Hobbs, J. R., & Shieber, S. M. (1987). An algorithm for generating quantifier scopings. Computational Linguistics, 13, 47-63.
The syntactic structure of a sentence often manifests quite clearly the predicate-argument structure and relations of grammatical subordination. But scope dependencies are not so transparent. As a result, many systems for representing the semantics of sentences have ignored scoping or generated scopings with mechanisms that have often been inexplicit as to the range of scopings they choose among or profligate in the scopings they allow. In this paper, we present an algorithm, along with proofs of some of its important properties, that generates scoped semantic forms from unscoped expressions encoding predicate-argument structure. The algorithm is not profligate as are those based on permutation of quantifiers, and it can provide a solid foundation for computational solutions where completeness is sacrificed for efficiency and heuristic efficacy.