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. (shrink)

This paper presents a new take on how argument dependencies in natural language are established and constrained. The paper starts with a rather standard view that (quantificational) argument dependencies are operator-variable dependencies. The interesting twist the paper offers is to eliminate the need for syntax that serves to enforce what the operator-variable dependencies are. Instead the role of ensuring grammatical and generally unambiguous forms is taken up by semantics imposing what are dependency requirements for any interpretation to go through at (...) evaluation time. With this viewpoint there emerges an essential need for localities as the hiding of (embedded) expression material, together with a (limited) form of garbage collection to release grammatical resources used in the current locality for reuse in subsequent localities. (shrink)

This paper uses a partially ordered set of syntactic categories to accommodate optionality and licensing in natural language syntax. A complex but well-studied data set pertaining to the syntax of quantifier scope and negative polarity licensing in Hungarian is used to illustrate the proposal. The presentation is geared towards both linguists and logicians. The paper highlights that the main ideas can be implemented in different grammar formalisms, and discusses in detail an implementation where the partial ordering on categories is given (...) by the derivability relation of a calculus with residuated and Galois-connected unary operators. (shrink)

This paper analyzes sluicing as anaphora to an anti-constituent (a continuation), that is, to the semantic remnant of a clause from which a subconstituent has been removed. For instance, in Mary said that [John saw someone yesterday], but she didn’t say who, the antecedent clause is John saw someone yesterday, the subconstituent targeted for removal is someone, and the ellipsis site following who is anaphoric to the scope remnant John saw ___ yesterday. I provide a compositional syntax and semantics on (...) which the relationship between the targeted subconstituent and the rest of the antecedent clause is one of scopability, not movement or binding. This correctly predicts that sluicing should be sensitive to scope islands, but not to syntactic islands. Unlike the currently dominant approaches to sluicing, there is no need to posit syntactic structure internal to the ellipsis site, nor is there any need for a semantic mutual-entailment requirement. Nevertheless, the fragment handles phenomena usually taken to suggest a close syntactic correspondence between the antecedent and the sluice, including case matching, voice matching, and verbal argument structure matching. In addition, the analysis handles phenomena exhibiting antecedent/sluice mismatches, including examples such as John remembers meeting someone, but he doesn’t remember who, , and especially so-called sprouting examples such as John left, but I don’t know when, in which there is no overt subconstituent to target for removal. In Sect. 5, I show how the analysis accounts for Andrews Amalgams such as Sally ate [I don’t know what] today, in which the antecedent surrounds the sluiced clause. Finally, in Sect. 6, I propose a new semantic constraint on sluicing: the Answer Ban, which says that the antecedent clause must not resolve, or even partially resolve, the issue raised by the sluiced interrogative. (shrink)

I propose the first strictly compositional semantic account of same. New data, including especially NP-internal uses such as two men with the same name, suggests that same in its basic use is a quantificational element taking scope over nominals. Given type-lifting as a generally available mechanism, I show that this follows naturally from the fact that same is an adjective. Independently-motivated assumptions extend the analysis to standard examples such as Anna and Bill read the same book via a mechanism I (...) call PARASITIC SCOPE, in which the scope of same depends on the scope of some other scopetaking element in the sentence. Although I will initially discuss the analysis in terms of a familiar Quantifier Raising framework, I go on to implement the analysis within an innovative continuation-based Type-Logical Grammar. The empirical payoff for dealing in continuations is that a simple generalization of the basic analysis gives the first ever formal account of cases in which same distributes over objects other than NP denotations, as in the relevant interpretation of John hit and killed the same man. (shrink)