[lkb] LKB Type Hierarchy

[Ann Copestake]

> I remember Ann saying that the algorithm was due to Carpenter and/or 
> Penn, which would have some irony since it is not in TRALE and I am 
> using the LKB to compute TRALE signatures.

If I recall (and I could very easily be wrong) is that Gerald Penn
invented an algorithm independently and published it in ACL/EACL,
stating (incorrectly) that the LKB didn't do type completion, despite
the fact we'd had an implementation in the LKB for some years at that
point.

Again, if I recall, the first type completion algorithm we had was one
I invented and implemented in the LKB, which added types
incrementally, but didn't produce an optimal solution in terms of the
number of types.  Ulrich Callmeier then implemented a proper lattice
solution in PET which John Carroll (I think - might have been Rob or
perhaps oe - I'll check if anyone wants accurate information) then
reimplemented in the LKB, replacing my code.  I think the Callmeier
version is based on Ait-Kaci.  

Best,

Ann