TY - GEN

T1 - Solving geometry problems using a combination of symbolic and numerical reasoning

AU - Itzhaky, Shachar

AU - Gulwani, Sumit

AU - Immerman, Neil

AU - Sagiv, Mooly

PY - 2013

Y1 - 2013

N2 - We describe a framework that combines deductive, numeric, and inductive reasoning to solve geometric problems. Applications include the generation of geometric models and animations, as well as problem solving in the context of intelligent tutoring systems. Our novel methodology uses (i) deductive reasoning to generate a partial program from logical constraints, (ii) numerical methods to evaluate the partial program, thus creating geometric models which are solutions to the original problem, and (iii) inductive synthesis to read off new constraints that are then applied to one more round of deductive reasoning leading to the desired deterministic program. By the combination of methods we were able to solve problems that each of the methods was not able to solve by itself. The number of nondeterministic choices in a partial program provides a measure of how close a problem is to being solved and can thus be used in the educational context for grading and providing hints. We have successfully evaluated our methodology on 18 Scholastic Aptitude Test geometry problems, and 11 ruler/compass-based geometry construction problems. Our tool solved these problems using an average of a few seconds per problem.

AB - We describe a framework that combines deductive, numeric, and inductive reasoning to solve geometric problems. Applications include the generation of geometric models and animations, as well as problem solving in the context of intelligent tutoring systems. Our novel methodology uses (i) deductive reasoning to generate a partial program from logical constraints, (ii) numerical methods to evaluate the partial program, thus creating geometric models which are solutions to the original problem, and (iii) inductive synthesis to read off new constraints that are then applied to one more round of deductive reasoning leading to the desired deterministic program. By the combination of methods we were able to solve problems that each of the methods was not able to solve by itself. The number of nondeterministic choices in a partial program provides a measure of how close a problem is to being solved and can thus be used in the educational context for grading and providing hints. We have successfully evaluated our methodology on 18 Scholastic Aptitude Test geometry problems, and 11 ruler/compass-based geometry construction problems. Our tool solved these problems using an average of a few seconds per problem.

KW - Geometry

KW - Reasoning

KW - Synthesis

UR - http://www.scopus.com/inward/record.url?scp=84893920020&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-45221-5_31

DO - 10.1007/978-3-642-45221-5_31

M3 - ???researchoutput.researchoutputtypes.contributiontobookanthology.conference???

AN - SCOPUS:84893920020

SN - 9783642452208

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 457

EP - 472

BT - Logic for Programming, Artificial Intelligence, and Reasoning - 19th International Conference, LPAR 2013, Proceedings

T2 - 19th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning, LPAR 2013

Y2 - 14 December 2013 through 19 December 2013

ER -