Our goal is to develop models that allow a robot to understand or "ground" natural language instructions in the context of its world model. Contemporary approaches estimate correspondences between an instruction and possible candidate groundings such as objects, regions and goals for a robot's action. However, these approaches are unable to reason about abstract or hierarchical concepts such as rows, columns and groups that are relevant in a manipulation domain, Figure 1. We introduce a probabilistic model that incorporates an expressive space of abstract spatial concepts as well as notions of cardinality and ordinality. Abstract concepts are introduced as explicit hierarchical symbols correlated with concrete groundings. Crucially, the abstract groundings form a Markov boundary over concrete groundings, effectively de-correlating them from the remaining variables in the graph which reduces the complexity of training and inference in the model. Empirical evaluation demonstrates accurate grounding of abstract concepts embedded in complex natural language instructions commanding a robot manipulator. The proposed inference method leads to significant efficiency gains compared to the baseline, with minimal trade-off in accuracy.
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