# Propositional formula

2010 Mathematics Subject Classification: *Primary:* 03-XX [MSN][ZBL]

A *propositional formula* is
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 $(A\mathbin\&B)$, $(A\lor B)$, $(A\supset B)$, 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

[Wó] | R. Wójcicki, "Theory of logical calculi", Kluwer (1988) pp. 13; 61 MR1009788 Zbl 0682.03001 |

[Zi] | Z. Ziembinski, "Practical logic", Reidel (1976) pp. Chapt. V, §5 Zbl 0372.02001 |

**How to Cite This Entry:**

Propositional formula.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Propositional_formula&oldid=43578