which branch of maths studies Standard Logical Matrices

Question

In classical logic you have truthtables like:

 & | T | F  
---|---|---  
 T | T | F  
 F | F | F  

In many valued logic you have tables like:

(this one is of four valued Łukasiewicz logic)

 Cpq q= | 0 | 1 | 2 | 3 || Np || Designated  
--------|---|---|---|---||----||-----    
 p = 0  | 3 | 3 | 3 | 3 || 3  ||  no  
 p = 1  | 2 | 3 | 3 | 3 || 2  ||  no  
 p = 2  | 1 | 2 | 3 | 3 || 1  ||  yes  
 p = 3  | 0 | 1 | 2 | 3 || 0  ||  yes  

Gottwald in ( http://plato.stanford.edu/entries/logic-manyvalued/ ) calls them "Standard Logical Matrices", and I also have seen names like Cayley matrices, and many valued truthtables.
But i was wondering is there an other name for them and which branch of mathematics does study them in depth?

In short the only criteria for these tables are:

1. a set $S$ of values (four in this case)
2. a (proper) subset of $S$ called the designated values

3. an (unrestricted) number of functions:

   $S \to S$
   $S \times S \to S$
   and maybe even $S^n \to S$

That are all fundamental criteria,

(for Standard Logical Matrices there is an extra truthp reservation criteria but can be overlooked here)

I had a look into abstract algebra / universal algebra/ algebraic structures but all these fields seems only to look into systems where the matrices have to submit to some strict criteria, or only allow a very limited amount of functions.

Is there a branch of mathematics that studies these matrices in a more general way? (and what is a good introduction to this branch?)

in many valued logic you study only one (set of) Standard Logical Matrices at a time, but i am wondering is there a branch of mathematics that study them in a more general way?