Propositional logic

Summary

Propositional logic is the part of logic that studies propositions and the connectives that join them. Its formulas are made from propositional variables with connectives such as $\neg$, $\land$, $\lor$, $\to$ and $\leftrightarrow$. It does not look inside a proposition, so it has no variables for objects and no quantifiers.

Remarks

Other names are sentential logic and propositional calculus. In classical propositional logic, the value of a formula depends only on the values of its variables. A truth table computes it. Predicate logic extends propositional logic with predicates and quantifiers.

Explanations

L1 human

In propositional logic, a sentence such as "$7$ is prime" is one unit $p$. You study only how such units combine with "not", "and", "or" and "if ... then". For example, $p \lor \neg p$ is true whatever $p$ says.