Mathematical Logic - Dandah symbol for discharging assumptions ....

In summary, the conversation is about a specific symbol called a 'dandah' and how to represent it using Latex code. The relevant text in the book Mathematical Logic by Ian Chiswell and Wilfred Hodges is referenced and it is explained that the >>cancel package<< can be used to achieve this symbol. Other authors use different methods to show a discharged assumption, such as enclosing it in square brackets or writing a number over it.
  • #1
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I am reading the book Mathematical Logic by Ian Chiswell and Wilfred Hodges (C&H) ... and am currently focused on Chapter 2: Informal Natural Deduction ...

I need help with what C&H call the 'dandah' or more specifically symbols with a dandah through them ...

The relevant text in C&H explaining and showing the use of the dandah is as follows (C&H page 17) ...
https://www.physicsforums.com/attachments/5002
In the above text we read the following:

" ... ... we discharge \(\displaystyle \phi\) by writing a dandah through it ... ... "

My question is as follows:

Is there Latex code so that we can represent \(\displaystyle \phi\) with a dandah through it as shown in the extract from C&H above ... can someone explain how such a symbol can be achieved in Latex?

Would be grateful for some help ... ...

Peter
 
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  • #2
Peter said:
I am reading the book Mathematical Logic by Ian Chiswell and Wilfred Hodges (C&H) ... and am currently focused on Chapter 2: Informal Natural Deduction ...

I need help with what C&H call the 'dandah' or more specifically symbols with a dandah through them ...

The relevant text in C&H explaining and showing the use of the dandah is as follows (C&H page 17) ...

In the above text we read the following:

" ... ... we discharge \(\displaystyle \phi\) by writing a dandah through it ... ... "

My question is as follows:

Is there Latex code so that we can represent \(\displaystyle \phi\) with a dandah through it as shown in the extract from C&H above ... can someone explain how such a symbol can be achieved in Latex?

Would be grateful for some help ... ...

Peter

Hi Peter,

What you need for this is the >>cancel package<<. In the documentation you'll find how to do this and some other similar stuff as well.
 
  • #3
Other authors show that an assumption is discharged by enclosing it in square brackets or by writing a number like (1) over it, which is then copied near the rule that discharges the assumption.
 
  • #4
Sudharaka said:
Hi Peter,

What you need for this is the >>cancel package<<. In the documentation you'll find how to do this and some other similar stuff as well.
Thanks Sudharaka ... appreciate your help ...

So I should be able to show a discharges assumption by \cancel{ \phi }

as follows: \(\displaystyle \cancel{ \phi }\)

Thanks again,

Peter

- - - Updated - - -

Evgeny.Makarov said:
Other authors show that an assumption is discharged by enclosing it in square brackets or by writing a number like (1) over it, which is then copied near the rule that discharges the assumption.
Thanks for the further help, Evgeny ...

Peter
 
  • #5
Peter said:
Thanks Sudharaka ... appreciate your help ...

So I should be able to show a discharges assumption by \cancel{ \phi }

as follows: \(\displaystyle \cancel{ \phi }\)

Thanks again,

Peter

Yes, MathJax seems to load the cancel package by default. In a document you'll have to load it in the beginning with the \usepackage command.
 
  • #6
Sudharaka said:
Yes, MathJax seems to load the cancel package by default. In a document you'll have to load it in the beginning with the \usepackage command.

In our implementation of MathJax here at MHB, we autoload all of their available packages. :D
 

1. What is the Dandah symbol used for in mathematical logic?

The Dandah symbol, also known as the turnstile symbol, is used to represent the concept of "entails" or "proves" in mathematical logic. It indicates that a conclusion can be logically derived from a set of assumptions or premises.

2. How is the Dandah symbol written?

The Dandah symbol is written as a horizontal line with a vertical line on the left side, followed by the assumptions or premises above the line and the conclusion below the line. For example:

P |- Q
Where P and Q represent statements, and the symbol |- represents the Dandah symbol.

3. Is the Dandah symbol used in all branches of mathematics?

Yes, the Dandah symbol is commonly used in all branches of mathematics, including algebra, geometry, calculus, and more. It is also used in computer science and philosophy.

4. How is the Dandah symbol different from other logical symbols?

The Dandah symbol is used specifically to indicate the relationship between assumptions and conclusions in a logical argument, while other logical symbols, such as the "and" symbol (∧) or the "if-then" symbol (→), represent different logical operations.

5. Can the Dandah symbol be used in everyday language?

While the Dandah symbol is primarily used in mathematical and logical contexts, it can also be used in everyday language to indicate that one statement or event logically follows from another. For example, "If it's raining (|-), then I will bring an umbrella." However, it is not commonly used in casual conversation.

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