We propose a formal system for representing the available readings of sentences displaying quantifier scope ambiguity, in which  partial  scopes may be expressed. We show that using a theory of scope availability based upon the function-argument structure of a sentence allows a deterministic, polynomial time test for the availability of a reading, while solving the same problem within theories based on the well-formedness of sentences in the meaning language has been shown to be NP-hard.
['Alistair Willis', 'Suresh Manandhar']
Two Accounts of Scope Availability and Semantic Underspecification