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What is the symbol for demonstrating syntactic conversion (transformation or translation)? For example, I want to show a calculation sequence, from $ \neg ( A \wedge B ) $ to $ \neg A \vee \neg B $. Now I just use $ \vdash $: $ \neg ( A \wedge B ) \vdash \neg A \vee \neg B $. Is there a suitable symbol to replace $ \vdash $?

Thank you.


share|cite|improve this question might help if you already know the symbol you want to use. – Asaf Karagila Mar 19 '11 at 20:07

2 Answers 2

up vote 1 down vote accepted

P :⇔ Q means P is defined to be logically equivalent to Q. This could be a suitable substitution, but I believe what you are using is best suited, since it is literally translated as "is derived from."

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The same symbol have different meaning in different literature :-) Mathematics is always evolving. – xando Mar 21 '11 at 17:24

You could use both $\Leftrightarrow$ (\Leftrightarrow) and $\equiv$ (\equiv), meaning that the statements are logically equivalent.

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You might also prefer $\iff$ (\iff), since it is easier to type. – yunone Mar 19 '11 at 23:30
That's a nice one! Even better since $\Longleftrightarrow$ (\Longleftrightarrow) is even worse ;) I think there is something like \newcommand{\iff}{\Longleftrightarrow} ;-) – Joost Mar 19 '11 at 23:36

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