Generalizing Conjunctive and Disjunctive Rule Learning to Learning m-of-n Concepts

Most rule learning algorithms learn rule concepts as conjunctions and disjunct them afterwards to rule sets, a few others swap the order of conjunction and disjunction so that rule concepts are learned as disjunctions. Depending on the domain, both approaches can have advantages or disadvantages in comparison to its counterpart. Instead of learning rule concepts only as conjunctions or only as disjunctions, one can also flexibly choose between these two representations. One way to do so is by using m-of-n concepts where m of conditions must be true in order for the expression to be true. This not only covers the two extreme cases where all conditions must be true (n-of-n, conjunctions) or any of them must be true (1-of-n, disjunctions) but also a smooth transition for other values of m, analogous to a customizable activation threshold in neural networks. In this paper, we discuss possibilities how to efficiently learn m-of-n rules using similar generalization and specialization operations as for conjunctions or disjunctions. Furthermore, we adjust the state-of-the-art rule learning algorithm LORD to learn m-of-n concepts instead of plain conjunctions and present an evaluation of the technique on artificial and real-world data sets.