  This paper extends a polynomial-time parsing algorithm that resolves
structural ambiguity in input to a speech-based user interface by calculating
and comparing the denotations of rival constituents, given some model of the
interfaced application environment (Schuler 2001). The algorithm is extended to
incorporate a full set of logical operators, including quantifiers and
conjunctions, into this calculation without increasing the complexity of the
overall algorithm beyond polynomial time, both in terms of the length of the
input and the number of entities in the environment model.
