A Tableaux Calculus for Ambiguous Quantification

TL;DR

This paper introduces a tableaux calculus for reasoning about ambiguous quantification in natural language, combining disambiguation with deduction to improve reasoning efficiency.

Contribution

It provides a sound and complete tableaux calculus that interleaves disambiguation with deduction, enhancing reasoning about ambiguous expressions.

Findings

The calculus is sound and complete for ambiguous quantification.

Interleaving disambiguation with deduction improves proof efficiency.

The method advances logical reasoning in natural language processing.

Abstract

Coping with ambiguity has recently received a lot of attention in natural language processing. Most work focuses on the semantic representation of ambiguous expressions. In this paper we complement this work in two ways. First, we provide an entailment relation for a language with ambiguous expressions. Second, we give a sound and complete tableaux calculus for reasoning with statements involving ambiguous quantification. The calculus interleaves partial disambiguation steps with steps in a traditional deductive process, so as to minimize and postpone branching in the proof process, and thereby increases its efficiency.