@@AtticPhilosophy I don't speak for everyone, but I'd definitely like to see some worked examples and an overview of all the different logical & structural rules.
@Pitometsu
Жыл бұрын
@@AtticPhilosophy video about LJ and LJ', please! Also double-negation LK embedding into LJ. And evaluation model of LJ (and continuation-style passing as an evaluation model for LK into LJ embedding). Also it would be super interesting to learn about the Category Theory behind the Sequent Calculus semantic, could it be generalized even more? Comparison of semantic of Sequent Calculus as a formal language with semantic of logics as a formal languages.
@woosix7735
8 ай бұрын
Personally, to me this interpretation makes less sense than the one I learned: A ⊢ B can be interpreted as "Knowing A, prove B." Thus the rule "..., A ⊢ A" is interpreted as, "knowing A, I have proved A." To me the advantage of this is that you can avoid thinking about this excluded middle-like "accept and reject."
@hilikliming
28 күн бұрын
Great lecture! Would appreciate more on sequent calculus, as others said, more worked examples and LK vs LJ discussion? Attic Phil is a real gem, thank you Dr. Jago
@johncrwarner
Жыл бұрын
Ooooh, I hadn't met Sequent Calculus before so this indeed wetted my appetite for more Do you have any book recommendations on learning the Sequent Calculus?
@johncrwarner
Жыл бұрын
or even better software to help explore the ideas
@AtticPhilosophy
Жыл бұрын
This handbook article is very good (and free): mathweb.ucsd.edu/~sbuss/ResearchWeb/handbookI/ChapterI.pdf For a book, this one is very good: Proofs and Models in Philosophical Logic, Greg Restall, www.cambridge.org/core/elements/abs/proofs-and-models-in-philosophical-logic/A1907B05C24E1000270CC5B684FA7AAB
@johncrwarner
Жыл бұрын
@@AtticPhilosophy Thank you for your prompt response. Interestingly the book is cheaper as a paperback than as an eBook.
@codework-vb6er
Жыл бұрын
@@AtticPhilosophy Thanks for these links I am digging through today Saturday.
@manavkhatarkar9983
Жыл бұрын
Thanks for the video Mark :)
@AtticPhilosophy
Жыл бұрын
You’re welcome!
@alieser7770
13 күн бұрын
Interesting semantics of proofs of sequent calculus!
@ebichan_nahcibe
9 ай бұрын
Thank you very much for making this video. Just to clarify, in your proof of the law of excluded middle in the natural deduction system are you implicitly using the law of double negation?
@toe_fans
Жыл бұрын
Thanks to your videos I finally understood natural deduction for quantifiers and now im excitedly trying to learn sequent calculus, thank you so much for making these videos mate!
@AtticPhilosophy
Жыл бұрын
You’re welcome!
@Rampag394
Жыл бұрын
This is great, thanks! I was wondering, could you please do a video on the Gentzen tree-style natural deduction system (like that used in Halbach's 'Logic Manual')? That would be SO helpful!
@AtticPhilosophy
Жыл бұрын
Ok, I’ll give it a go
@martinbarra4616
Жыл бұрын
Can you make a video talking about free logic? 🙏
@AtticPhilosophy
Жыл бұрын
Good call! I'll add it to the list.
@alieser7770
13 күн бұрын
Sir, I love and appreciate you and your work
@AtticPhilosophy
3 күн бұрын
Thanks!
@kostagacinovic
3 ай бұрын
Thank you so much, this really opened my eyes
@EE-tj6pq
11 ай бұрын
Can you do a video on linear logic? It's not quite clicking for me
@roychess
Жыл бұрын
Would another way to express the ideas on the LHS and the RHS as this: it is (or would be) set of propositions would be deemed inconsistent. That is to say to the term inconsistent means I accept the LHS and at the same time reject the RHS? Also I am wondering how close is this to the principle of Identity? That is to say if I have two identical portraits of ME on wall [where one is on the left and the other is to the right] that the right portrait is ugly while the left portrait is handsome. If both portraits are identical they must be described in the same way: one can not be ugly unless both are ugly. I hope I expressed that well. Another example, is X+2 = 2 + X but the X on the right hand side is 7 but the X on the left is 2. How can that be if it is the same X (otherwise we need two different variables)? It is inconsistent!
@AtticPhilosophy
Жыл бұрын
It’s not the propositions themselves that are inconsistent, for A |- A is a proof with nothing inconsistent. Rather, it would be bad to accept the LHS but reject the RHS.
@frankavocado
Жыл бұрын
I am new to the system and would probably have not found it so easy to get without this introduction. Always assuming, of course, that I did get it. I read that LHS implies RHS when LHS is taken as a conjunction of statements, while RHS is a disjunction. In these terms I guess that, for a proof to work, at least one statement must be accepted on the LHS, and any additional statement is always accepted there, while everything on the RHS is provisionally reject-able, with the proviso that at least one statement must ultimately be accepted.
@AtticPhilosophy
Жыл бұрын
That's it - conjunction on the left, disjunction on the right.
@patrickwithee7625
Жыл бұрын
Though I can get my head around it, I can’t get used to interpreting sequents in terms of acceptance/rejection. Isn’t the left of a sequent just your assumptions and the right of a sequent just the possible conclusions, given whatever’s on the left?
@AtticPhilosophy
Жыл бұрын
Not quite as simple as “possible conclusions” on the right. Take, for example: |- p,~p. A valid sequent, but neither p nor ~p are possible conclusions, since neither is derivable from zero premises. What you can infer is their disjunction, so you could say: the disjunction of the stuff on the right is the conclusion.
@patrickwithee7625
Жыл бұрын
@@AtticPhilosophy I guess the word “conclusion” is too proofy, but clearly the right of the sequent is saying that at least one of the formulas separated by a comma holds.
@AtticPhilosophy
Жыл бұрын
@@patrickwithee7625 That's right, but no saying which, and difficult to out this in proof-theoretic-acceptable terms (many proof theorists will want to avoid 'is true' altogether). Hence the disjunctive 'either-or' reading.
@Nicoder6884
Жыл бұрын
@@AtticPhilosophy So if the stuff on the right makes up a conclusion, how exactly are we "rejecting" the stuff on the right then?
@AtticPhilosophy
Жыл бұрын
@@Nicoder6884 The idea is to think of X |- Y as saying: its bad to accept the Xs and reject the Ys.
@ЯковЛифшиц-ф1ю
Жыл бұрын
What book would you recommend for an in-depth study of logic?
@AtticPhilosophy
Жыл бұрын
There are loads of good intro & more advanced textbooks, none covers it all, so it very much depends on what you want to cover. Some good choices: Intro: Logic, by Wilfrid Hodges Logic, by Greg Restall Logic: The Laws of Truth, Nick JJ Smith Logic, its Scope & Limits, by Richard Jeffrey More advanced: Computability & Logic, Boolos & Jeffrey (a standard grad-level reference) Logic For Philosophers, Ted Sider (aimed at philosophers) Graham Priest, 2001: An Introduction to Non-Classical Logic (Good for propositional modal, intuitionistic and 3-valued logics and proof trees)
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