# On Verifying and Engineering the Well-gradedness of a Union-closed Family

@article{Eppstein2007OnVA, title={On Verifying and Engineering the Well-gradedness of a Union-closed Family}, author={D. Eppstein and J. Falmagne and Hasan Uzun}, journal={ArXiv}, year={2007}, volume={abs/0704.2919} }

Abstract Current techniques for generating a knowledge space, such as QUERY, guarantee that the resulting structure is closed under union, but not that it satisfies wellgradedness, which is one of the defining conditions for a learning space. We give necessary and sufficient conditions on the base of a union-closed set family that ensures that the family is well-graded. We consider two cases, depending on whether or not the family contains the empty set. We also provide algorithms for… CONTINUE READING

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