To install click the Add extension button. That's it.

The source code for the WIKI 2 extension is being checked by specialists of the Mozilla Foundation, Google, and Apple. You could also do it yourself at any point in time.

4,5
Kelly Slayton
Congratulations on this excellent venture… what a great idea!
Alexander Grigorievskiy
I use WIKI 2 every day and almost forgot how the original Wikipedia looks like.
Live Statistics
English Articles
Improved in 24 Hours
Added in 24 Hours
Languages
Recent
Show all languages
What we do. Every page goes through several hundred of perfecting techniques; in live mode. Quite the same Wikipedia. Just better.
.
Leo
Newton
Brights
Milds

Double turnstile

From Wikipedia, the free encyclopedia

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:

  • To show semantic consequence, with a set of sentences on the left and a single sentence on the right, to denote that if every sentence on the left is true, the sentence on the right must be true, e.g. . This usage is closely related to the single-barred turnstile symbol which denotes syntactic consequence.
  • To show satisfaction, with a model (or truth-structure) on the left and a set of sentences on the right, to denote that the structure is a model for (or satisfies) the set of sentences, e.g. . This is typically done inductively along with restricting the range of a variable assignment, a function mapping each variable symbol to a value in it might hold. [2]
    • In this context, the semantic consequence in the previous list can be stated as "For a given model , if then ".
  • To denote a tautology, . which is to say that the expression is a semantic consequence of the empty set.
  • You can also use this symbol as follows: ⊭ to denote the statement 'does not entail'.

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 (⊨, ⊨) , and the opposite of it is U+22AD NOT TRUE () .

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.


This page was last edited on 25 March 2022, at 11:14
Basis of this page is in Wikipedia. Text is available under the CC BY-SA 3.0 Unported License. Non-text media are available under their specified licenses. Wikipedia® is a registered trademark of the Wikimedia Foundation, Inc. WIKI 2 is an independent company and has no affiliation with Wikimedia Foundation.