We have been developing an end-to-end math problem solving system that accepts natural language input. The current paper focuses on how we analyze the problem sentences to produce logical forms. We chose a hybrid approach combining a shallow syntactic analyzer and a manually-developed lexicalized grammar. A feature of the grammar is that it is extensively typed on the basis of a formal ontology for pre-university math. These types are helpful in semantic disambiguation inside and across sentences. Experimental results show that the hybrid system produces a well-formed logical form with 88% precision and 56% recall.

This paper reports on an experiment where 795 human participants answered to the questions taken from second language proficiency tests that were translated to their native language. The output of three machine translation systems and two different human translations were used as the test material. We classified the translation errors in the questions according to an error taxonomy and analyzed the participants’ response on the basis of the type and frequency of the translation errors. Through the analysis, we identified several types of errors that deteriorated most the accuracy of the participants’ answers, their confidence on the answers, and their overall evaluation of the translation quality.