---
tag: 09K9MWD2QQ
kind: concept
name: Propositional logic
aliases: [sentential-logic, propositional-calculus]
msc: [03B05]
uses: [0ZGC7ZESYN, 0XR7A7RSXB, 0M28ASWG8T, 0H5GKDTB01, 0ZNX6DQ3EJ, 0V6GAWTBYW]
sources:
  - url: https://en.wikipedia.org/wiki/Propositional_logic
    locator: lead section
same_as:
  wikidata: Q200694
  wikipedia: Propositional logic
---

## Summary

Propositional logic is the part of logic that studies [[propositions|0ZGC7ZESYN]] 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|05RSK4Q657]] computes it.
[[Predicate logic|086QKPF0A6]] 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.