Logic: order of precedence

Hello Plato Quote:

Originally Posted by

**Plato** ...

In formal logic the order of precedence is: $\displaystyle \equiv \; \Rightarrow \; \vee \; \wedge \;\neg$.

...

Would you like to confirm that this order of precedence is from lowest precedence to highest? I think many people (myself included) would have written this in reverse order - from highest to lowest.

Grandad

Logic: order of precedence

Hello Plato Quote:

Originally Posted by

**Plato** Reading from left to right the order of precedence is from highest to lowest.

I am in the habit of following Copi’s conventions. Here is a example from his last book:

$\displaystyle P \Rightarrow Q \vee \neg R \wedge S\text{ is rendered }P \Rightarrow \left(Q \vee \left[ {\left( {\neg R} \right)\wedge S} \right]\right)$.

But as I said, in a forum such as this it is best to use groupings for clarity.

Sorry, but you leave me still confused. In your posting where you referred to an order of precedence, you said it was

$\displaystyle \equiv \; \Rightarrow \; \vee \; \wedge \; \neg$

and in this post, you say that this reads from left to right, highest to lowest.

And yet your example would appear to demonstrate the opposite: namely that the highest precedence (i.e the operation that is carried out first) is given to $\displaystyle \neg$, then $\displaystyle \wedge$, and so on. Thus your interpretation of $\displaystyle P \Rightarrow Q \vee \neg R \wedge S$ is exactly the same as mine.

So are we talking at cross-purposes here, and we mean different things by 'highest to lowest'?

Grandad