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Improvements in cameras, computer vision, and machine learning are enabling real-time object recognition in interactive systems. Reliable recognition of uninstrumented objects opens up exciting new scenarios using the real-world objects that surround us. At the same time, it introduces the need to understand and manage the uncertainty and ambiguities that are inherent to such sensing. This paper examines this problem in the context of LEGO OASIS, a camera and projector-based system that recognizes LEGO toys and augments them with projected digital content. We focus on an interaction language to model the creation and manipulation of relationships between physical objects and their digital capabilities. We use this set of abstractions to examine different notions of recognition errors and explore interactive approaches to overcoming fundamental challenges in interactive object-aware systems.