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cs.LO2025
The Index and Core of a Relation. With Applications to the Axiomatics of Relation Algebra
Roland Backhouse, Ed Voermans
We introduce the general notions of an index and a core of a relation. We postulate a limited form of the axiom of choice -- specifically that all partial equivalence relations hav…
cs.LO2024
An example of goal-directed, calculational proof
Roland Backhouse, Walter Guttmann, Michael Winter
An equivalence relation can be constructed from a given (homogeneous, binary) relation in two steps: first, construct the smallest reflexive and transitive relation containing the…
cs.LO2024
The Thins Ordering on Relations
Ed Voermans, Jules Desharnais, Roland Backhouse
Earlier papers \cite{VB2022,VB2023a,VB2023b} introduced the notions of a core and an index of a relation (an index being a special case of a core). A limited form of the axiom of c…