High Quality Content by WIKIPEDIA articles! In mathematical logic, a rational consequence relation vdash is a logical consequence relation satisfying the properties listed below.The rational consequence relation is non-monotonic, and the relation theta vdash phi is intended to carry the meaning theta usually implies phi or phi usually follows from theta. In this sense it is more useful for modeling some everyday situations than a monotone consequence relation because the latter relation models facts in a more strict boolean fashion - something either follows under all circumstances or it does not.

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