{"type":"ScholarlyArticle","title":"Constraint Based Automatic Construction and Manipulation of Geometric Figures","authors":[{"name":"Richard Allen","slug":"richard-allen","given":"Richard","family":"Allen","affiliation":"Olaf College Northfield , MN 55057 USA"},{"name":"Jeanne Idt","slug":"jeanne-idt","given":"Jeanne","family":"Idt","affiliation":""},{"name":"Laurent Trilling","slug":"laurent-trilling","given":"Laurent","family":"Trilling","affiliation":"IMAG-LGI , BP 53X 38041 Grenoble cedex , FRANCE; jeanne ldt IMAG-LGI , BP 53X 38041 Grenoble cedex , FRANCE"}],"abstract":"An imJX>rtant comJX>neQt of an Intelligent Tutoring System (ITS) for teaching geometry is its capacity to transform a figure into as many different figures as JX>Ssible, yet all of which respect the same underlying logical specification. Given a logical specification for a figure, (i) a figure can be constructed automatically from the objects and properties in the speP.fication; and (ii) once constructed, one can transform a figure through displacement of any of its objects and still obtain a figure that respects the specification. For a student user, this feature provides an invaluable tool for graphical exploration and discovery of properties induced by the logical specification. Our problem domain is automatic construction of figures; and we address this issue in restricted cases using Constraint Logic Programming. We present solutions to cases in which figures can be constructed automatically and in which there is also a natural notion of completeness for our system. For this automatic figure construction system, we describe an implementation, written in Prolog III, which makes use of both constraints and coroutines provided in the language. Results of experimentation are also included, as well as ways in which the system can be extended to handle non restricted cases.","doi":null,"url":"https://ijcai.org/proceedings/1993/64","pdf":"https://ijcai.org/proceedings/1993/0064.pdf","markdown":"https://ijcai.org/proceedings/1993/64.md","bibtex":"https://ijcai.org/proceedings/1993/bibtex/64","volume":{"slug":"1993","title":"Proceedings of the Thirteenth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 1993","url":"https://ijcai.org/proceedings/1993/","year":1993,"location":"Chambéry, France","dates":"","editors":"Ruzena Bajcsy","isbn":"","publisher":"International Joint Conferences on Artificial Intelligence","doi_prefix":""},"section":"Intelligent Tutoring Systems","track":"Intelligent Tutoring Systems","number":64,"pages":{"first":453,"last":458},"keywords":[],"videos":[],"references":[{"position":1,"raw":"Allen, R., Nicolas, P., Trilling, L., \"Figure Correctness in an Expert System for Teaching Geometry,\" Proceedings of the eight biennial conference of the Canadian society for computational studies of intelligence, Ottawa, May 22-25, 1990, pp. 154-160.","title":"Figure Correctness in an Expert System for Teaching Geometry","authors":"R Allen, P Nicolas, L Trilling","year":"1990","venue":"Proceedings of the eight biennial conference of the Canadian society for computational studies of intelligence","doi":null,"url":null,"internal_url":null},{"position":2,"raw":"Allen, R., Nicolas, P., Trilling,. 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