Referential transparency, definiteness and unfoldability

On Referential Transparency in the Presence of Uniform Sharing

Factotum, a software system for implementing symbolic computing systems, provides an uniform subterm sharing facility based on congruence that automatically detects and imposes sharing of equivalent structures independantly of client code. In the presence of this automatic facility, the meaning of structure updates is dangerously ambiguous. We explain how we resolve this problem in the Factotum...

Indestructible Strong Unfoldability

Using the lottery preparation, we prove that any strongly unfoldable cardinal κ can be made indestructible by all <κ-closed κ+-preserving forcing. This degree of indestructibility, we prove, is the best possible from this hypothesis within the class of <κ-closed forcing. From a stronger hypothesis, however, we prove that the strong unfoldability of κ can be made indestructible by all <κ-closed ...

Preschool Children Can Assess Common Ground: Effect of Definiteness Status of Referential Terms

Zipper Unfoldability of Domes and Prismoids

We study Hamiltonian unfolding—cutting a convex polyhedron along a Hamiltonian path of edges to unfold it without overlap—of two classes of polyhedra. Such unfoldings could be implemented by a single zipper, so they are also known as zipper edge unfoldings. First we consider domes, which are simple convex polyhedra. We find a family of domes whose graphs are Hamiltonian, yet any Hamiltonian unf...

Definiteness and Indefiniteness *

The prototypes of definiteness and indefiniteness in English are the definite article the and the indefinite article a/an, and singular noun phrases (NPs) determined by them. That being the case it is not to be predicted that the concepts, whatever their content, will extend satisfactorily to other determiners or NP types. However it has become standard to extend these notions. Of the two categ...