Semantic Parsing of Pre-university Math Problems

Proceedings of the 55th Annual Meeting of the Association for Computational Linguistics, pages 2131–2141 Vancouver, Canada, July 30 - August 4, 2017. c⃝2017 Association for Computational Linguistics https://doi.org/10.18653/v1/P17-1195 Proceedings of the 55th Annual Meeting of the Association for Computational Linguistics, pages 2131–2141 Vancouver, Canada, July 30 - August 4, 2017. c⃝2017 Association for Computational Linguistics https://doi.org/10.18653/v1/P17-1195 Semantic Parsing of Pre-university Math Problems Takuya Matsuzaki1, Takumi Ito1, Hidenao Iwane2, Hirokazu Anai2, Noriko H. Arai3 1 Nagoya University, Japan {matuzaki,takumi i}@nuee.nagoya-u.ac.jp 2 Fujitsu Laboratories Ltd., Japan {iwane,anai}@jp.fujitsu.com 3 National Institute of Informatics, Japan arai@nii.ac.jp Abstract 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 shal- low 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% preci- sion and 56% recall. 1 Introduction Frege and Russell, the initiators of the mathemati- cal logic, delved also into the exploration of a the- ory of natural language semantics (Frege, 1892; Russell, 1905). Since then, symbolic logic has been a fundamental tool and a source of inspira- tion in the study of language meaning. It suggests that the formalization of the two realms, mathe- matical reasoning and language meaning, is ac- tually the two sides of the same coin – probably, we could not even conceive the idea of formaliz- ing language meaning without grounding it onto mathematical reasoning. This point was first clari- fied by Tarski (1936; 1944) mainly on formal lan- guages and then extended to natural languages by Davidson (1967). Montague (1970a; 1970b; 1973) further embodied it by putting forward a terrify- ingly arrogant and attractive idea of seeing a natu- ral language as a formal language. The automation of end-to-end math problem solving thus has an outstanding status in the re- Define the two straight lines L1 and L2 on the xy-plane as L1: y = 0 (x-axis) and L2: y = √ 3x. Let P be a point on the xy-plane. Let Q be the point symmetric to P about the straight line L1, and let R be the point symmetric to P about the straight line L2. Answer the following questions: (1) Let (a, b) be the coordinates of P, then represent the coordinates of R using a and b. (2) Assuming that the distance between the two points Q and R is 2, find the locus C of P. (3) When the point P moves on C, find the maximum area of the triangle PQR and the coordinates of P that gives the maximum area. (Hokkaido Univ., 1999-Sci-3) Figure 1: Example problem search themes in natural language processing. The conceptual basis has been laid down, which …

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