A Deductive Account of Quantification in LFG
<|reference_start|>A Deductive Account of Quantification in LFG: The relationship between Lexical-Functional Grammar (LFG) functional structures (f-structures) for sentences and their semantic interpretations can be expressed directly in a fragment of linear logic in a way that explains correctly the constrained interactions between quantifier scope ambiguity and bound anaphora. The use of a deductive framework to account for the compositional properties of quantifying expressions in natural language obviates the need for additional mechanisms, such as Cooper storage, to represent the different scopes that a quantifier might take. Instead, the semantic contribution of a quantifier is recorded as an ordinary logical formula, one whose use in a proof will establish the scope of the quantifier. The properties of linear logic ensure that each quantifier is scoped exactly once. Our analysis of quantifier scope can be seen as a recasting of Pereira's analysis (Pereira, 1991), which was expressed in higher-order intuitionistic logic. But our use of LFG and linear logic provides a much more direct and computationally more flexible interpretation mechanism for at least the same range of phenomena. We have developed a preliminary Prolog implementation of the linear deductions described in this work.<|reference_end|>
@article{dalrymple1994a,
    title={A Deductive Account of Quantification in LFG},
    author={Mary Dalrymple (Xerox PARC, Palo Alto CA), John Lamping (Xerox PARC,
  Palo Alto CA), Fernando Pereira (AT&T Bell Laboratories, Murray Hill NJ),
  Vijay Saraswat (Xerox PARC, Palo Alto CA)},
    journal={arXiv preprint arXiv:cmp-lg/9404009},
    year={1994},
    number={ISTL-NLTT-1993-06-01},
    archivePrefix={arXiv},
    eprint={cmp-lg/9404009},
    primaryClass={cmp-lg cs.CL}
}