Please add comments to "A comparison of Stochastic Logic Programs and Bayesian Logic Programs" by Aymeric Puech and Stephen Muggleton.
From James Cussens: Yes, these translations seem to work. The one in section 4, didn't have a proof but looks believable. I noticed that you used the clause s(X) :- p(x), q(X) rather than s(X) :- p(x), p(X) was there any reason for this?
I'm uncomfortable with the idea that SLPs use a domain-frequency approach. As far as I'm concerned an SLP (together with some particular query) defines a distribution over bindings for the variables in that query. Thus an SLP is an uninterpreted mathematical object. How it is interpreted depends on the user. Similarly eg binomial distributions can represent subjective or objective probabilities (not that I believe in objective probabilities outside quantum physics!)
From Aymeric Puech: Thank you for the comments; some proofs have not been included in this (short) version of the paper, if you're interested I can send you the complete version, in which the theorem in section 4 is demonstrated (
atp02@doc.ic.ac.uk). The reason why we used the clause s(X) :- p(x), q(X) instead of the original s(X) :- p(x), p(X) is that it does not make much sense to write the Bayesian clause s(X) | p(x), p(X) (although it is correct with regard to the syntax), which would mean that s(X) is influenced by p(X) and p(X) (which will represent the same Bayesian atoms whatever the binding of X is...). Furthermore, it would be inconsistent with the remark at the end of section 2.2.
I agree with the fact that SLPs are mathematical objects which are not restricted to the definition of probabilities over a domain (in some way, the aim of the paper is to prove that SLPs are more general than that, and can define probabilities over possible worlds!). We refer to SLPs as a natural way to express probabilities over a domain because it is a straightforward approach to understand the differences between SLPs and BLPs and the way inter-translations are constructed.