Dynamic Semantics: Modern Type Theoretic and Category Theoretic Approaches

Dynamic Semantics: Modern Type Theoretic and Category Theoretic Approaches


Carl Pollard (carl.pollard37@gmail.com), Ohio State University

Robert Levine (levine.1@osu.edu), Ohio State University

Yusuke Kubota (kubota.yusuke.fn@u.tsukuba.ac.jp), University of Tsukuba, Ohio State University

Workshop description

In the last few years, a variety of new compositional approaches to dynamic semantics have emerged, including: Dynamic Categorial Grammar (Martin2013, Martin and Pollard 2014); Dependent Type Semantics (Bekki 2014, Tanaka et al. 2014), and Monadic Dynamic Semantics (Charlow 2014). These different varieties of dynamic semantics make use of broadly similar formal techniques, such as dependent type theory, continuations, and monads, but have very different conceptual underpinnings. These different new models of dynamic semantics potentially have very different empirical consequences as well. But since these approaches are all still relatively new, there has not as yet been much communication among researchers advocating each approach. The aim of this workshop is to provide a venue for such an exchange of ideas.


Ohio State University, Baker Systems Engineering (BE) Room 285


Saturday, October 24

8:30-8:50 Coffee, light breakfast

8:50-9:00 Introduction by the organizers

9:00-10:45 Scott Martin (Nuance Communications) It all depends: a modern, type-theoretic, compositional dynamic semantics for projection and beyond


I give a detailed exposition of an approach to dynamic semantics that is fully compositional while preserving the core insights of the dynamic tradition: that indefinites do not quantify, and that every component of an utterance both updates the context and depends upon the context for its interpretation. This semantics is built in mainstream type theory extended with dependent types, which are used to always ensure that a context is suitable for the utterances being interpreted against it. It is flexible enough that it can be based on a wide range of static semantic theories, and can be hooked up to a variety of categorial grammars. It has built-in mechanisms for judging entailment and modeling anaphoric dependencies, which, on one view, is the central task of theories that attempt to capture projective meaning. I will demonstrate its empirical coverage for standard definite anaphora, iterative adverbs like 'too', and supplements. I will also discuss a preliminary account of VP ellipsis and related phenomena that harnesses the theory's anaphora machinery.

10:45-11:00 Coffee Break

11:00-12:15 Murat Yasavul (Ohio State University) A dynamic context model for questions


Martin 2013 and Martin & Pollard 2014 present a fully compositional model of dynamic semantics that builds on related approaches like Muskens 1996; Beaver 2001, and de Groote 2006 that use higher-order logic to model context change. The framework, called Dynamic Categorial Grammar (DyCG), is expressed in type theory and captures all the central insights of the dynamic semantics tradition (Kamp, 1981; Heim, 1983). In addition, DyCG provides an interface between this kind of dynamic semantics and a linear logic based form of categorial grammar called Linear Categorial Grammar (LCG, Pollard & Smith, 2012; Mihaliček, 2012; Pollard, 2013), which in turn is inspired by Oehrle 1994.

Despite the desirable characteristics of the framework, previous work on DyCG did not concern itself with the analysis of questions and answers in discourse. An adequate model of context, however, would inevitably include a way to capture the interpretation of questions and answers since, as it has been argued by Ginzburg (1994, 1995a,b); Roberts (1996/2012, 2004); Zeevat (2007); Farkas & Bruce (2009), among others, contexts consist of more than the common ground (CG) and a list of discourse referents (DRs). In particular, they include a way to keep track of questions that are uttered in discourse.

In this talk, I extend the previous work on DyCG in order to provide a dynamic analysis of questions and answers. The dynamic analysis incorporates the original characterization of questions and answers in Hamblin 1957 and Hamblin 1971. As a case study, I illustrate how the enriched context model captures the interpretations of constituent questions and their answers.

12:15-14:15 Lunch

14:15-16:00 Simon Charlow (Rutgers University) Monadic dynamic semantics for anaphora


Dynamic semantics has two key components: state and nondeterminism. The former allows expressions to introduce discourse referents, and the latter allows indefinites to be analyzed as nondeterministic analogs of proper names. This talk motivates a picture in which state and nondeterminism are analyzed as linguistic side effects, and formalizes this in terms of the category-theoretic notion of a monad. In contrast with standard dynamic semantics, the semantics I propose is dynamic down to the morpheme, has no use for an operation of dynamic conjunction, and explains a wide variety of exceptional scope phenomena (encompassing both familiar and novel data) without stipulation. Because of the inherent modularity of the monadic approach, it is straightforward to extend the theory to handle phenomena like conventional implicature (a la Potts) and focus. In addition, the monadic perspective suggests a fundamental connection between dynamic and static, alternatives-based analyses of indefinites, while offering a precise accounting of the way in which they differ.

16:00-16:15 Coffee Break

16:15-17:30 Colin Zwanziger (Carnegie Mellon University) Comonadic categorical semantics of Montague's Intensional Logic


As noted by Lambek (1988), the model-theoretic semantics of Montague (1973) resembles an interpretation into the topos of presheaves on a set 'of possible worlds'. To make this resemblance precise, we develop an interpretation for Montague's Intensional Logic in which the semantics of the 'intension' and 'extension' operators are provided respectively by the coKleisli lift and counit operations of a suitable comonad on a topos. While it maintains essential aspects of Montague's presentation, the comonadic semantics is felicitously modular. In this approach, the modal de re/de dicto distinction is understood as arising from the noncommutativity of precomposition (substitution) and the lift operation. Since this arises naturally from the use of the comonad, there is no need to effect de re interpretations via a semantics for variables and function abstraction which invalidates the laws of the lambda calculus.

Sunday, October 25

8:30-9:00 Coffee, light breakfast

9:00-10:15 Carl Pollard (Ohio State University) Hyperintensionality meets monadic semantics


10:15-10:30 Coffee Break

10:30-12:15 Daisuke Bekki (Ochanomizu University) Anaphora and presuppositions in Dependent Type Semantics

theory slides

empirical slides

Dependent type semantics (DTS) is a framework of discourse semantics based on dependent type theory, following the line of Sundholm and Ranta. DTS attains compositionality as required to serve as a semantic component of modern formal grammars including variations of categorial grammars, which is achieved by adopting a mechanism for underspecified terms. In DTS, the calculation of presupposition projection reduces to type checking, and the calculation of anaphora resolution and presupposition binding both reduce to proof search in dependent type theory, inheriting the paradigm of anaphora resolution as proof construction. I will demonstrate how DTS gives solutions to classical benchmarks for presupposition and anaphora, including presupposition projection and filtering, bridging anaphora, weak crossover, VP-ellipsis, event pronouns and factive presuppositions.

12:15-14:15 Lunch

14:15-15:30 Ribeka Tanaka (Ochanomizu University) Generalized quantifiers in Dependent Type Semantics


In this talk, I will present a formalization of generalized quantifiers (GQs) in the framework of dependent type semantics (DTS), a proof-theoretic semantics of natural language. Sundholm (1989) first proposed a proof-theoretic analysis of GQs in the framework of constructive type theory. It sketched the idea to deal with the so-called proportion problem associated with proportional quantifier "most". Tanaka (2014) improved Sundholm's analysis and integrated the idea into DTS's dynamic setting to provide an alternative analysis of GQs, including "most" and numerical determiners, which can account for both the proportion problem and donkey anaphora. I will show that the formalism based on DTS has strong potential to serve as an alternative to the traditional model-theoretic approach.

15:30-15:45 Coffee Break

15:45-17:00 Yusuke Kubota (University of Tsukuba, Ohio State University) & Robert Levine (Ohio State University) Scope parallelism in coordination in Dependent Type Semantics


The scope parallelism in the so-called Geach sentences in right-node raising (Every boy admires, and every girl detests, some saxophonist) poses a difficult challenge to many analyses of right-node raising, including ones formulated in the type-logical variants of categorial grammar (e.g. Kubota & Levine 2015). In this paper, we first discuss Steedman's (2012) solution to this problem in Combinatory Categorial Grammar, and point out some empirical problems for it. We then propose a novel analysis of the Geach problem within Hybrid Type-Logical Categorial Grammar (Kubota & Levine 2015), by incorporating Dependent Type Semantics (Bekki 2014) as the semantic component of the theory. The key solution for the puzzle consists in linking quantifiers to the argument positions that they correspond to via an anaphoric process. Independently motivated mechanisms for anaphora resolution in DTS then automatically predicts the scope parallelism in Geach sentences as a consequence of binding parallelism independently observed in right-node raising sentences.

17:00-17:30 Discussion


We gratefully acknowledge the support of the following institutions: The Ohio State University Department of Linguistics for a Targeted Investment in Excellence grant; the University of Tsukuba Institute for Comparative Research; and the Japan Society for the Promotion of Science for KAKENHI Grant number 15K16732.