauses in Lakhota, serial verbs in Yoruba and VP ellipsis in English. (shrink)

This paper proposes that the meanings of some natural language expressions should be thought of as functions on their own continuations. Continuations are a well-established analytic tool in the theory of programming language semantics; in brief, a continuation is the entire default future of a computation. I show how a continuation-based grammar can unify several aspects of natural language quantification in a new way: merely stating the truth conditions for quantificational expressions in terms of continuations automatically accounts for scope displacement (...) and scope ambiguity. To prove this claim, I exhibit a simple finite context-free grammar with a strictly compositional semantics in which quantificational NPs are interpreted in situ but take semantic scope over larger constituents. There is no Quantifier Raising (nor any use of a level of Logical Form distinct from overt syntax), no Cooper Storage (or similar mechanisms used in many recent HPSG, Categorial, or Type-logical treatments), and no need for type-shifting (as in Hendriks' Flexible Types account). Continuations also provide a natural account of generalized coordination that does not require either type-shifting or type polymorphism. Compositionality issues are discussed in some detail. (shrink)

This book takes concepts developed by researchers in theoretical computer science and adapts and applies them to the study of natural language meaning. Summarizing over a decade of research, Chris Barker and Chung-chieh Shan put forward the Continuation Hypothesis: that the meaning of a natural language expression can depend on its own continuation.

Chapter. 1. Logical. Form. as. a. Level. of. Linguistic. Representation. What is the relation of a sentence's syntactic form to its logical form? This issue has been of central concern in modern inquiry into the semantic properties of natural ...

Barry Schein proposes combining a second-order treatment of plurals with DonaldDavidson's suggestion that there are positions for reference to events in ordinary predicates inorder to account for several of the more puzzling features of ...

An analysis of the structural properties of collections or pluralities, homogeneous objects like water, and the semantics and philosophy of events.

The main claim of this book is that the very same distinction between semantic singularity and plurality that is fundamental to the semantics of nouns in the nominal domain is operative and fundamental in the verbal domain as well, applying ...

This book offers a unique synthesis of past and current work on the structure, meaning, and use of negation and negative expressions, a topic that has engaged thinkers from Aristotle and the Buddha to Freud and Chomsky. Horn's masterful study melds a review of scholarship in philosophy, psychology, and linguistics with original research, providing a full picture of negation in natural language and thought; this new edition adds a comprehensive preface and bibliography, surveying research since the book's original publication.

This extended investigation of the semantics of event (and state) sentences in their various forms is a major contribution to the semantics of natural language, simultaneously encompassing important issues in linguistics, philosophy, and logic. It develops the view that the logical forms of simple English sentences typically contain quantification over events or states and shows how this view can account for a wide variety of semantic phenomena. Focusing on the structure of meaning in English sentences at a &"subatomic&" level&-that is, (...) a level below the one most theories accept as basic or &"atomic&"&-Parsons asserts that the semantics of simple English sentences require logical forms somewhat more complex than is normally assumed in natural language semantics. His articulation of underlying event theory explains a wide variety of apparently diverse semantic characteristics of natural language, and his development of the theory shows the importance of seeing the distinction between events and states. Parsons demonstrates that verbs, also, indicate kinds of actions rather than specific, individual actions. Verb phrases, too, he argues, depend on modifiers to make their function and meaning in a sentence specific. An appendix gives many of the details needed to formalize the theory discussed in the body of the text and provides a series of templates that permit the generation of atomic formulas of English. (shrink)

Written by two of the leading figures in the field, this is a lucid and systematic introduction to semantics as applied to transformational grammars of the ...

This is the second in a pair of papers that aim to provide a comprehensive analysis of the semantic phenomenon of distributivity in natural language. This paper describes and explains observable cross-linguistic differences in overt distributive items in the framework of Neo-Davidsonian algebraic event semantics. The previous paper, Champollion 2016, postulated two covert distributivity operators, D and Part, in the grammar, even though the semantic effects of D can be subsumed under the workings of Part. This paper motivates the split (...) by arguing that distance-distributive items across languages are in essence overt versions of these operators. For example, English 'each' lexicalizes D while German 'jeweils' lexicalizes Part. For this reason, 'jeweils' occurs in a wider range of distributive environments, including distribution over salient occasions. The proposed analysis explains why distributive items that can also be used as determiners, such as 'each' and 'every', never allow distribution over occasions. It also accounts for the ability of these determiners to take part in cumulative readings and to interact with nondistributive event modifiers. The paper and its companion include an explicit proposal for the compositional process in event semantics. (shrink)

This is the first in a pair of papers that aim to provide a comprehensive analysis of the semantic phenomenon of distributivity in natural language. This paper investigates and formalizes different sources of covert distributivity. Apart from lexical distributivity effects, which are modeled by meaning postulates, phrasal distributivity is captured via two covert operators: (i) a D operator distributing over atoms only (Link 1987), and (ii) a cover-based Part operator, which can also distribute over non-atomic pluralities under contextual licensing (Schwarzschild (...) 1996). The resulting theory surpasses accounts in which nonatomic distributivity is freely available, or not available at all; furthermore, it correctly predicts differences between lexical and phrasal nonatomic distributivity. D and Part are reformulated in Neo-Davidsonian algebraic event semantics, so that they apply to event predicates and make the sum event available for further modification by arguments and adjuncts. This paves the way for an account of the context-dependency of distributivity phenomena under for-adverbials, which improves on theories that predict indefinites to either always or never covary with for-adverbials. The paper and its companion include an explicit proposal for the compositional process in event semantics. (shrink)

In Groenendijk & Stokhof [1989] a system of dynamic predicate logic (DPL) was developed, as a compositional alternative for classical discourse representation theory (DRT ). DPL shares with DRT the restriction of being a first-order system. In the present paper, we are mainly concerned with overcoming this limitation. We shall define a dynamic semantics for a typed language with λ-abstraction which is compatible with the semantics DPL specifies for the language of first-order predicate logic. We shall propose to use this (...) new logical system as the semantic component of a Montague-style grammar (referred to as dynamic Montague grammar, DMG), which will enable us to extend the compositionality of DPL to the subsentential level. Furthermore, we shall extend this analysis also in this sense that we shall add new, dynamic interpretations for logical constants which in DPL were treated in a static fashion. This will substantially increase the descriptive coverage of DMG. (shrink)

The distinction between telic and atelic predicates has been described in terms of the algebraic properties of their meaning since the early days of model-theoretic semantics. This perspective was inspired by Aristotle’s discussion of types of actions that do or do not take time to be completed1 which was taken up and turned into a linguistic discussion of action-denoting predicates by Vendler (1957). The algebraic notion that seemed to be most conducive to express the Aristotelian distinction appeared to be the (...) mereological notion of a part, applied to the time at which these predicates hold: atelic predicates, like push a cart, have the subinterval property, that is, whenever they are true at a time interval, then they are true at any part of that interval; this does not hold for telic predicates, like eat an apple, cf. Bennett & Partee (1972), Taylor (1977), and Dowty (1979)2. Bach (1986) integrated these insights into a semantics based on events. (shrink)

The puzzle of English until is well-known. Karttunen 1974 argues that until is ambiguous between a durative and a punctual negative polarity (NPI) meaning. Mittwoch 1977 claims that there is no ambiguity and that the two meanings are due to scope differences: NPI-until is in fact until above negation. Mittwoch’s account relies crucially on the assumption that negation is an aspectual operator that ‘stativizes’ verb meanings (a position recently argued for in de Swart 1996, and de Swart and Molendijk 1999; (...) see also Klima 1964, Seuren 1974, Verkuyl 1993). Thus far, the correct analysis of until remains an open issue. (shrink)

This paper describes a novel pedagogical software program that can be seen as an online companion to one of the standard textbooks of formal natural language semantics, Heim and Kratzer (1998). The Penn Lambda Calculator is a multifunctional application designed for use in standard graduate and undergraduate introductions to formal semantics: Teachers can use the application to demonstrate complex semantic derivations in the classroom and modify them interactively, and students can use it to work on problem sets provided by the (...) teacher. The program supports demonstrations and exercises in two main areas: (1) performing beta reduction in the simply typed lambda calculus; (2) application of the bottom-up algorithm for computing the compositional semantics of natural language syntax trees. The program is able to represent the full range of phenomena covered in the Heim and Kratzer textbook by function application, predicate modification, and lambda abstraction. This includes phenomena such as intersective adjectives, relative clauses and quantifier raising. In the student use case, emphasis has been placed on providing “live” feedback for incorrect answers. Heuristics are used to detect the most frequent student errors and to return specific, interactive suggestions. (shrink)