/sci/ - Science & Math

[Anonymous No.6625510]

Has anyone else tried to design their own algebraic structure? I'm trying to come up with a variant of Boolean algebra where conjunction and disjunction aren't commutative (i.e. p ^ q =/= q ^ p in general).

[Anonymous No.6625555]

>>6625510
>conjunction and disjunction

Kill yourself you fucking CS major

[Anonymous No.6625593]

>>6625510
>design their own algebraic structure
http://ncatlab.org/nlab/show/monad
Don't bother.
>conjunction and disjunction aren't commutative
n3xt lev3l -

[Anonymous No.6625685]

If you got a non-commutative operation, I'd argue it's difficult to justify calling it the conjunction or disjunction of your theory. Those concepts don't really have many other defining properties, which you can drop.

There are temporal logics, which have a rich range of conjunctions and some are not commutative: E.g. these logic take into account a running time variable, and then there is a binary connective <span class="math">u[/spoiler] with

<span class="math">\psi u \phi[/spoiler] ... <span class="math">\psi[/spoiler] holds, at least until <span class="math">\phi[/spoiler] is also true. After <span class="math">\phi[/spoiler] has set in, <span class="math">\psi[/spoiler] is allowed to fail.

Your thread is kinda similar to the one I posted at the beginning of the week
https://archive.foolz.us/sci/thread/6621023/#q6621023
(You can use the same approach and what you then want to do is to look out for are monodial categories, which are not symmetric.)

>>6625593
I'm not sure to what extend a monad is related. (?)
In case you want to say that the subject is exhausted, that might be true. As far as possible propositional logics go, I imagine these have been classified in the 30's, see
http://en.wikipedia.org/wiki/Universal_algebra#Varieties
I think the modern shit that digs deepest is
http://en.wikipedia.org/wiki/Operad_theory

[Anonymous No.6625689]

>>6625685
wikipedia.org/wiki/Temporal_logic