In logic, the symbol ⊨, ⊧ or is called the double turnstile. It is often read as "entails", "models", "is a semantic consequence of" or "is stronger than".[1] It is closely related to the turnstile symbol , which has a single bar across the middle, and which denotes syntactic consequence (in contrast to semantic).

Meaning

The double turnstile is a binary relation. It has several different meanings in different contexts:

Typography

In TeX, the turnstile symbols and are obtained from the commands \vDash and \models respectively. In Unicode it is encoded at U+22A8 TRUE (HTML ⊨ · ⊨, ⊨)

In LaTeX there is the turnstile package, which issues this sign in many ways, including the double turnstile, and is capable of putting labels below or above it, in the correct places. The article A Tool for Logicians is a tutorial on using this package.

See also

References

  1. ^ Nederpelt, Rob (2004). "Chapter 7: Strengthening and weakening". Logical Reasoning: A First Course (3rd revised ed.). King's College Publications. p. 62. ISBN 0-9543006-7-X.
  2. ^ Open Logic Project, First-order logic (p.7). Accessed 4 January 2022.