Modal Logic Semantics | Attic Philosophy
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- เผยแพร่เมื่อ 2 ก.ค. 2024
- Modal logic is the logic of possibility and necessity, past and future, knowledge and belief, and dynamic change. It's one of the most exciting areas of logic to learn, and one of the best for philosophers and linguists. In this tutorial video, we'll look at how to understand what the key concepts mean, in terms of possible world (Kripke) semantics.
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
More videos on modal logic coming next! 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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Instagram: / atticphilosophy
Twitter: / philosophyattic
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Thank you for making this video! I love the enthusiasm in your voice, making learning so fun.
Thanks! Much appreciated!
@@AtticPhilosophy
Hey Attic philosophy! Very much like your work and videos explaining this not so taught subject :) Id be happy to give my 2 cebts with some constructive critisicm ^^
Your presentation is very clear, and well communicated, and the visuals are spot on.
Theres a bit of a feeling of hopping from
subject to subject, from trees to axioms to proofs back to trees again semantics though there were semantics before but again... a bit jumbled up, maybe a bit more of a transition from a topic to another or a table of contents.
The explination of each subject feels messy with to few examples, leaves quite a bit to be desired, and to be frank - I don't know if I could say I actually learned how to properly reiterate the skills you introduce, even in the most simplest of way, it seems lacking.
Apologies if it seems harsh a bit, thats my feedback and hope it helps!😁
Loving this series so far Dr. Jago. What I would like to see are some examples of good English language deductive arguments that are best proved with modal logic. A good classical logic example of what I mean is something like "It is raining or the dog is not wet ; The dog is wet. Therefore it is raining." Like, I can convert it into symbols in order to prove the conclusion from the premises. It would be nice to see an analogous example for sentences like "It is necessary that X" or even "I believe X" or "I know that X".
It would also be nice to see some English-language scenarios which help motivate why you might choose K4 versus K45 versus KB as a "good" foundation for the deductive argument. Or maybe why the extra rules that something like K5 gives you would NOT be appropriate,
Hopefully that makes sense. Greetings from the USA!
Good idea! Here's a simple alethic example:
P1 It's necessary that either p or q
P2 Not p
C Therefore, q
Some good examples come from epistemic modalities: 'If one knows that p, then p' as Kp -> p
And temporal modalities: 'If it's always going to be p or q, and today isn't p, then today is q'
As to why we might prefer one system to another, it depends on how we read [] and . If alethic ('necessary' and 'possible'), then S5 is very plausible: what's necessary is necessarily necessary; what's possible is necessarily possible. But 5 is not so plausible for epistemic uses: we don't know all the things we don't know (~Kp doesn't seem to imply K~Kp).
@@AtticPhilosophy What does epistemic Kp correspond to in alethic modal logic? Box p or Diamond p?
[]p. It's saying: in all epistemic possibilities (for the agent in question), p.
@@AtticPhilosophy The alethic example only works if we assume that every world has an arrow that connects back to itself. Otherwise there could be some world W such that "p v q" is true in every world that W can see, but false in W itself.
@@Nicoder6884 That's right. Nearly everyone believes that 'necessarily' is factive, which amounts to reflexivity (every world has an arrow to itself). But as you say, it's perfectly ok to have logical systems which lack this feature.
Keep up good work!
Thanks, I’ll try!
These are amazing
Thanks!
if it is always the case a -> b, then for any world a -> b
[ ] (a -> b) = [ ] a -> [ ] b
super clear examples
Thanks!
I was trying to figure out which modal logic system corresponds to a partial order relation, but it seems that the property of antisymmetri is not included in any of the systems. Or can it be implied from the other properties?
I can't comprehend w
Weather your saying modal or model?
I would truly appreciate if you could answer this. I have looked everywhere online, and I believe there is something that is vague about modal logic. Does the valuation function need to have an infinite domain? For example, the valuation function V is defined as V: F x W -> {true, false} , where F is a collection of sentences and W is the set of worlds in the model. It is never specified what kind of set F is. Is it always the infinite set containing all the possible sentences that can be built in the formal language of modal logic (let's call it L)? Or is F just a subset of L? I'm confused about this and I can't find an answer anywhere. Thank you for reading my message
Valuations assign true or false to each sentence letter, p,q,r etc., not to every sentence of the language. Complex sentences get assigned a truth-value by the recursive clauses, based on a valuation. There are (usually) countably many sentence letters p,q,r… (and so countably many sentences is total). Countable = same size infinity as the natural numbers.
@@AtticPhilosophy Thanks, so does V assign a truth value to every single primitive sentence in the whole language L (and never just a finite subset of Lp)? (Lp is the subset of L containing all and just the primitive sentences of L)
@@user-wt7vb4yv1s Yes, otherwise, for some p, pv~p wouldn't be true.
13:28 Distribution doesn't seem to always hold for epistemic modality. It seems like one could know "A --> B" and know "A", but not know "B" since they do not know how to use implication elimination. I also suppose that by that line of reasoning, necessitation does not hold for epistemic modality either; just because a statement is valid does not mean it is known.
Epistemic modalities are really tricky! The issue is known as 'the problem of logical omniscience': just because something is valid, or necessarily true, doesn't mean we automatically know it. And relatedly, you can know p->q and know p without knowing q. (Although some people deny this!) If you want to do epistemic modalities without these features, you need to go beyond possible world semantics. Either impossible worlds (my favourite), or use some other approach entirely.
do paraconsistent logic
Already ahead of you! Try these ones:
Paraconsistent logic th-cam.com/video/l_ricFIfzMo/w-d-xo.html
Three-valued logic: th-cam.com/video/buwONfUZMXE/w-d-xo.html
No fact of the matter: th-cam.com/video/fZLg1r1zapg/w-d-xo.html
This binary true or false model makes me nervous, the actual real world ain't like that.
Sure, language is often vague, but logical sentences are meant to be perfectly precise.
Philosophy is counter intuitive- if you wanted to be a philosopher you need to train yourself for all the people who will oversimplify just because they have preconceived notions about it.
@@AtticPhilosophyI'm gonna have to rewatch to see wtf I meant by my comment, on a video about modal logic 😂😂🥰