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My native language is Portuguese, so I'll translate the question.

Note that I haven't found relative content to that question on my language, but I found out that one of the abbreviations means Main Connective.


I know only some part of the others abbreviations.
Can you help me to find out what the others abbreviations means? They might be correlated.
enter image description here


Thank you very much.

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    $\begingroup$ The first one is ill-formed, the $P\to \neg R\to Q$ bit doesn't make sense. And what is $w$? Do you have any idea of what the main connective is? $\endgroup$
    – Git Gud
    Apr 12, 2014 at 20:21
  • $\begingroup$ I know what main connective is, I mean, I need to know the abbreviations on the enunciation, like C.P means Main Connective, I don't know what is P.I, P.M and P.U, I know the symbols. $\endgroup$
    – André Ikvmo
    Apr 12, 2014 at 20:23
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    $\begingroup$ It might be a good idea to also post the question in portuguese below the english version. Someone can help you translate it. $\endgroup$
    – Git Gud
    Apr 12, 2014 at 20:24
  • $\begingroup$ I did, the portuguese question is also in the image, the problem is that there's only the abbreviations. $\endgroup$
    – André Ikvmo
    Apr 12, 2014 at 20:25
  • $\begingroup$ Well, where did you get this problem from? This should be explained on your notes, text or whatever. $\endgroup$
    – Git Gud
    Apr 12, 2014 at 20:28

1 Answer 1

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I think that they are connected with the formation tree for propositional formulae.

See for example : R.Smullyan, First-Order Logic (1968), page 8:

The notion of immediate subformula is given explicitly by the conditions:

(i) Propositional variables have no immediate subformulas.

(ii) $\lnot X$ has $X$ as an immediate subformula and no others.

(iii) The formulas $X \lor Y, X \land Y, X \rightarrow Y$ have $X,Y$ as immediate subformulas and no others.

We shall sometimes refer to $X,Y$ respectively as the left immediate subformula, right immediate subformula of $X \lor Y, X \land Y, X \rightarrow Y$.

The main connective is the first connective that "pops up" when you start from a "complex" formula $\alpha$ written with all the couples of parentheses and you start deleting the outermost couple; i.e.it is the connective labelling the root of the formation tree.

In $(P→(¬(Q→R)))$ is the leftmost $\rightarrow$. In $((P→(\lnot Q))→R)$ it is the rightmost.

Please, check...

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