Learning a semantic lexicon is often an important first step in building a system that learns to interpret the meaning of natural language. It is especially important in language grounding where the training data usually consist of language paired with an ambiguous perceptual context. Recent work by Chen and Mooney (2011) introduced a lexicon learning method that deals with ambiguous relational data by taking intersections of graphs. While the algorithm produced good lexicons for the task of learning to interpret navigation instructions, it only works in batch settings and does not scale well to large datasets. In this paper we introduce a new online algorithm that is an order of magnitude faster and surpasses the state-of-the-art results. We show that by changing the grammar of the formal meaning representation language and training on additional data collected from Amazon's Mechanical Turk we can further improve the results. We also include experimental results on a Chinese translation of the training data to demonstrate the generality of our approach.
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