The syntax and semantics of natural language can provide essential structural information for recognition of multiword speech. A syntactic theory based on probability-weighted context-free grammars and a Bayesian treatment of uncertainty is advanced, and then extended to take account of semantic restrictions on word combinations. A fast parser for this structure is described. For applications in speech recognition, the parser can interact with the pattern-matching hardware through lists of speech-elements with prior and posterior probabilities, and maintains those sentences which are compatible both with the input data and with the grammar with high probability.