Syntax of Propositional Logic

Formulas of $P{L}^0$ are made up from:

• countably infinite propositional variables
  • ${\mathcal{V}}_0:=\left\{P,Q,R,P^1,P^2,\dots \right\}$
• connectives
  • ${\Sigma }_0:=\{T,F,\neg ,\vee ,\wedge ,\Rightarrow ,\iff ,\dots \}$
• well-formed propositional formulas (wffs)
  • propositional variables
  • $T$ true and $F$ false
  • negations
  • Conjunction
  • Disjunktion
  • Implication
  • equivalences / biimplications
  • where the variables used for the formulas are again wffs

A single formula without any connectives is called an Atom.

The list above can be formulated in terms of a Grammar: