[extropy-chat] Non-classic logics

[scerir]

Technotranscendence:
> Anyone interested in them 
> as a general topic for discussion?  
> For the last year or so, I've been studying 
> them in earnest, [...]

In algebra (or algebra of operators) 
there is something called non-distributivity:
(AxBxC) =/= Ax(BxC) =/= (AxB)xC.
(Non-distributivity is different from
non-commutativity).
Is there a non-standard logic reproducing,
somehow, a property like this? 
Or is this property something usual?
In economy, sociology, politics, chemistry?
Thanks,
-serafino