On Pregroups, Freedom, and (Virtual) Conceptual Necessity

Pregroups were introduced in (Lambek, 1999), and provide a founda-tion for a particularly simple syntactic calculus. Buszkowski (2001) showed that free pregroup grammars generate exactly the -free context-free lan-guages. Here we characterize the class of languages generable by all pre-groups, which will be shown to be the entire class of recursively enumerable languages. To show this result, we rely on the well-known representation of recursively enumerable languages as the homomorphic image of the inter-section of two context-free languages (Ginsburg et al., 1967). We define an operation of cross-product over grammars (so-called because of its behaviour on the types), and show that the cross-product of any two free-pregroup grammars generates exactly the intersection of their respective languages. The representation theorem applies once we show that allowing ‘empty cat-egories ’ (i.e. lexical items without overt phonological content) allows us to mimic the effects of any string homomorphism.

Eliding the derivation: A minimalist formalization of ellipsis

Abstract In this paper I use the formal framework of minimalist grammars to implement a version of the traditional approach to ellipsis as 'deletion under syntactic (derivational) identity', which, in conjunction with canonical analyses of voice phenomena, immediately allows for voice mismatches in verb phrase ellipsis, but not in sluicing. This approach to ellipsis is naturally implemented in a parser by means of threading a state encoding a set of possible antecedent derivation contexts through the derivation tree. Similarities between ellipsis and pronominal resolution are easily stated in these terms. In the context of this implementation, two approaches to ellipsis in the transformational community are naturally seen as equivalent descriptions at different levels: the LF-copying approach to ellipsis resolution is best seen as a description of the parser, whereas the phonological deletion approach a description of the underlying relation between form and meaning

On the Form-Meaning Relations Definable by CoTAGs

Kobele GM, Michaelis J. On the Form-Meaning Relations Definable by CoTAGs. In: Proceedings of the 11th International Workshop on Tree Adjoining Grammars and Related Formalisms (TAG+11). Paris; 2012: 207-213

LF-Copying without LF

A copying approach to ellipsis is presented, whereby the locus of copying is not a level of derived syntactic structure (LF), but rather the derivation itself. The ban on prepo-sition stranding in sprouting follows without further stipulation, and other, seemingly structure sensitive, empirical generalizations about elliptical constructions, including the preposition stranding generalization, follow naturally as well. Destructive operations which ‘repair ’ non-identical antecedents are recast in terms of exact identity of deriva-tions with parameters. In the context of a compositional semantic interpretation scheme, the derivational copying approach to ellipsis presented here is revealed to be a particular instance of a proform theory, thus showing that the distinctions between, and arguments about, syntactic and semantic theories of ellipsis need to be revisited

On Pregroups, Freedom, and (Virtual) Conceptual Necessity

Pregroups were introduced in (Lambek, 1999), and provide a foundation for a particularly simple syntactic calculus. Buszkowski (2001) showed that free pregroup grammars generate exactly the ɛ-free context-free languages. Here we characterize the class of languages generable by all pregroups, which will be shown to be the entire class of recursively enumerable languages. To show this result, we rely on the well-known representation of recursively enumerable languages as the homomorphic image of the intersection of two context-free languages (Ginsburg et al., 1967). We define an operation of cross-product over grammars (so-called because of its behaviour on the types), and show that the cross-product of any two free-pregroup grammars generates exactly the intersection of their respective languages. The representation theorem applies once we show that allowing ‘empty categories’ (i.e. lexical items without overt phonological content) allows us to mimic the effects of any string homomorphism.