How to Build Models for Modal Logic | Logic Tutorial | Attic Philosophy

Modal logic is all about relational models, in which possible worlds are related together in order to say which are possible relative to which. In this video, we'll find out how to build models which make a sentence true, and how to construct counter-models to a given argument in modal logic.
00:00 - Intro
00:53 - Relational Structures
02:31 - The Connectives
03:00 - Box and Diamond
03:33 - Models
04:48 - The Accessibility Relation
05:41 - Truth in a Model
08:46 - Entailment
10:04 - Validity
10:39 - The Necessitation Principle
12:57 - The Distribution Principle
14:40 - Wrap-up
If there’s a topic you’d like to see covered, leave me a comment below.
Links:
My academic philosophy page: markjago.net
My book What Truth Is: bit.ly/JagoTruth
Most of my publications are available freely here: philpapers.org/s/Mark%20Jago
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[@raimondiand]

you're so good at teaching logic

[@AtticPhilosophy]

Thanks Andrea! Hope your teaching is going well.

[@natalyakidman8365]

Your teaching is so easy to follow. Could you possibly make a video about tense logics in the future?

[@AtticPhilosophy]

Thanks! Good suggestion, I’ll give it a go.

[@grantsanders82]

I am studying via correspondence and learning these concepts from a textbook is tough and often tedious. This Logic series has been a game changer for me. Th explanations of these concepts are so easy to follow and understand and Mark really draws you in to the subject. While it might not be everyone's cup of tea, logic is something that everyone should dip their toes into at some point. Thank you Mark, great series!

[@AtticPhilosophy]

Thanks so much for this comment - that’s exactly why I make these videos, and it’s great to hear that they’re helping! Good luck on the course - feel free to drop questions here!

[@nineironshore]

This is the first time I’ve seen you build new worlds with necessity operator I wasn’t sure if you could do that

[@SatoBois]

Hello I was just confused about something, if the negation appears before the diamond and the square do we pull the negation to the variable and turn the diamond into a square and vice versa? Thanks!

[@AtticPhilosophy]

If you have ~A True, turn it into A False, and similarly, ~A False becomes A True.

[@ranam]

If three is a logic for all there exist and necessary and necessarily , nessacity like modal is there a logic for whatever because it can be used in construct in functional programming and chip level where you can change logic to computation is it out there but diamond and square means necessity but acessable in your terms is bit confusing

[@AtticPhilosophy]

There's logics of computation - usually based on intuitionistic logic and intuitionistic type theory. There, proofs are identified with possible computations, or possible runs of the system.

[@ranam]

@@AtticPhilosophy sure sir I will try

[@JoshKings-tr2vc]

I know this is old, but I just face a bit of curiosity enticing me. It seems that these modal symbols have to do with the relational states instead of the state itself, (ie. Describes something about the states around it that are accessible).

[@AtticPhilosophy]

The symbols [] and aren’t really about states at all - they’re about the status of propositions, necessary or possible. They’re interpreted as quantifiers over related states. Not sure that was what you were asking tho!

[@JoshKings-tr2vc]

@@AtticPhilosophy OH! Yes, that makes it much clearer and makes more sense that way. Thank you!