Consider a set A of first-order sentences a1, ..., an describing some Turing machine M. Let h be the sentence asserting "at some point the machine halts". We have that A |= h iff indeed at some point M halts. And if that is the case then the sentence g = (a1 & ... & an) β h is valid and thus deducible.
Though what if the machine doesn't halt?
My first impression was that then in turn we would be able to refute g, but soon I realised that this would only be the case if its negation was valid, and the negation of a nonvalid sentence is not valid of course. So of course if the machine doesn't halt we can't always prove that it doesn't halt.
So, is this correct? I am still overall confused though. I can see that the negation of a nonvalid sentence is not valid, yes, but I can't make the connection... why can we always prove valid sentences, why can't we in general decide the validity/satisfiability of a first-order sentence (I know how to prove it from the fact that we cannot decide implication) but I STILL feel something missing... so if anyone can help me, maybe go Socratic on me or can tell what is it that I'm missing...
I was watching a YouTube video, and the presenter said to read this paper. Well, I did some googling, hit some paywalls, pdf previews, but not the whole paper, and of course the classic 'you don't have permission to access this server' error.
As a computer science student, I have often been confronted with the Entscheidungsproblem and the work done by Alonzo Church and Alan Turing that showed no general solution to it can exist. However I never really understood the significance of this or what it really means in a practical sense. Can anyone shed some light on this topic for me and explain what the consequences of the Entscheidungsproblem are?
What exactly is the Entsheidungsproblem from David Hilbert, I am doing research on Alan Turing and have encountered this, I do not understand what I've read on this problem, so perhaps someone could explain it like I'm 5?
Do your worst!
It really does, I swear!
For context I'm a Refuse Driver (Garbage man) & today I was on food waste. After I'd tipped I was checking the wagon for any defects when I spotted a lone pea balanced on the lifts.
I said "hey look, an escaPEA"
No one near me but it didn't half make me laugh for a good hour or so!
Edit: I can't believe how much this has blown up. Thank you everyone I've had a blast reading through the replies π
Theyβre on standbi
Pilot on me!!
Buenosdillas
Dad jokes are supposed to be jokes you can tell a kid and they will understand it and find it funny.
This sub is mostly just NSFW puns now.
If it needs a NSFW tag it's not a dad joke. There should just be a NSFW puns subreddit for that.
Edit* I'm not replying any longer and turning off notifications but to all those that say "no one cares", there sure are a lot of you arguing about it. Maybe I'm wrong but you people don't need to be rude about it. If you really don't care, don't comment.
When I got home, they were still there.
What did 0 say to 8 ?
" Nice Belt "
So What did 3 say to 8 ?
" Hey, you two stop making out "
I won't be doing that today!
You take away their little brooms
This morning, my 4 year old daughter.
Daughter: I'm hungry
Me: nerves building, smile widening
Me: Hi hungry, I'm dad.
She had no idea what was going on but I finally did it.
Thank you all for listening.
There hasn't been a post all year!
