• Corpus ID: 238258996

Consistency between transitive relations and between cones

  title={Consistency between transitive relations and between cones},
  author={Tom Fischer},
A relation extends another relation consistently if its symmetric, respectively its asymmetric, part contains the corresponding part of the smaller relation. It is shown that there exists no finite circular chain made from two transitive relations A and B with at least one link from their asymmetric parts if and only if there exists a total preorder which consistently extends both. Additionally, this extension is uniquely determined if and only if the reflexive transitive closure of the union… 


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