Propositional formula

An expression constructed from propositional variables (cf. Propositional variable) by means of the propositional connectives (cf. Propositional connective) $\&,\lor,\supset,\neg,\equiv$ (and possibly others) in accordance with the following rules: 1) each propositional variable is a propositional formula; and 2) if $A,B$ are propositional formulas, then so are $(A\&B)$, $(A\lor B)$, $(A\supset B)$, and $(\neg A)$.

If $\sigma$ is a set of propositional connectives (a fragment), then a propositional formula in the fragment $\sigma$ is a propositional formula in whose construction rule 2) only connectives from $\sigma$ are used.

References

[a1]	Z. Ziembinski, "Practical logic" , Reidel (1976) pp. Chapt. V, §5
[a2]	R. Wójcicki, "Theory of logical calculi" , Kluwer (1988) pp. 13; 61