What are the rules for the use of dots rather than parentheses in logical formulae?

What are the rules of omission of parentheses of formulas in mathematical logic ?

in my text , first order logic mathematical logic by angelo margaris ed 1990 dover , the paretheses is omitted for example in page 49 ,

$S$ $\rightarrow$ $.$ $P$ $\rightarrow$ $Q$ $:$$\rightarrow$$:$$S$$\rightarrow$$P$ $.$$\rightarrow$ $.$ $S$$\rightarrow$ $Q$

when the paretheses should be ?!!

how can i translate this " ." points to the right parentheses ??

what are the rules of these translation in general ?

"What are the rules of omission of parentheses?" The answer is: different rules in different texts!

But what is really being asked is something different, i.e. "What are the rules for using dots instead of parentheses?" [and I have edited the title question to fit]. Again, though, the answer is that there are different rules in different texts. Church's Mathematical Logic (1956) is a canonical text here, though Church's rules are slightly different from Principia's. There's a slightly simpler set of rules, as I recall, in Robbin's Mathematical Logic. (1969) Anyway, the shared basic idea for using dots is revealed in the rules for getting rid of them again in favour of brackets:

A dot/dots to the immediate left of an implication sign indicates a right bracket, and its matching left bracket would appear as far left as we can go before encountering a higher number of dots.

Symmetrically for a dot/dots to the immediate right of an implication sign: this indicates a left bracket, and its matching right bracket would appear as far right as we can go before encountering a higher number of dots.

And we are to eliminate single dots before double dots, etc. Phew!

That sounds messy, but in practice isn't at all bad. So consider ...

$$S \to . P \to Q :\to:S \to P .\to. S \to Q$$

$$S \to (P \to Q) :\to:S \to P .\to. S \to Q$$

$$S \to (P \to Q) :\to:(S \to P) \to. S \to Q$$

$$S \to (P \to Q) :\to:(S \to P) \to (S \to Q)$$

$$(S \to (P \to Q)) \to:(S \to P) \to (S \to Q)$$

$$(S \to (P \to Q)) \to ((S \to P) \to (S \to Q))$$

You might wonder, indeed, about the virtues of this kind of bracketing system! But in fact, if you stick to single dots and mix with the use of parentheses it can be surprisingly readable. But I can't immediately think of any book (first) published in the last thirty years that uses the dotty system: it has fallen into disuse.

I think this should rather read $$ S.\to.P\to Q:\to:S\to P.\to.S\to Q$$ If I remember correctly, the number of dots in such a notation marks the precedence, hence this is $ S.\to.P\to Q$ and $S\to P.\to.S\to Q$ joined by a $\to$ and similarly, $ S.\to.P\to Q$ is $S$ and $P\to Q$ joined by a $\to$ and $S\to P.\to.S\to Q$ is $S\to P$ and $S\to Q$ joined by a $\to$. Thus in "readable" form all this becomes $$ \bigl(S\to(P\to Q)\bigr)\to\bigl((S\to P)\to(S\to Q)\bigr)$$ Note that the dot-count is reflected here by the size of parentheses.