As far the context-dependent problem goes, it's really nice to see fairly simple, intuitive rules that produce generally high accuracy. The 2005 paper presents both a simple method of contextual analysis along with a bare-bones linear model to produce roughly 80% accuracy. Looking at the results, we also see that even examining just the most recent statement before a sentence, almost doubles the accuracy. Alas, the marginal benefits after looking further into the past drop almost to nothing. The assigned paper is a different kind of monster. Although it took some time to understand even just what was going on, the use of high-order unification to do the lexical splitting and the CCG to reconstruct the expression seemed pretty cool (when it started to make some sense). The approach is fairly complicated, and maybe not intuitive, but yielding high accuracy over multiple languages and meanings definitely marks progress.