Editing Propositional calculus (section)

=== Propositional variables ===
{{Main article|Propositional variable}}
Since propositional logic is not concerned with the structure of propositions beyond the point where they cannot be decomposed any more by logical connectives,<ref name=":13" /><ref name=":1" /> it is typically studied by replacing such ''atomic'' (indivisible) statements with letters of the alphabet, which are interpreted as variables representing statements ([[Propositional variable|''propositional variables'']]).<ref name=":1" /> With propositional variables, the {{section link||Example argument}} would then be symbolized as follows:

:'''Premise 1:''' <math>P \to Q</math>
:'''Premise 2:''' <math>P</math>
:'''Conclusion:''' <math>Q</math>

When {{mvar|P}} is interpreted as "It's raining" and {{mvar|Q}} as "it's cloudy" these symbolic expressions correspond exactly with the original expression in natural language. Not only that, but they will also correspond with any other inference with the same [[logical form]].

When a formal system is used to represent formal logic, only statement letters (usually capital roman letters such as <math>P</math>, <math>Q</math> and <math>R</math>) are represented directly. The natural language propositions that arise when they're interpreted are outside the scope of the system, and the relation between the formal system and its interpretation is likewise outside the formal system itself.