On the characterizations of complete distributive lattices by up-sets1

This paper first describes a characterization of a lattice L which can be represented as the collection of all up-sets of a poset. It then obtains a representation of a complete distributive lattice L0 which can be embedded into the lattice L such that all infima, suprema, the top and bottom elements are preserved under the embedding by defining a monotonic operator on a poset. This paper finally studies the algebraic characterization of a finite distributive.

On wh-exclamatives and gradability. An argument from Romance

This paper discusses a type ofwh-exclamative whosewh-component and degree component do not seem to go hand in hand. These arewh-exclamatives in Catalan whose movedwh-phrase is headed by the determinerquin‘what, which’, and whose NP contains an optional DegP headed bytan‘so’ ormés‘more’. By taking a closer look at thesewh-exclamatives, we will be able to contribute to the debate on the role of gradability and of thewh-component in the semantics ofwh-exclamatives. My claim is that the DegP in thesewh-exclamatives leaves behind a degree variable that is ultimately bound by an expressive speech act operator. Following Castroviejo (2006) and building on Rett (2009), I adhere to the claim thatwh-exclamatives in Catalan are necessarily scalar as a requirement of the expressive operator. Moreover, as a downward-monotonic operator, I show that it licenses upward-directed inferences, which ensures thatwh-exclamatives express unexpectedness toward a high degree.