Despite the ubiquity of ambiguity in natural language, it is often ignored or deliberately removed in semantic parsing tasks, which generally assume that a given surface form has only one correct logical form. We attempt to address this shortcoming by introducing AmP, a framework, dataset, and challenge for parsing with linguistic ambiguity. We define templates and generate data for five well-documented linguistic ambiguities. Using AmP, we investigate how several few-shot semantic parsing systems handle ambiguity, introducing three new metrics. We find that large pre-trained models perform poorly at capturing the distribution of possible meanings without deliberate instruction. However, models are able to capture distribution well when ambiguity is attested in their inputs. These results motivate a call for ambiguity to be explicitly included in semantic parsing, and promotes considering the distribution of possible outputs when evaluating semantic parsing systems.
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