Duality means that for any logical formula Y, if "+"is replaced by "+",0 is replaced by 1 and 1 is replaced by 0, a new logical formula Y' is obtained, which is the dual formula of Y. Obviously, Y and Y' are dual to each other.
Duality in propositional logic: In propositional formula A, only conjunctions and (∧), or (∨) and not (┐ ?) are included, and ∨ is changed into ∧ and ∧ is changed into ∨. If a still contains 0 or 1, then. For example, the dual formula A * = ┐ (p ∨1) of the propositional formula A = ┐ (p ∧ 0).
Theorem 1: A and A* are dual, P, P2 ... and Pn are atomic independent variables appearing in A and A*, then ┐ A (P, ..., PN).
Theorem 2: Let A* and B* be dual forms of A and B, respectively. If A
Extended data
If the dual form of a logical function expression is the original function expression itself, that is, f'= f, then the function f is called a self-dual function. For example, a function is a self-dual function.
Because: f' = (A C+B) (A C) = (A B) (C B) (A B) (A C) = A (B C) (A C)+B (B C) (A C).
Baidu encyclopedia-duality
Baidu encyclopedia-duality theorem