Variations on an Original Theme

Variations on an Ordering Theme with Constraints

We investigate the problem of finding a total order of a finite set that satisfies various local ordering constraints. Depending on the admitted constraints, we provide an efficient algorithm or prove NP-completeness. We discuss several generalisations and systematically classify the problems.

Variations on a theme.

A ring satisfying x = x is necessarily commutative. We consider a variety of weaker forms of this condition and show that many but not all of them imply commutativity. We also present a variety of elementary proofs of the fact that x = x implies commutativity.

Variations on a Theme

Variations on a Montagovian theme

What are the objects of knowledge, belief, probability, apriority or analyticity? For at least some of these properties, it seems plausible that the objects are sentences, or sentence-like entities. However, results from mathematical logic indicate that sentential properties are subject to severe formal limitations. After surveying these results, I argue that they are more problematic than ofte...

Improving WYSIWYG Search: Variations on an Experiential Theme

The Problem As the quantity and availability of information have increased unboundedly, our ability to distill from the information ocean the particular knowledge we need has not kept pace. Ramesh Jain has noted that what is really needed is a data infrastructure that supports the extraction and communication of insight and experience [1]. One of the problems he observes with current query-base...