What's the difference between boolean algebra and propositional logic? Are they isomorphic to each other?

What's the difference between boolean algebra and propositional logic? Are they isomorphic to each other?

I fail to see the difference between them.

boolean algebra, propositional logic, and predicate logic are all pretty similar

the different names are used to refer to distinct subtle differences between them between each field (e.g. you wont find sets in propositional, but will in predicate)

tl:dr their the same for all intents and purposes and even if you mix them up in your PhD thesis, no one will care and even if they do you are still technically correct

Its all jargon from a leftover era

who cares? the real question is why anyone would study this nonsense

lol go back to /b/

I'm pretty sure proving their isomorphism wouldn't be too hard OPEE
It would be a nice excercise too.
Do it.

>isomorphism
stop abusing notation

except prop and pred logic are very different. one is complete the other is not.

notation != concepts
btw mathematicians abuse whatever they like

Propositional logic is just about the syntax of formulas: which logical connectives are allowed in them ?

Now, what can you say about these formulas, what do they *mean*?
Boolean algebra is one answer to this question, this is called Tarski's semantics. The idea is that "A \/ B is true whenever A is true or B is true", etc.
This is the interpretation that is behind classical logic.
But it is not the only possible one. For example, Heyting-Kolmogorov is another semantics, which focuses on the probability and not on the truth of formulas.

In short: Prop logic == syntax; Boolean algebra == one possible semantics for prop logic

shut the fuck up you autist

Boolean logic is literally the same thing as propositional logic. Just a different way of talking about the same thing. They are "isomorphic" in a sense but not formally. Other logics are similarly represented by other types of algebras (Heyting algebra for intuitionistic logic for example).

Is Modal Logic worth studying or is it applied autism?

Yes, there is a correspondence between Boolean algebra and classical propositional logic. No it is not the same with classical predicate logic.

Boolean algebra is actually a special case of a Heyting algebra that has a correspondence with intuitionistic propositional logic (of which classical logic is a special case). You can take this further and show that there is a correspondence between the typed lambda calculus and intuitionistic propositional logic (see Curry Howard correspondence) as well as a correspondence between these and bicartesian closed categories (note that by adding a weird/arbitrary rule to your bicartesian closed category you can also get a correspondence to classical logic).

By looking at System F (an extension of typed lambda calculus) you can get predicate propositional logic too. In general there are many correspondences between logic, type theory, and category theory. At times also with lattices (e.g. Boolean algebra and Heyting algebra). These topics are studied further in computer science because of their direct application to programming language theory.

Ignore this drooling retard .

this is whats wrong with the world.
notice the guy said nuanced
Im not a fucking genius. but Ill say being complete is nuanced

What's the point of doing that? You can prove anything with a contradiction:

1. ~p and ~~p

2. ~p

3. ~p or (((if p then q) and (if q then r)) and (p and ~r))

4. ~~p and ~p

5. ~~p

6. (((if p then q) and (if q then r)) and (p and ~r))

Is there something interesting about that way other than it's one step shorter?

They're correct though and it's not autism to know one of the most introductory concepts in formal logic.

>whats the difference in airplanes and cars
>Im a freshman
>oh they are actually pretty similar
>they are vechiles that are powered by engines
>one just happens to be for use on land and the other in air

>ACTUALLY, THEY ARE SO DIFFERENT LOL
>ONE USES FLUID DYNAMICS AND THE OTHER SOLID/ROTATIONAL HURR FUCKING DURR

>Im not a fucking genius.
No shit, you are clearly brain damaged. I'm not even the person you're responding to. Saying that this is a nuanced difference is far worse than saying that the difference between a monoid and a module is nuanced.

Moar like
>Here is a car.
>Here is a car factory.
>Durr same thing you autist! No one has time for your nuanced differences!!
Amirite?

The difference between the reals and the natural numbers is nuance bro.

No it would be like saying rowing boats and motorboats are the same thing because boats are the same. One of them is an obvious step upwards in complexity though.

lol found the math fag. heres a wake up call. I make more money than you.

fuck off loser. not everyone studies module theory in their spare time you pedagogical cancer

Yes, if you consider the fact that you can perform induction on one of them but not on the other to be nuanced then sure, but keep in mind, that would also make you a retard, so yea.

Mostly for computer scientists

It's not one step up in complexity. It's on another fucking floor.

I was being sarcastic. The difference between those two sets is maths until 1900 pretty much.

keep in mind that not everyone you talk to cares

if you are speaking to a high schooler and they ask the difference, just say its a type of numbers

no need to break out the vocab and kill enthusiasm with your autism

>I, an anonymous person on the internet, make more money than you. That means I'm better than you and I win arguments by default.
this should be pasta.

See
They were calling the difference nuanced in the context of PhD level research, not highschool.

does the OP sound like a Phd candidate to you?

Just jumping in, but i think the people who are angry at the "one is complete the other isn't" guy, are just saying that he could just have said "one has quantifier the other doesn't" instead of bringing out big words for no reason

>i, an imaginary poisson on the interjection, make more cash dough than you. that means i'm more beta as i question the axiomatic foundations of your arguments.

...

Saying that one has quantifiers really doesn't sound like a big difference. One being complete while the other is an important (fundamental) difference.

To use the natural/reals analogy: Saying that the reals cover all numbers and the natural only the possitive whole numbers really doesn't convey the very important aspect of the reals being infinitely more than the already infinitely many naturals.

While the later way of saying it might sound "overcomplicated" it's what has to be said to really convey the fundamental difference.

>Saying that one has quantifiers really doesn't sound like a big difference.
Why not?
It makes it extremely more expressive. Wittgenstein first even thought it'd be expressive enough so you can drop everything that can't be captured in that language.

...

Why not?
because he is a giant loser who wasted his 20s and 30s studying a useless subject and needs to constantly reassure himself that he is a special snowflake by explicit obfuscation masqueraded as the behavior of remaining "mathematically exact"

Yes but saying it makes it incomplete shows you just how very much more expressive it is. If you know stuff about it then both statements are fine obviously.

But saying that there are more reals than there are naturals doesn't really capture how very very very many more reals there are then naturals (to use the same analogy).

Is there a reason not to be exact?

I honestly cant tell if youre real or just an elaborate troll

Obvious troll