Dynamic semantics with static
types (with Dylan Bumford)
Submitted to Linguistics and Philosophy. Semantic analyses of natural language typically rely on variables for the interpretation of binding relationships. This is true of standard static setups, where sentences might denote sets of variable assignments, as well as standard dynamic ones, where they might denote relations between (sets of) variable assignments. Several well-known alternative frameworks eschew object-language variables in favor of representing semantic dependencies as functional dependencies. This obviates assignments, and has the benefit that any expression’s binding needs are discoverable directly from its type. But these popular variable-free approaches are limited to static, in-scope binding relationships, those in which dependents occur in the arguments of their binders. In this paper we develop a semantics that is variable-free in the same sense, but captures traditional notions of dynamic anaphora. We demonstrate the value of anaphoric type transparency with novel analyses of crossover, ellipsis, and sloppy/paycheck anaphora, and compare the new semantics, which introduces the notions of parameterized monads and lenses to the linguistics literature, with other list-based dynamic systems and other accounts of crossover.
Static and dynamic exceptional scope
Accepted with minor revisions at Journal of Semantics. This paper proposes a formal account of indefinites’ exceptional quantificational and binding scope properties — static and dynamic exceptional scope. I argue that minimal dynamic extensions of tools independently motivated and widely used for questions and indefiniteness offer a unified explanation of indefinites’ multifaceted exceptional scope behavior. The account improves on existing static and dynamic theories of indefiniteness, and predicts a wide range of attested exceptional scope behavior for a range of expressions, both indefinite and not.
Post-suppositions and semantic
Accepted with minor revisions at Journal of Semantics. I explore two alternatives to post-suppositions for generating cumulative readings of sentences with multiple modified numerals. The first uses higher-order dynamic generalized quantifiers (GQs), functions whose ‘trace’ is itself typed as a dynamic GQ. Such functions, though a hop-and-a-skip up the type hierarchy from dynamic GQs, are already available to any standard-issue Montagovian dynamic semanticist, and dealing with them compositionally requires nothing beyond whatever machinery already underwrites quantifiers in object position, scope ambiguity, and so on (though the analysis is presented using a handy continuations-oriented tower notation). I build on this theory by exploring a type-theoretic elaboration of it (technically, in terms of subtype polymorphism) that rules out arguably unattested ‘pseudo-cumulative’ readings.
Second, I show that these steps (higher-order dynamic GQs subtyping) are unnecessary if the usual ‘point-wise’ dynamic semantics of Dynamic Predicate Logic or Compositional DRT, where propositions are typed as relations on assignments, is replaced with an update semantics, where propositions are typed as functions from sets of assignments into sets of assignments. Conservative update-semantic meanings for modified numerals — direct analogs of their point-wise counterparts — automatically yield cumulative readings and fail to derive pseudo-cumulative readings. This gives an argument for an update semantics in the anaphoric domain (so far as I know the first of its kind).
I compare these two kinds of analyses with each other and consider their relation to post-suppositions in semantic theory more generally, concluding: (i) the theories canvassed here have modest empirical advantages over post-suppositions; (ii) the update-theoretic account offers the most direct route to an empirically adequate analysis of modified numerals; (iii) the reasons for this turn out to be specific to modified numerals; theories of other ‘post-suppositional’ phenomena are better formulated with higher-order GQs.
Scalar implicature and
Resubmitted to Linguistic Inquiry. There is lots of work on scalar implicature, lots of work on the exceptional scope properties of indefinites, and comparatively little work on the scalar implicatures of exceptionally scoping indefinites. This note points out that a phenomenon of 'exceptional scalar distributivity' suggests that the scalar alternatives of indefinites are more abstract than we might have figured: they don’t correspond to any actually expressible lexemes, and they aren't, strictly speaking, alternatives of the indefinite determiner at all! I develop a rudimentary account, pointing out various issues, predictions, and choice points along the way. I show that two different kinds of theories can be used to explain the data: one uses choice functions for exceptional scope, and another uses alternatives directly.
A modular theory of pronouns
Under revision for Natural Language Semantics. Since Shan’s (2002) pioneering work, a number of researchers have argued that monads offer a flexible, robust compositional interface for expressions that denote in "enriched spaces". This paper argues that a monadic treatment of pronouns and assignment-sensitivity has a number of theoretical and empirical benefits, including (i) a maximally simple lexicon and a fully categorematic treatment of abstraction; (ii) centrally, immediate analyses of paycheck pronouns and binding reconstruction, with a unitary, simple semantics for pronouns and traces. The treatment involves abstracting out the two functions that underlie standard treatments of assignment-friendly composition -- yielding a so-called applicative functor -- and then adding a third function to deal with 'higher-order' variables, yielding a monad.
Two developments of the basic idea are briefly explored. First, I argue that a mere applicative functor turns out to be sufficient after all, if we (a) adopt a more type-theoretically conservative treatment of assignments than is standard, and (b) countenance sentence meanings that depend on multiple assignments. Second, I demonstrate an equivalence of the resulting theory with a variable-free semantics, one which extends both to the combinatory apparatus underwriting composition, and to the resulting semantic values.
On Jacobson’s “Towards a Variable-Free Semantics”
Studies in Linguistics and Philosophy 100, 171-196. [official] Jacobson (1999) proposes an account of anaphora and binding that eschews variables and variable assignments, instead treating pronouns as identity functions and extending functional application with operations that pass up and close off anaphoric dependencies. This paper reviews the central aspects of Jacobson’s variable-free semantics, counterpoising it with the standard, variable-full framework. I discuss conceptual and empirical virtues of Jacobson’s theory, and some shortcomings, one significant. I argue that these limitations can be overcome by drawing on certain design features of the standard account, connect this approach to the computer science concept of ‘applicative functors’ (and thereby to frameworks as varied as alternative semantics and continuations), and clarify which of the variable-free theory’s properties should be regarded as proprietary, and which can be easily repurposed into a theory with variables.
∃-closure and Alternatives
Linguistic Inquiry 52(1), 143-152. [official] This remark considers the interaction of Alternative Semantics (AS) with various binding operations -- centrally, Predicate Abstraction and ∃-closure; less centrally, intensionalization. Contra Griffiths's (2019, Beyond MaxElide, Linguistic Inquiry 50(3)) theory of ellipsis, I argue that it is technically problematic to appeal to the inherent incompatibility of Predicate Abstraction and AS, while assuming the compatibility of ∃-closure and AS. I show that the formal pressures which characterize the interaction of Predicate Abstraction and alternatives apply equally to ∃-closure and alternatives, and that it is impossible to define a true ∃-closure operation within what might be termed ‘standard’ AS. A well-behaved AS reflex of ∃-closure can only be defined in compositional settings where a well-behaved AS reflex of Predicate Abstraction is definable too. I consider various technical and empirical consequences of these points for Griffiths’s theory of ellipsis, and for linguistic theory more generally.
The scope of alternatives: indefiniteness and islands
Linguistics and Philosophy 43, 427-472. [official] I argue that alternative-denoting expressions interact with their semantic context by taking scope. With an empirical focus on indefinites in English, I show how this approach improves on standard alternative-semantic architectures that use point-wise composition to subvert islands, as well as on in situ approaches to indefinites more generally. Unlike grammars based on point-wise composition, scope-based alternative management is thoroughly categorematic, doesn’t under-generate readings when multiple sources of alternatives occur on an island, and is compatible with standard treatments of binding. Unlike all in situ (pseudo-scope) treatments of indefinites, using a true scope mechanism prevents over-generation when an operator binds into an indefinite.
My account relies only on function application, some mechanism for scope-taking, and two freely-applying type-shifters: the first is Karttunen’s (1977) proto-question operator, aka Partee’s (1986) IDENT, and the second can be factored out of extant approaches to the semantics of questions in the tradition of Karttunen (1977). These type-shifters form a decomposition of LIFT, the familiar function mapping values into scope-takers. Exceptional scope of alternative-generating expressions arises via (snowballing) scopal pied-piping: indefinites take scope over their island, which then itself takes scope.
Where is the destructive update problem?
In press at Semantics & Pragmatics. I critically examine several objections to ‘destructive update’ of assignment functions in dynamic theories of anaphora, using a modular compositional treatment of the static/dynamic divide to highlight what static and dynamic approaches to assignment functions have in common, and how they differ.
Parsing with Dynamic Continuized CCG
(with Michael White, Jordan Needle, & Dylan Bumford)
TAG+13, Association for Computational Linguistics, 71–83. We present an implemented method of parsing with Combinatory Categorial Grammar (CCG) that for the first time derives the exceptional scope behavior of indefinites in a principled and plausibly practical way. The account implements Charlow’s (2014) monadic approach to dynamic semantics, in which indefinites’ exceptional scope taking follows from the way the side effect of introducing a discourse referent survives the process of delimiting the scope of true quantifiers in a continuized grammar. To efficiently parse with this system, we extend Barker and Shan’s (2014) method of parsing with continuized grammars to only invoke monadic lifting and lowering where necessary, and define novel normal form constraints on lifting and lowering to avoid spurious ambiguities. We also integrate Steedman’s (2000) CCG for deriving basic predicate-argument structure and enrich it with a method of lexicalizing scope island constraints. We argue that the resulting system improves upon Steedman’s CCG in terms of theoretical perspicuity and empirical coverage while retaining many of its attractive computational properties.
Bound 'de re' pronouns and the LFs of attitude reports (with Yael Sharvit)
Semantics & Pragmatics 7(3), 1-43. An empirical argument is given in support of Percus & Sauerland’s (2003) theory of ‘de re’ ascription, according to which the internal argument of believe is a function from concept-generators to propositions. The argument concerns pronouns in the scope of attitude verbs that are interpreted both ‘de re’ and as bound variables. It is argued that more traditional theories of ‘de re’ ascription — specifically, theories that take the ‘res’ to be an internal argument of believe — fail to account for such pronouns, as they predict that a pronoun cannot simultaneously be an argument of believe and bound by a quantifier in the scope of believe.
Stochastic time analysis of
syllable-referential intervals and simplex onsets
(with Adamantios I. Gafos, Jason A. Shaw, and Philip Hoole)
Journal of Phonetics 44, 152-166. [official] We pursue an analysis of the relation between qualitative syllable parses and their quantitative phonetic consequences. To do this, we express the statistics of a symbolic organization corresponding to a syllable parse in terms of continuous phonetic parameters which quantify the timing of the consonants and vowels that make up syllables: consonantal plateau durations, vowel durations, and their variances. These parameters can be estimated from continuous phonetic data. This enables analysis of the link between symbolic phonological form and the continuous phonetics in which this form is manifest. Pursuing such an analysis, we illustrate the predictions of the syllabic organization corresponding to simplex onsets and derive a number of previously experimentally observed and simulation results. Specifically, we derive not only the canonical phonetic manifestations of simplex onsets but also the result that, under certain conditions we make precise, the phonetic indices of the simplex onset organization change to a range of values characteristic of the complex onset organization. Finally, we explore the behavior of phonetic indices for syllabic organization over progressively increasing sizes of lexical samples, thereby concomitantly diversifying the phonetic context over which these indices are taken.
Lecture Notes in Computer Science vol. 7218: Selected Papers from the 18th Amsterdam Colloquium, 261-270. [official] Data from surprising sloppy readings of verb phrase ellipsis constructions argue that ellipsis sites can partially or totally consist of dynamically bound pro-forms. I give an account, integrating Muskens’ CDRT with a focus-based theory of ellipsis and deaccenting.
Free and bound pro-verbs: a unified treatment of anaphora
Proceedings of Semantics and Linguistic Theory 18, 194-211. This paper argues that certain phenomena related to verb ellipsis in English suggest a degree of interpretive flexibility for ellipsis sites close to that exhibited by pronominals. Specifically, it is claimed that (a) like pronouns, ellipsis sites may be bound or free, and (b) one set of grammatical mechanisms affords analyses of both free and bound pronominals and free and bound pro-verbs.
Rutgers graduate courses
- Semantics I (Fall 2014, Fall 2015) [course site]
- Semantics II (Spring 2018, Spring 2019, Spring 2020) [course site]
- Semantics III (Fall 2018, Fall 2019, Fall 2020)
- Qualifying paper workshop (Spring 2015, Spring 2016)
Rutgers seminars in semantics
- Spring 2015: Alternatives in semantics [course site]
- Spring 2017: Computational semantics [course site]
- Spring 2022: Dynamic semantics
- Fall 2022: Effectful composition in natural language semantics [materials]
Rutgers undergraduate courses
- Introduction to Linguistic Theory (Fall 2016, Fall 2018)
- Honors Introduction to Linguistic Theory (Fall 2016, Spring 2020)
- Semantics (Spring 2016, Spring 2018)
- Computational Linguistics (Fall 2021) (co-developed with Adam Jardine)
Teaching outside Rutgers
Effectful composition in natural language semantics (with Dylan Bumford)
ESSLLI 2022, Galway, Ireland [course site]
Invited minicourse, Yale University, Aug 28–Sep 10, 2019.
Alternatives in semantics
Invited advanced course, Eastern Generative Grammar Summer School (EGG), Wrocław, Jul 29–Aug 9, 2019.
Invited minicourse, Massachusetts Institute of Technology, April 3–4, 2019.
Sreekar Raghotham (co-chair: Mark Baker)
Title TBD (verbal reflexivity)
Be flexible, but not too flexible: limited variable-force modals in Kinande and the typology of modal force [pdf]
Lecturer in Linguistics, Yale University
Plurality and quantification in graph representation of meaning [pdf]
Applied Researcher, eBay
Haoze Li (NYU Linguistics, co-chair: Anna Szabolcsi)
A dynamic semantics for wh-questions [pdf]
Yunshan Scholar (Assistant Professor), Guangdong University of Foreign Studies; Visiting Assistant Professor, UC Santa Cruz
Cross-categorial definiteness/familiarity [pdf]
Visiting Assistant Professor, Boston College
Jess H.-K. Law (co-chair: Veneeta Dayal)
Constraints on distributivity [pdf]
Assistant Professor, UC Santa Cruz
I'm an Associate Professor in the Rutgers Department of Linguistics.
I'm a formal and computational semanticist using computer science, type theory, and lambda calculus to develop scalable, compositional, and implemented models of how language is generated, parsed, and understood.
Programming languages are unlike natural language in many ways, but they are, after all, languages—with form, meaning, and a systematic relationship between the two. The connection between linguistic semantics and functional programming is especially close: in both domains, complex concepts or procedures are built compositionally, by iteratively applying functions to arguments. My research uses techniques developed for extending pure functional languages with 'side effects' as engines for better models of how natural language meanings are composed.
As long as I've been a linguist, I've been fascinated by quantification, scope, indefiniteness, anaphora, and ellipsis, interacting domains in which the relationship between form and meaning is especially rich, and revealing. I've developed new frameworks for doing semantics in the presence of dynamic effects (state) and alternatives (nondeterminism). I have longstanding interests and projects in Combinatory Categorial Grammar, (semantic) parsing, and continuations. And I am a fan of implementing semantic theories as runnable, debuggable code.
At Rutgers I teach courses at the undergraduate and graduate levels in formal semantics, computational linguistics, and general linguistics.
This website has info on my papers, teaching, and students. Further details of my academic life (including materials from talks) are in my CV. My github is here.
Email me at