On the Complexity of Inductively Learning Guarded Rules
This work addresses a foundational problem in automated reasoning and knowledge representation, with incremental contributions to complexity theory.
The paper tackles the computational complexity of learning guarded clauses in inductive logic programming, proving it is NP-complete and identifying a tractable fragment for practical use on large datasets.
We investigate the computational complexity of mining guarded clauses from clausal datasets through the framework of inductive logic programming (ILP). We show that learning guarded clauses is NP-complete and thus one step below the $σ^P_2$-complete task of learning Horn clauses on the polynomial hierarchy. Motivated by practical applications on large datasets we identify a natural tractable fragment of the problem. Finally, we also generalise all of our results to $k$-guarded clauses for constant $k$.