Experience-based learning of symbolic numerical constraints

Learning symbolic-level numerical constraints is key to use abstractions in effective reasoning and transfer of knowledge for robot systems. We investigate this problem in an experience-based learning framework which uses inductive logic programming as the learning method. Our particular focus is on learning numerical constraints which is an open issue for ILP systems. Some approaches overcome this by using background knowledge given by domain experts. However, using expert knowledge is both expensive and domain dependent. To obtain more general solutions, numerical constraints should be induced by the robot system itself. For this purpose, we present a constraint induction method based on lazy evaluation, designed for deriving general numerical constraints from observations. We extend Aleph, an existing ILP system based on inverse entailment, with a constraint induction approach using a constraint solver. We analyze our method on some sample scenarios and demonstrate the cases where our method can induce the target concept while the prior lazy evaluation method cannot. Our results indicate that our method can generalize numerical constraints by the self observations of robots.