Reclaim the Lost Promise of the Semantic Web

I was eager to learn about the latest developments in the Semantic Web through the lens of a "new kind of semantics" as Abraham Bernstein et al. explored in their Viewpoint "A New Look at the Semantic Web" (Sept. If I understand it correctly, semantics is a mapping function that leads from manifest expressions to elements in a given arbitrary domain. Based on set theory, logicians have developed a framework to set up such mapping for formal languages like mathematics, provided one can fix an interpretation function. On the other hand, 20th-century logicians (notably Alfred Tarski) warned of the limits of the framework when applied to human languages. Now, to the extent it embraces a set-theoretic semantics (as in the W3C's Ontology Web Language), the Semantic Web seems to be facing exactly such limitations or experiencing, dealing with, and suffering them.