What is the order of operations for $p \implies q \implies r$ I've been studying mathematical logic recently and we have briefly covered the order of operations for operators like AND/OR/IMPLIES, etc.
However, we have a challenge question regarding how the following statement should be interpreted in terms of order of operations, and I don't believe we have covered this material nor can I find the same question answered online. 
The statement is
$p \implies q \implies r$
The question asks if the above statement is correctly represented by $(p \implies q) \implies r$, or $p \implies (q \implies r)$, or neither - i.e. what is the correct order of operations when there are no brackets and the two logic operators are equally weighted.
I have used a truth table to determine that the above two statements are not equivalent, but are either the logical equivalent to the first statement, or neither?
 A: The usual convention for omitting parentheses (see e.g. Herbert Enderton, A Mathematical Introduction to Logic, Academic Press (2nd ed. 2001)) is:


*

*The outermost parentheses need not be explicitly mentioned.


*The negation symbol applies to as little as possible.


*The conjunction and disjunction symbols apply to as little as possible.


*Where one connective symbol is used repeatedly, grouping is to
the right.

Thus, $p \to q \to r$ must be read as:

$p \to (q \to r)$.

But every convention may be checked with the formal specifications of the language used in your textbook.
A: The answer for the purposes of your course (or if you were to see it in a paper specifically on logic) may be different, but in general mathematical usage this is shorthand for "$p\Rightarrow q$ and $q\Rightarrow r$", similar to constructs like $a\leq b\leq c$. 
(If something other than this is meant, I think parentheses should always be used.)
A: I don't know how widely used it is, but I find the following convention to be the most natural and convenient:
Descending Order of Precedence for Logical Operators


*

*Innermost most brackets from left to right

*NOT ($\neg$) from right to left

*AND ($\land$) from left to right

*OR ($\lor$) from left to right

*IMPLIES ($\implies$) from left to right

*IFF ($\iff$) from left to right


Examples


*

*$P\implies Q \implies R$
would be interpreted as $[P\implies Q ]\implies R$.

*$A\land B\space \lor  C \land \neg D$ would be interpreted as
$[A\land B] \lor [ C \land [\neg D]]$.


But, as Mauro said, "Every convention may be checked with the formal specifications of the language used in your textbook."
