A Deductive Account of Quantification in LFG

TL;DR

This paper presents a deductive, logic-based framework using linear logic and LFG to analyze quantifier scope and anaphora, offering a direct, computationally flexible approach that avoids additional mechanisms like Cooper storage.

Contribution

It introduces a novel deductive approach combining LFG and linear logic to model quantifier scope without extra mechanisms, enhancing computational flexibility.

Findings

Correctly models quantifier scope interactions

Provides a direct logical representation of quantifiers

Preliminary Prolog implementation developed

Abstract

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.