guys you all are computer and or math people so like, if i am solving a tableaux/truth tree and have this formula
(P ∨ Q) ∧ (¬R → S) ∧ (¬(T ∨ U)) ∧ V
how do i solve this? ik that for multiple conjuctions consisting of literals you just write the components all underneath each other but like what if the components are expandable themselves? how/in what order do i break them down
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cc @tiskaanplacholdr@comp.lain.la @Merc@lab.nyanide.com @enigmatico@mk.absturztau.be ik its not math directly but still cc @shibao did you have to do this during your degree cc @lucy@netzsphaere.xyz @nik you guys dont even have degrees but your brains are prolly massive
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@vivi I’m going to give you a couple hints. Let’s see if you can figure it out on your own.
First, break down the problem into parts. Work with each parenthesis first. For instance, start with (P \vee Q) (That’s the standard OR table). Then work on (\neg R \rightarrow S).
When working on each case, do the following. Make a table of four rows. The first column is the first predicate. The values are T, T, F, F in that order. Then, if the predicate is negated, make another column right next to the first with the inverse (F, F, T, T). Then put the other predicate next to it (V, F, V, F). You need (2^n) rows in your table, where n is the number of predicates.
Once you have your table ready, make another row with the whole predicated. Like (\displaystyle{\neg R \rightarrow S }). Following the two last columns, figure out the logic.
You’ll notice that the table for (\displaystyle{\neg R \rightarrow S }) is the same as for another logic operation (it’s equivalent to that logic operation). So you can simplify this to that other logic operation.
The same goes for (\displaystyle{\neg (T \vee U)}). Once you figure out it’s logic, you can just simplify to another logic operation.
Once you have those figured out, make a final table of truth. Place two parenthesis in two rows and compute the AND. Then place the next one and compute the AND. So on, until you complete the whole table.
Take note of the equivalent tables of truth (alternative forms) so that you can memorize them, as they will help you simplify more complex problems.
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@enigmatico@mk.absturztau.be that wasnt rly what i was even asking for but honestly i learned something anyway this seems better than writing a massive gigachonker whenever i use truth tables for something, thank you !
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@tiskaanplacholdr@comp.lain.la @shibao@misskey.bubbletea.dev @nik@misskey.bubbletea.dev @enigmatico@mk.absturztau.be @lucy@netzsphaere.xyz @Merc@lab.nyanide.com the example is not important, i am just using it to ask my quesstions abt trees since i am practicing trees rn
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tiskaanplacholdr@comp.lain.la
tiskaanplacholdr@comp.lain.la
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@tiskaanplacholdr@comp.lain.la @shibao@misskey.bubbletea.dev @nik@misskey.bubbletea.dev @enigmatico@mk.absturztau.be @lucy@netzsphaere.xyz @Merc@lab.nyanide.com but i figured out how it works im p sure since someone dmed me smth similar to whatever i ended up working out for myself so i think i got i tthank you
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@vivi @tiskaanplacholdr@comp.lain.la @Merc@lab.nyanide.com @enigmatico@mk.absturztau.be @lucy@netzsphaere.xyz @nik i loved these in school honestly. i even took a math class that goes into then in more detail lol
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tiskaanplacholdr@comp.lain.la
tiskaanplacholdr@comp.lain.la
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@tiskaanplacholdr@comp.lain.la @nik@misskey.bubbletea.dev @enigmatico@mk.absturztau.be @vivi@misskey.bubbletea.dev @lucy@netzsphaere.xyz @Merc@lab.nyanide.com a class about proofs, it started with these (im talking about my real analysis class again)
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Lucy [hiatus era] 𒌋𒁯
lucy
next life im gonna get born into a supportive middle class family or else im gonna abort myself taking casualties in the process
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@lucy @shibao @nik @enigmatico @Merc @tiskaanplacholdr
you guys dont even have degrees
? this wasnt a value judgement? dont just ignore the subclause or whatever the thing starting with “but” is, it gives that statement most of its meaning
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tiskaanplacholdr@comp.lain.la
tiskaanplacholdr@comp.lain.la
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tiskaanplacholdr@comp.lain.la
tiskaanplacholdr@comp.lain.la
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@arcana@fedi.layer02.net @lucy@netzsphaere.xyz @tiskaanplacholdr@comp.lain.la @Merc@lab.nyanide.com @shibao@misskey.bubbletea.dev @nik@misskey.bubbletea.dev @enigmatico@mk.absturztau.be yea arcana is correct, i was being like "i am asking you because you two arent as retarded as i am where i need a preplaned curriculum broken down into bite sized pieces that point me in the right direction to learn this, chances are that you (and taylor) will just know about this through self study"
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@vivi i do not know how a formal logic or math or anything works 😶 sry it is something ive been meaning to learn
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tiskaanplacholdr@comp.lain.la
tiskaanplacholdr@comp.lain.la
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@tiskaanplacholdr@comp.lain.la @Merc@lab.nyanide.com @shibao@misskey.bubbletea.dev @nik@misskey.bubbletea.dev @enigmatico@mk.absturztau.be @lucy@netzsphaere.xyz you let an emacs user teach a logic class ONCE
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@vivi I read “truth table” instead of “truth tree”
Maybe this can help you: https://www.formallogic.com/en/truth-tree-solver
Also https://www.csus.edu/indiv/m/mayesgr/phl60/classnotes/deduction%20chapter3.pdf
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@enigmatico@mk.absturztau.be holy shit that tree solver is so fucking sick ive been searching for a good one one but not finding it. this will make checking my results so much simpler, thank you so much
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You'd break the expression down using the order of operations into an Abstract Syntax Tree (ie, imagine rewriting this as a Scheme expression) with the variables as leaves then you'd solve each subtree expression working your way from the leaves up to the root. Fortunately even though there are 7 variables they aren't shared between expressions, which makes this task much easier.
You might find the attached documents helpful
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@vivi Also the calculator breaks down each case sequentially (because machines), but if you break down the non-branching ones first, you reach the same conclusion. I just tested it.
The key here is, break them step by step (in big chunks if necessary), go for the non-branching rules first, then the branching ones. Then stop as soon as you see a contradiction.
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demorgan also appears to apply for ¬(T ∨ U)
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@scathach@stereophonic.space can you use an AST to find contradictions like you would with a truth tree?
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@enigmatico@mk.absturztau.be thank you! do you know if like, i complete a tree like that, i will get all models for whatever formula I am trying to solve? because i completed one for a different formula but i am not getting all of the models i do if i do a truth table for the same formula
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