---
tag: C7YWCR87QJ
kind: concept
name: Paraconsistent logic
msc: [03B53]
sources:
  - url: https://en.wikipedia.org/wiki/Paraconsistent_logic
same_as:
  wikidata: Q426592
  wikipedia: Paraconsistent logic
---

## Summary

A paraconsistent logic is a logic in which a contradiction does not imply every statement.
In classical and [[intuitionistic logic|Q11N8X99FK]], the principle of explosion derives any $\psi$ from $\varphi$ and $\neg\varphi$; paraconsistent logics reject it.
They allow reasoning with inconsistent information, such as a database with conflicting entries, without collapse.

## Explanations

### L1 human

In ordinary logic, one contradiction ruins everything: from "$p$" and "not $p$" you can prove anything at all.
A paraconsistent logic blocks this, so a contradiction stays local.
Suppose a database says both "the train leaves at 9" and "the train does not leave at 9".
It should not let you conclude that the moon is made of cheese.