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.
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.