Inverse Entailment

Definition

Inverse entailment is a generality relation in inductive logic programming. More specifically, when learning from entailment using a background theory B, a hypothesis H covers an example e, relative to the background theory B if and only if B ∧ H⊧e, that is, the background theory B and the hypothesis H together entail the example (see entailment). For instance, consider the background theory B:

• bird :- blackbird.

• bird :- ostrich.

and the hypothesis H:

• flies :- bird.

Together B ∧ H entail the example e:

• flies :- blackbird, normal.

This can be decided through deductive inference. Now when learning from entailment in inductive logic programming, one starts from the example e and the background theory B, and the aim is to induce a rule H that together with B entails the example. Inverting entailment is based on the observation that B ∧ H⊧e is logically equivalent to B ∧¬ e⊧¬ H, which in turn can be used to compute a hypothesis Hthat will cover the example relative to the...