''k'' conditions ''d'' serial ''t'' reflexive ''b'' reflexive symmetric ''s '' reflexive transitive ''s '' reflexive euclidean euclidean property along reflexivity yields symmetry transitivity euclidean property obtained well symmetry transitivity hence accessibility relation ''r'' reflexive euclidean ''r'' provably symmetric transitive well hence models ''r'' equivalence relation ''r'' reflexive symmetric transitive prove frames produce set valid sentences frames
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