Add comments here for Representational power of probabilistic-logical models: From upgrading to downgrading" by Kristian Kersting.
From James Cussens: I'm in agreement with the spirit behind this. However, the issue is: how should this downgrading be done in practice. For example, the parameter estimation we hope to eventually produce for SLPs should be such that eg if the SLP is failure-free (and so is essentially a PCFG), the software realises this and takes available shortcuts. But there, you're not really downgrading the formalism, just exploiting peculiarities of a particular instance of it. On the other hand, if you study particular special cases of a more general formalism (ie study algorithms for LOHMMS - I wasn't aware of the relationship to SLPs, thanks), then I guess that's how you find out what these shortcuts are.
From Kristian Kersting: Dear James, thanks for the interesting comment. I agree that "downgrading" as discussed in the position statement specifies "only" the first steps towards a general understanding of PLMs. It does not provide any concrete way to come up with specially purposed algorithms but it should pave a way (I hope). First, we are forced to think about the relations among different frameworks (including the downgraded ones). Second, many interesting questions (such as semantics and how to do model estimation/selection from data) are already answered -- although in a principle way. Now, inspecting known algorithms for the more general framework should provide some initial ideas for specialized algorithms. Maybe it is a good idea to include the development and comparison of specially purposed algorithm as a third step. What do you think?