Arm rules and arm rule discovery in knowledge bases

Rules are important for knowledge bases as they allow for logical reasoning and inference. Rule learning extracts patterns from existing knowledge, mainly focusing on first-order logic rules where atoms represent relations with variables for entity positions and rules are often in the form of closed paths. However, in reality, rules should not be limited to relations alone. They may also include specific entities and may take the form of an open path. In this study, we introduce a novel type of rule in knowledge bases, which we term “arm rules”. Specifically, an arm is the predicate-object portion of a knowledge triple, and an arm rule states that the existence of any arm following a head entity $h$ forces or forbids the presence of certain other arms or relations following $h$. We also present the fundamental properties of these rules and introduce the rule discovery problem for such rules. Two algorithmic solutions are presented. One modifies the existing PCA confidence algorithm to this setting, while the other uses factor graph modelling framework and the belief propagation (or sum-product) algorithm therein. These two solutions are evaluated empirically using both real and synthetic data sets. Our experimental results demonstrate a superior performance of the factor graph approach.