Not naive at all! One common categorisation of ILP approaches is by whether they search for programs from the most to the least general (least general is more specific), or from the least to the most general. Some approaches do a little bit of both. Approaches that search from general to specific are known as "top-down" and approaches that search from specific to general are known as "bottom-up".
The "top" and "bottom" terms refer to a lattice of generality between programs, where generality is typically measured by subsumption or entailment etc. Subsumption in particular is a syntactic relation (that implies a semantic one, entailment) so "searching" a space of logic programs ordered by subsumption means in practice that the space of programs is constructed by generalising or specialising some starting program by means of syntactic transformation according to subsumption (e.g. a first order clause can be specialised by adding literals to it: P(x):- Q(x) subsumes P(x):- Q(x), R(x). The simplest intuition is to remember that by adding more conditions to a rule we make it harder to satisfy).
A more general program entails more logical atoms and ILP algorithms are typically trained on both positive and negative example atoms of a target program, so top-down approaches begin with an over-general program that entails all the positive examples and some or all of the negative examples and specialise that program until it entails only the positive examples. Bottom-up approaches start with an over-specialised program that entails none of the positive examples and generalise it until it entails all the positive examples.
The mathematics of generalisation are at the core of ILP theory and practice. It's what sets ILP apart from statistical machine learning which is based on the mathematics of optimisation.
The "top" and "bottom" terms refer to a lattice of generality between programs, where generality is typically measured by subsumption or entailment etc. Subsumption in particular is a syntactic relation (that implies a semantic one, entailment) so "searching" a space of logic programs ordered by subsumption means in practice that the space of programs is constructed by generalising or specialising some starting program by means of syntactic transformation according to subsumption (e.g. a first order clause can be specialised by adding literals to it: P(x):- Q(x) subsumes P(x):- Q(x), R(x). The simplest intuition is to remember that by adding more conditions to a rule we make it harder to satisfy).
A more general program entails more logical atoms and ILP algorithms are typically trained on both positive and negative example atoms of a target program, so top-down approaches begin with an over-general program that entails all the positive examples and some or all of the negative examples and specialise that program until it entails only the positive examples. Bottom-up approaches start with an over-specialised program that entails none of the positive examples and generalise it until it entails all the positive examples.
The mathematics of generalisation are at the core of ILP theory and practice. It's what sets ILP apart from statistical machine learning which is based on the mathematics of optimisation.