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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

Quantifier scope challenges the mantra of Tree Adjoining Grammar (TAG) that all syntactic dependencies are local once syntactic recursion has been factored out. The reason is that on current TAG analyses, a quantifier and the furthest reaches of its scope domain are in general not part of any (unicomponent) elementary tree. In this paper, I consider a novel basic TAG operation called COSUBSTI-TUTION. In normal substitution, the root of one tree (the argument) replaces a matching non-terminal on the frontier of another tree (the functor). In cosubstitution, the syntactic result is the same, leaving weak and strong generative capacity unchanged, but the derivational and semantic roles are reversed: the embedded subtree is viewed as the functor, and the embedding matrix is viewed as its semantic argument, i.e., as its nuclear scope. On this view, a quantifier taking scope amounts to entering a derivation at the exact moment that its nuclear scope has been constructed. Thus the relationship of a quantifier and its scope is constrained by DERIVATIONAL LOCALITY rather than by elementary-tree locality. 1

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ABSTRACT: Recently, it has been claimed that event semantics does not go well together with quantification, especially if one rejects syntactic, LF-based approaches to quantifier scope. This paper shows that such fears are unfounded, by presenting a simple, variable-free framework which combines a Neo-Davidsonian event semantics with a type-shifting based account of quantifier scope. The main innovation is that the event variable is bound inside the verbal denotation, rather than at sentence level by existential closure. Quantifiers can then be interpreted in situ. The resulting framework combines the strengths of event semantics and type-shifting accounts of quantifiers and thus does not force the semanticist to posit either a default underlying word order or a syntactic LF-style level. It is therefore well suited for applications to languages where word order is free and quantifier scope is determined by surface order. As an additional benefit, the system leads to a straightforward account of negation, which has also been claimed to be problematic for event-based frameworks. 1.

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.

We present a general two-step algorithm which transforms a graph expressing the semantic dependencies between the words of an utterance into logic formulae representing the different semantic interpretations of the utterance. The algorithm focuses on the scopal elements of the utterance, i.e. quantifiers and scopal predicates. First, the scope of every scopal element is computed as a subgraph of the whole graph, given an order on these elements. Second, we use these scopes with their order to build a logic formula incrementally from the most internal to the most external scopal elements. 1

This thesis investigates three topics relating to the semantics of phi features on pronouns. Part I focuses on gender features on pronouns. Following previous studies (Cooper 1983, Heim & Kratzer 1998), I claim that they are presupposition triggers. Based on this assumption, I show that predicates containing bound gendered pronouns have an assertive meaning that does not entail the gender presupposition, and further point out that such predicates pose a serious challenge for existing theories of presupposition projection, especially with respect to quantified sentences. A conclusion drawn from this discussion is that the presupposition needs to be dissociated from the assertive meaning, as in Karttunen & Peters’s (1979) two dimensional theory. However, such a theory is known to run into the so-called binding problem in quantified sentences. I propose a solution to the binding problem using the mechanism of cross-sentential anaphora, and show that the resulting theory