Automated conjecturing III

Property-relations conjectures
  • C. E. Larson
  • N. Van Cleemput


Discovery in mathematics is a prototypical intelligent behavior, and an early and continuing goal of artificial intelligence research. We present a heuristic for producing mathematical conjectures of a certain typical form and demonstrate its utility. Our program conjectures relations that hold between properties of objects (property-relation conjectures). These objects can be of a wide variety of types. The statements are true for all objects known to the program, and are the simplest statements which are true of all these objects. The examples here include new conjectures for the hamiltonicity of a graph, a well-studied property of graphs. While our motivation and experiments have been to produce mathematical conjectures—and to contribute to mathematical research—other kinds of interesting property-relation conjectures can be imagined, and this research may be more generally applicable to the development of intelligent machinery.


Automated conjecturing Automated mathematical discovery Property-relations conjectures 

Mathematics Subject Classification (2010)

05C45 05C69 05-04 


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The authors are grateful to the referees, whose comments helped us clarify and improve this paper.


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© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of Mathematics and Applied MathematicsVirginia Commonwealth UniversityRichmondUSA
  2. 2.Department of Applied Mathematics, Computer Science and StatisticsGhent UniversityGhentBelgium

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