Well as a PhD climbing down from the ivory tower and trying
to sell ILP like its Nescafé instant powder, could be a nobel
cause for a community project like SWI-Prolog.
The original Plotkin dissertation, already posted in this SWI-Prolog
discourse forum some time ago in 2020, is a rather repelling
example for the casual Prolog user I guess?
On the other hand the academic freedom of PhD could also
yield real gold nuggets. Now I have a suspicion, since the
TOIL paper mentions polynomial complexity.
So the higher order patterns are bounded, one might have:
Q(X,Y) :- P(X,Z), R(Z,Y).
But not necessarily:
Q(X,Z,Y) :- P(X,Z), R(Z,Y).
So if such building blocks are applied, maybe its indeed
the case that the Hypothesis Space stays relatively tame,
concerning the complexity of evaluation.
Its possibly similar like trying to stay in 2-SAT and not go into
3-SAT. Means we don’t have an arbitrary factor |V|
like in this formula here?
Disclaimer: I know I am comparing apples with oranges,
since the above is for Datalog. But I guess “2nd order SLD / MIL”
doesn’t want to see itself restricted to Datalog?