*sorry if I'm double-posting*
As for where 'getting computers understanding predicate logic' is, I'm
not sure what to say, but I always thought that first-order predicate
logic was the foundation of declarative languages like prolog.
Anyhow, as I understand the state of Machine Translation,
everyone is investigating hybrid models of various dynamic
programming algorithms to raise BLEU scores-- everyone's invested in
the statistical (i.e. NOT interlingual) approach, and trying to figure
out how to maximize performance. I think that there would be real
advantages to using lojban as an interlingual medium, instead of
essentially trying to imitate humans through machine learning, but
when you have huge corpora of bilingual (or better) natural language
data and virtually no bilingual corpora with lojban, it's just
infeasible. There were a few attempts to use Esperanto for that
purpose a while back (even before this paper), and no one seems to
cite them, except as failures.
Here's a really good up-to-date intro to MT:
http://docs.google.com/Doc?docid=0AYZKIeNnTBe2ZGd4azRrZm1fNTI2ZnpnYmRrZ2g
And a powerpoint version with lots of diagrams:
http://people.csail.mit.edu/people/koehn/publications/tutorial2003.pdf
Here's the origin of those two documents, if you're interested in more:
http://www.statmt.org/