Codish et al. have a background in SAT solving, which is somewhat related to logic programming. In SAT solving subsumption of clauses usually doesn't involve any substitutions. That's the notion of subsumption I was familiar with before reading Codish et al. Given that, extending subsumption to handle the symmetries inherent in the problem felt like a natural extension as it maintains all the relevant properties, but I also wouldn't be surprised if this was inspired by ILP.
>> In SAT solving subsumption of clauses usually doesn't involve any substitutions.
I guess not, because SAT is propositional so just substituting variables for terms would yield a ground propositional clause. Actually I wasn't even sure we say "clause" in propositional logic. Anyway Plotkin's subsumption is really based off Robinson's unification algorithm and it makes a lot more sense in that context and in the context of resolution theorem proving. Or I'm just hopelessly stuck forever thinking in the first order.
Do you know if Codish et al. were based on an earlier paper for their definition of subsumption? It really sounds like they are simply describing it, rather than introducing it as a new concept.
Edit: of course, the obvious question in my mind now is whether it would be possible to learn sorting networks using one of the ILP approaches that build on Plotkin's work and don't have to perform an expensive search of a large hypothesis space.
The paper where they introduce subsumption is "Michael Codish, Luís Cruz-Filipe, Michael Frank, and Peter Schneider-Kamp. 2016. Sorting nine inputs requires twenty-five comparisons. Journal of Computer and System Sciences 82, 3 (May 2016), 551–563." and I just realized that I lost the actual citation while editing my blog post, fixed that now.
Codish et al. have a background in SAT solving, which is somewhat related to logic programming. In SAT solving subsumption of clauses usually doesn't involve any substitutions. That's the notion of subsumption I was familiar with before reading Codish et al. Given that, extending subsumption to handle the symmetries inherent in the problem felt like a natural extension as it maintains all the relevant properties, but I also wouldn't be surprised if this was inspired by ILP.