Proof trees for different modal logics | Logic tutorial | Attic Philosophy

Proof trees are a great way to build proofs and test arguments in modal logic. They're also a helpful way to understand the possible world semantics for modal logic. In the previous video, I showed you how to use proof trees for the basic system of modal logic, K. In this video, I'll show you how to extend proof trees for other modal system: KT, KD, KB, K4 and K5, as well as combinations – systems like KD45. It's much simpler than it sounds!

Correction: at 2:20, the rule written on the right should read:

¬♢A, n
|
☐¬A, n

Here's some general background on Proof Trees:

Proof Trees for Modal Logic Part 1:    • Proof Trees for Modal Logic | Attic P...  
How to use proof trees:    • Logic tutorial: how to use proof tree...  

00:00 - Intro
01:01 - Recap: modal trees
01:35 - Recap: rules for modalities
02:30 - How to construct a proof
02:47 - Other modal systems
03:22 - 5 new systems: D, T, B, 4, 5
04:33 - The D rule
05:04 - The T rule
05:28 - The B rule
05:51 - The 4 rule
06:15 - The 5 rule
06:40 - Combining modal systems
07:44 - Wrap up

If there’s a topic you’d like to see covered, leave me a comment below.

Links:

My academic philosophy page: http://markjago.net
My book What Truth Is: http://bit.ly/JagoTruth
Most of my publications are available freely here: https://philpapers.org/s/Mark%20Jago

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#logic #modality #proofs