what is the difference between formula and the abbrevation of a formula?

Question

there is a problem which is asking me to determine whether a string is a formula or an abbrevation of a formula

but i don't know the diffrence of formula and the abbrevation of a formula

i know the definition of a formula , but what about the abbrevation of it ? what does it mean ?

how can i get it from a fromula ?

so my question is :

what is the diffrence between formula and the abbrevation of a formula ?

can you give examples to make the diffrence clear ?

Answer 1

It will depend entirely on the local conventions of the text you are using. To give a very simple example from propositional logic:

1. Some texts take the basic connectives to be $\neg$ and $\to$, and then introduce $\lor$ with the rule that $(A \lor B)$ is an abbreviation of $(\neg A \to B)$.

2. But another text can take $\neg$ and $\lor$ as basic, and then introduce $(A \to B)$ as an abbreviation of $(\neg A \lor B)$.

3. Other texts again might have all of $\neg$, $\land$, $\lor$, $\to$ as basic connectives introduced on a par.

As I say, you'll just have to see by inspecting the details of your text whether it counts $(A \lor B)$, for example, as a formula in the official strict sense or merely as a useful 'slang' abbreviation for one.