In mathematical logic and computer science the symbol has taken the name turnstile because of its resemblance to a typical turnstile if viewed from above. It is also referred to as tee and is often read as "yields", "proves", "satisfies" or "entails".
In epistemology, Per Martin-Löf (1996) analyzes the symbol thus: "...[T]he combination of Frege's Urteilsstrich, judgement stroke [ | ], and Inhaltsstrich, content stroke [—], came to be called the assertion sign." Frege's notation for a judgement of some content A
Consistent with its use for derivability, a "⊢" followed by an expression without anything preceding it denotes a theorem, which is to say that the expression can be derived from the rules using an empty set of axioms. As such, the expression
means that Q is a theorem in the system.
In proof theory, the turnstile is used to denote "provability" or "derivability". For example, if T is a formal theory and S is a particular sentence in the language of the theory then
means that S is provable from T. This usage is demonstrated in the article on propositional calculus. The syntactic consequence of provability should be contrasted to semantic consequence, denoted by the double turnstile symbol . One says that is a semantic consequence of , or , when all possible valuations in which is true, is also true. For propositional logic, it may be shown that semantic consequence and derivability are equivalent to one-another. That is, propositional logic is sound ( implies ) and complete ( implies )
In sequent calculus, the turnstile is used to denote a sequent. A sequent asserts that, if all the antecedents are true, then at least one of the consequents must be true.
In APL the symbol is called "right tack" and represents the ambivalent right identity function where both X⊢Y and ⊢Y are Y. The reversed symbol "⊣" is called "left tack" and represents the analogous left identity where X⊣Y is X and ⊣Y is Y.
In Hewlett-Packard's HP-41C/CV/CX and HP-42S series of calculators, the symbol (at code point 127 in the FOCAL character set) is called "Append character" and is used to indicate that the following characters will be appended to the alpha register rather than replacing the existing contents of the register. The symbol is also supported (at code point 148) in a modified variant of the HP Roman-8 character set used by other HP calculators.
On the Casio fx-92 Collège 2D and fx-92+ Spéciale Collège calculators, the symbol represents the modulo operator; entering will produce an answer of , where Q is the quotient and R is the remainder. On other CASIO calculators (such as on the Belgian variants—the fx-92B Spéciale Collège and fx-92B Collège 2D calculators—where the decimal separator is represented as a dot instead of a comma), the modulo operator is represented by ÷R instead.
In TeX, the turnstile symbol is obtained from the command \vdash.
In Unicode, the turnstile symbol (⊢) is called right tack and is at code point U+22A2. (Code point U+22A6 is named assertion sign (⊦).)