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Motivated by functional interpretations of spatial language terms, and the need for cognitively plausible and practical abstractions for mobile service robots, we present a spatial representation based on the physical support of one object by another, corresponding to the preposition “on”. A perceptual model for evaluating this relation is suggested, and experiments - simulated as well as using a real robot - are presented. We indicate how this model can be used for important tasks such as communication of spatial knowledge, abstract reasoning and learning, taking as an example direct and indirect visual search. We also demonstrate the model experimentally and show that it produces intuitively feasible results from visual scene analysis as well as synthetic distributions that can be put to a number of uses.