The Mathematical Symbol "Double Vertical Bar Double Right Turnstile (⊫)"

The Double Vertical Bar Double Right Turnstile (⊫): An Examination

The Double Vertical Bar Double Right Turnstile, represented as ⊫ is a symbol with deep roots in logic and proof theory. It is often used to indicate that a certain statement or proposition is a semantic consequence of a set of premises. This article will delve into the primary applications of this symbol with two descriptive examples.

Role in Logic and Proof Theory

In the landscape of logic, the ⊫ symbol is employed to show that a proposition is a logical consequence or result, given a specific set of premises or axioms. The left side of the turnstile represents the assumptions, while the right side denotes the conclusion derived from these assumptions.

Example 1:

If we are given the premises \(P\) and \(P \rightarrow Q\), and from these, we deduce the proposition \(Q\), this relationship can be captured as:

\(P, P \rightarrow Q ⊫ Q\)

This symbolizes that given the premises \(P\) and \(P \rightarrow Q\), the conclusion \(Q\) logically follows.

Example 2:

Consider the premises: "All men are mortal" and "Socrates is a man". From these, the conclusion that "Socrates is mortal" can be drawn. In symbolic representation:

AllMenAreMortal, SocratesIsAMan ⊫ SocratesIsMortal

These instances illuminate the use of the Double Vertical Bar Double Right Turnstile in logic to express semantic consequences. As always, understanding the precise interpretation hinges on the context and the specific premises and conclusions in consideration.

Mathematical symbol 'Double Vertical Bar Double Right Turnstile'

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Codes for the ⊫ Symbol

The Symbol
Alt CodeAlt 8875
HTML Code⊫
HTML Entity⊫
CSS Code\22AB
Hex Code⊫

How To Insert the ⊫ Symbol

(Method 1) Copy and paste the symbol.

The easiest way to get the ⊫ symbol is to copy and paste it into your document.

Bear in mind that this is a UTF-8 encoded character. It must be encoded as UTF-8 at all stages (copying, replacing, editing, pasting), otherwise it will render as random characters or the dreaded �.

(Method 2) Use the "Alt Code."

If you have a keyboard with a numeric pad, you can use this method. Simply hold down the Alt key and type 8875. When you lift the Alt key, the symbol appears. ("Num Lock" must be on.)

(Method 3) Use the HTML Decimal Code (for webpages).

HTML TextOutput
<b>My symbol: &#8875;</b>My symbol: ⊫

(Method 4) Use the HTML Entity Code (for webpages).

HTML TextOutput
<b>My symbol: &VDash;</b>My symbol: ⊫

(Method 5) Use the CSS Code (for webpages).

CSS and HTML TextOutput
span:after {
content: "\22AB";}
<span>My symbol:</span>
My symbol: ⊫

(Method 6) Use the HTML Hex Code (for webpages and HTML canvas).

HTML TextOutput
<b>My symbol: &#x22AB;</b>My symbol: ⊫
On the assumption that you already have your canvas and the context set up, use the Hex code in the format 0x22AB to place the ⊫ symbol on your canvas. For example:
JavaScript Text
const x = "0x"+"E9"
ctx.fillText(String.fromCodePoint(x), 5, 5);

(Method 7) Use the Unicode (for various, e.g. Microsoft Office, JavaScript, Perl).

The Unicode for ⊫ is U+22AB. The important part is the hexadecimal number after the U+, which is used in various formats. For example, in Microsoft Office applications (e.g. Word, PowerPoint), do the following:
[Hold down Alt]
[Press x]

(The 22AB turns into ⊫. Note that you can omit any leading zeros.)
In JavaScript, the syntax is \uXXXX. So, our example would be \u22AB. (Note that the format is 4 hexadecimal characters.)
JavaScript TextOutput
let str = "\u22AB"
document.write("My symbol: " + str)
My symbol: ⊫