eolas/Logic/Proofs/Disjunction_Introduction.md

---
categories:
  - Logic
tags: [derivation-rules]
---

# Disjunction Introduction

This rule can seem a little odd: like we are randomly introducing an additional proposition without giving any justification. However this is just a consequence of the fact if $P$ is true, so is $P \lor Q$ since disjunction is not the same as conjunction: only one disjunct needs to be true for the compound disjunction to be true. This is represented in the context of [truth-trees](Truth-trees.md#disjunction-decomposition) by the fact that truth can pass up via either branch of a disjunction pattern.
This rule is sometimes also referred to (confusingly) as _Addition_.

![](/_img/disjunc-intro.png)
Initial commit, pure MD 2022-04-23 13:26:53 +01:00			`---`
Last Sync: 2022-08-20 13:00:04 2022-08-20 13:00:04 +01:00			`categories:`
Autosave: 2022-12-25 15:00:05 2022-12-25 15:00:05 +00:00			`- Logic`
			`tags: [derivation-rules]`
Initial commit, pure MD 2022-04-23 13:26:53 +01:00			`---`

Autosave: 2022-12-25 15:00:05 2022-12-25 15:00:05 +00:00			`# Disjunction Introduction`

Reindexing 2022-09-06 13:26:44 +01:00			This rule can seem a little odd: like we are randomly introducing an additional proposition without giving any justification. However this is just a consequence of the fact if $P$ is true, so is $P \lor Q$ since disjunction is not the same as conjunction: only one disjunct needs to be true for the compound disjunction to be true. This is represented in the context of [truth-trees](Truth-trees.md#disjunction-decomposition) by the fact that truth can pass up via either branch of a disjunction pattern.
			`This rule is sometimes also referred to (confusingly) as _Addition_.`
Initial commit, pure MD 2022-04-23 13:26:53 +01:00
Create script to rename image URLs and apply 2022-12-29 20:22:34 +00:00			`![](/_img/disjunc-intro.png)`