Making linguistic theory is like specifying a programming language...

Using the programming-language concept of CONTINUATIONS, we propose a new, multimodal analysis of quantification in Type Logical Grammar. Our approach provides a geometric view of in-situ quantification in terms of graphs, and motivates the limited use of empty antecedents in derivations. Just as continuations are the tool of choice for reasoning about evaluation order and side effects in programming languages, our system provides a principled, type-logical way to model evaluation order and side effects in natural language. We illustrate with an improved account of quantificational binding, weak crossover, wh-questions, superiority, and polarity licensing.

Abstract not found

is lost or not), is a phenomenon which a linguistic semantics ought to explain, rather than ignore. (van Benthem 1986, p 213) The Lambek-Grishin calculus is a symmetric version of categorial grammar obtained by augmenting the standard inventory of type-forming operations (product and residual left and right division) with a dual family: coproduct, left and right difference. Interaction between these two families is provided by distributivity laws. These distributivity laws have pleasant invariance properties: stability of interpretations for the Curry-Howard derivational semantics, and structure-preservation at the syntactic end. The move to symmetry thus offers novel ways of reconciling the demands of natural language form and meaning. 1 1

From the mid-1970s until the emergence of Chomsky’s Minimalist Program (MP, Chomsky 1995) in the 1990s, the mainstream of research on natural-language syntax in much of the world embraced a theoretical architecture for syntactic derivations that came to be known as the T-model. According to this model,

Why can some NPs take scope where others cannot? In particular, why is it that indefinite NPs can often take wider scope than other NPs can in the same context (Fodor and Sag 1982)? For example, a professor in (1) can take scope over every paper, as shown in (1b). If a is changed to every as in (2), then that reading becomes unavailable, as shown in (2b). (1) I read every paper that a professor in my department recommended.... a. ∀x. � paper(x) ∧ ∃y. professor(y) ∧ recommend(y, x) � ⇒ read(me, x)... Yet I skipped this paper because no professor recommended it. b. ∃y. professor(y) ∧ ∀x. � paper(x) ∧ recommend(y, x) � ⇒ read(me, x)... I understood her research interests very well when I finally finished. (2) I read every paper that every professor in my department recommended.... a. ∀x. � paper(x) ∧ ∀y. professor(y) ⇒ recommend(y, x) � ⇒ read(me, x)... It only took a week because the professors ’ interests are so diverse. b. *∀y. professor(y) ⇒ ∀x. � paper(x) ∧ recommend(y, x) � ⇒ read(me, x)... Yet I skipped this paper because no professor recommended it. It is widely noted that quantifier scope in English is bounded by relative clauses, if-clauses, and perhaps tensed clauses in general. It is also well known that indefinite determiners such as a, some, and a certain are exempt from this restriction. We can try to explain this discrepancy in two ways. On one hand, maybe indefinite NPs take scope through a mechanism separate from (and more liberal than) that for “genuine quantifiers”. The analysis

Making a linguistic theory is like making a programming language: one typically devises a type system to delineate the acceptable utterances and a denotational semantics to explain observations on their behavior. Via this connection, the programming language concept of delimited continuations can help analyze natural language phenomena such as quantification and polarity sensitivity. Using a logical metalanguage whose syntax includes control operators and whose semantics involves evaluation order, these analyses can be expressed in direct style rather than continuation-passing style, and these phenomena can be thought of as computational side effects.

Abstract not found

Abstract not found

Abstract Expressives (damn in the damn dog left), supplements (who is smart in John, who is smart, left) and some other expression types contribute meanings that are not part of the normal at-issue content of a sentence. Following Potts (2005), we will say that they occupy separate dimension of meaning. Potts ’ formal analysis is suitably multi-dimensional, but not compositional. Kubota & Uegaki (2009) provide a compositional analysis, but conflate the new dimension with their mechanism for handling ordinary scope-taking, implicitly predicting that expressives and supplements could take effect within at-issue content. However, the key property of these constructions is that they take semantic effect only at the level of the complete utterance: they are speaker-oriented (non-displaceable). We draw an analogy between expressions that launch side issues and indexicals. Indexicals also find their values only at the level of the complete utterance, and likewise are not affected semantically by surrounding material. The main difference, of course, is that the direction of information flow for indexicals is from the context to the indexical, whereas for side issues, the direction of information flow is from the expression to the context. The challenge, then, is to construct a compositional semantics on which side issues not only can, but must, take effect only at the utterance level. We propose that because the Lambek-Grishin calculus (Bernardi & Moortgat 2010) provides access to undelimited continuations, it is well-suited to capture the behavior of expressives and supplements in a principled fashion.