Any model of the world a robot constructs on the basis of its sensor data 
is necessarily both incomplete, due to the robot's limited window on the 
world, and uncertain, due to sensor and motor noise.  This paper proposes a 
logic-based framework in which such models are constructed through an 
abductive process whereby sensor data is explained by hypothesising the 
existence, locations, and shapes of objects.  Symbols appearing in the 
resulting explanations acquire meaning through the theory, and yet are 
grounded by the robot's interaction with the world.  The proposed framework 
draws on existing logic-based formalisms for representing action, 
continuous change, space, and shape, but a novel solution to the frame 
problem is employed.  Noise is treated as a kind of non-determinism, and is 
dealt with by a consistency-based form of abduction.