{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,18]],"date-time":"2026-04-18T16:20:54Z","timestamp":1776529254800,"version":"3.51.2"},"reference-count":32,"publisher":"World Scientific Pub Co Pte Ltd","issue":"07","funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61272206"],"award-info":[{"award-number":["61272206"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61802142"],"award-info":[{"award-number":["61802142"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Patt. Recogn. Artif. Intell."],"published-print":{"date-parts":[[2019,6,30]]},"abstract":"<jats:p> This paper presents an algorithm for proving plane geometry theorems stated by text and diagram in a complementary way. The problem of proving plane geometry theorems involves two challenging subtasks, being theorem understanding and theorem proving. This paper proposes to consider theorem understanding as a problem of extracting relations from text and diagram. A syntax\u2013semantics (S<jats:sup>2<\/jats:sup>) model method is proposed to extract the geometric relations from theorem text, and a diagram mining method is proposed to extract geometry relations from diagram. Then, a procedure is developed to obtain a set of relations that is consistent with the given theorem with high confidence. Finally, theorem proving is conducted by using the existing proving methods which take the extracted geometric relations as input. The experimental results show that the proposed theorem proving algorithm can prove 86% of plane geometry theorems in the test dataset of 200 theorems, which is all the theorems in the popular textbook. The proposed algorithm outperforms the existing algorithms mainly because it can extract relations not only from text but also from diagram. <\/jats:p>","DOI":"10.1142\/s0218001419400032","type":"journal-article","created":{"date-parts":[[2018,10,26]],"date-time":"2018-10-26T03:22:00Z","timestamp":1540524120000},"page":"1940003","source":"Crossref","is-referenced-by-count":27,"title":["Automatically Proving Plane Geometry Theorems Stated by Text and Diagram"],"prefix":"10.1142","volume":"33","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3342-5534","authenticated-orcid":false,"given":"Wenbin","family":"Gan","sequence":"first","affiliation":[{"name":"National Engineering Research Center for E-Learning, Central China Normal University, Wuhan, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xinguo","family":"Yu","sequence":"additional","affiliation":[{"name":"National Engineering Research Center for E-Learning, Central China Normal University, Wuhan, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ting","family":"Zhang","sequence":"additional","affiliation":[{"name":"National Engineering Research Center for E-Learning, Central China Normal University, Wuhan, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mingshu","family":"Wang","sequence":"additional","affiliation":[{"name":"National Engineering Research Center for E-Learning, Central China Normal University, Wuhan, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2019,6,7]]},"reference":[{"issue":"4","key":"S0218001419400032BIB001","first-page":"39","volume":"10","author":"Ahuja N. J.","year":"2013","journal-title":"Int. J. Comput. Sci. Issues"},{"key":"S0218001419400032BIB002","first-page":"383","volume-title":"Int. Conf. Math. Asp. Comput. Inf. Sci.","author":"An W.","year":"2015"},{"key":"S0218001419400032BIB003","doi-asserted-by":"publisher","DOI":"10.1016\/j.jsc.2018.04.007"},{"key":"S0218001419400032BIB004","doi-asserted-by":"publisher","DOI":"10.1007\/s11424-014-0316-0"},{"key":"S0218001419400032BIB005","doi-asserted-by":"publisher","DOI":"10.1142\/2196"},{"key":"S0218001419400032BIB006","doi-asserted-by":"publisher","DOI":"10.1023\/A:1006171315513"},{"key":"S0218001419400032BIB007","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2007.01.012"},{"issue":"1","key":"S0218001419400032BIB008","first-page":"83","volume":"14","author":"Gan W.","year":"2018","journal-title":"Int. J. Innov. Comput. Inf. Control (IJICIC)"},{"key":"S0218001419400032BIB009","first-page":"366","volume-title":"8th Pacific-Rim Symp. Image and Video Technology (PSIVT)","author":"Gan W.","year":"2017"},{"issue":"6","key":"S0218001419400032BIB010","first-page":"503","volume":"39","author":"Guo Q.","year":"2012","journal-title":"Comput. Sci."},{"key":"S0218001419400032BIB011","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-45221-5_31"},{"key":"S0218001419400032BIB013","doi-asserted-by":"publisher","DOI":"10.1007\/s11424-012-2048-3"},{"key":"S0218001419400032BIB014","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-46493-0_15"},{"key":"S0218001419400032BIB015","first-page":"1098","volume-title":"AAAI Conf. Artificial Intelligence (AAAI)","author":"Matsuzaki T.","year":"2014"},{"key":"S0218001419400032BIB016","first-page":"138","volume-title":"13th Int. Conf. Artificial Intelligence and Soft Computing","author":"Mukherjee A.","year":"2009"},{"key":"S0218001419400032BIB017","doi-asserted-by":"publisher","DOI":"10.1007\/s10462-009-9110-0"},{"key":"S0218001419400032BIB018","doi-asserted-by":"publisher","DOI":"10.1016\/j.patcog.2014.08.027"},{"key":"S0218001419400032BIB019","first-page":"2831","volume-title":"Conf. on Association for Advancement of Artificial Intelligence (AAAI)","author":"Seo M. J.","year":"2014"},{"key":"S0218001419400032BIB020","doi-asserted-by":"publisher","DOI":"10.18653\/v1\/D15-1171"},{"key":"S0218001419400032BIB021","doi-asserted-by":"publisher","DOI":"10.18653\/v1\/D15-1135"},{"key":"S0218001419400032BIB022","doi-asserted-by":"publisher","DOI":"10.1007\/s10618-017-0494-1"},{"issue":"1","key":"S0218001419400032BIB023","first-page":"10","volume":"6","author":"Stapleton G.","year":"2015","journal-title":"ACM Trans. Intell. Syst. Technol. (TIST)"},{"key":"S0218001419400032BIB024","doi-asserted-by":"publisher","DOI":"10.1007\/s00138-013-0548-3"},{"key":"S0218001419400032BIB025","doi-asserted-by":"publisher","DOI":"10.1109\/TMM.2015.2463218"},{"key":"S0218001419400032BIB026","first-page":"1193","volume-title":"24th Int. Joint Conf. Artificial Intelligence","author":"Wang K.","year":"2015"},{"key":"S0218001419400032BIB027","doi-asserted-by":"publisher","DOI":"10.18653\/v1\/D17-1088"},{"issue":"3","key":"S0218001419400032BIB028","first-page":"231","volume":"3","author":"Wong W.","year":"2009","journal-title":"Int. J. Intell. Inf. Database Syst."},{"key":"S0218001419400032BIB029","doi-asserted-by":"publisher","DOI":"10.1142\/9789812791085_0012"},{"issue":"8","key":"S0218001419400032BIB030","first-page":"898","volume":"28","author":"Wu W. T.","year":"2008","journal-title":"J. Syst. Sci. Math. Sci."},{"key":"S0218001419400032BIB031","first-page":"189","volume-title":"Int. Workshop on Automated Deduction in Geometry (ADG)","author":"Ye Z.","year":"2008"},{"key":"S0218001419400032BIB032","doi-asserted-by":"publisher","DOI":"10.1109\/IALP.2017.8300590"},{"key":"S0218001419400032BIB033","doi-asserted-by":"publisher","DOI":"10.3115\/1119250.1119280"}],"container-title":["International Journal of Pattern Recognition and Artificial Intelligence"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218001419400032","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,9,21]],"date-time":"2019-09-21T22:42:47Z","timestamp":1569105767000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218001419400032"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,6,7]]},"references-count":32,"journal-issue":{"issue":"07","published-online":{"date-parts":[[2019,6,7]]},"published-print":{"date-parts":[[2019,6,30]]}},"alternative-id":["10.1142\/S0218001419400032"],"URL":"https:\/\/doi.org\/10.1142\/s0218001419400032","relation":{},"ISSN":["0218-0014","1793-6381"],"issn-type":[{"value":"0218-0014","type":"print"},{"value":"1793-6381","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,6,7]]}}}