Is there an algebra of logic with a logical subtraction operator?

Question

Electronics

There are three operations in Boolean algebra: AND(conjunction), OR(disjunction), NOT(negation);
which can be converted to mathematical expressions as: *, +, 1-;
respectively. Thus, the expression NOT (A AND B) AND (A OR B), aka XOR, can be written as
(1-(A*B))*(A+B) = A+B-(A+B) *(A*B) = A+B-(A*A*B+A*B*B)
Based on the idempotency property, we can simplify the expression to
A+BA*BA*B = A+B-2*A*B = A+B*(1-2A) = A OR (B AND NOT 2A)

truth table

A B  !2A  B&!2A  R 
0 0   1     0    0
0 1   1     1    1
1 0  -1     0    1
1 1  -1    -1    0

This is incredibly convenient for simplifying complex logical expressions, however, sometimes the result is a subtraction and the expression becomes impossible to write through Boolean algebra without inverse transformations.
Is there a logical operation that represents subtraction? Should I use the ternary number system if the result is 100% binary?
In search of material on this topic, I found only this article , which says that logical subtraction / division does not make sense, as well as a bunch of others about subtractors and adders that are not related to the topic.

Answer 1

Let's make a truth table for mathematical subtraction.

A B A-B
0 0 0
0 1 1
1 0 1
1 1 0

We get that A-B=A xor B, therefore -:= XOR.
Open Google: Modulo 2 addition (exclusive "or", XOR, strict disjunction, bitwise addition, mask inversion, Zhegalkin addition, logical subtraction , logical disparity) - a boolean function, as well as a logical and bit operation, in the case of two variables, the result is true if and only if one of the arguments is true and the other is false.
Accordingly, its meaning is in the mutual difference of two sets, i.e. the result does not belong to two sets at the same time.

A B (Необщая часть A) (Необщая часть B) (Объединения частей)
0 0 0 0 1
0 1 0 1 1
1 0 1 0 1
1 1 0 0 0

Answer 2

! (A || B) = (! A) && (! B)