In this paper we motivate a new technique for automatic recognition of hand-sketched digital ink. By viewing sketched drawings as utterances in a visual language, sketch recognition can be posed as an ambiguous parsing problem. On this premise we have developed an algorithm for ink parsing that uses a statistical model to disambignate. Under this formulation, writing a new recognizer for a visual language is as simple as writing a declarative grammar for the language, generating a model from the grammar, and ffaining the model on drawing examples. We evaluate the speed and accuracy of this approach for the sample domain of the SILK visual language and report positive initial results.