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A vertical stroke with two bars, meaning 'entails' or 'models'.
Also known as: Entails, Models sign, Semantic consequence
The double turnstile says that whatever makes the left-hand assumptions true makes the right-hand formula true as well. It is a claim about meaning rather than about derivation, and the difference from the single turnstile is the difference between semantics and proof.
States semantic entailment: every interpretation making the assumptions true also makes the conclusion true.
Contexts: Mathematics
Is also read 'models' when written between a structure and a formula, saying the structure satisfies the formula.
Contexts: Mathematics
An upright stroke of full height with two short parallel horizontal lines joining its middle and extending to the right.
One means true in every model, the other means derivable.