A generalization of the laws and theorems of classical logic for truth values ​​x and y

A translation of https://dialoogid2.blogspot.com/2026/01/klassikalise-loogika-seaduste-ja.html 

 

A generalization of the laws and theorems of classical logic for truth values ​​x and y 

Karmo Talts 

 

Let's generalize the laws of logic for truth values ​​x and y. A statement P cannot have a truth value x and not have the truth value x at the same time. A statement P has a truth value x or a statement P has a truth value different from x. 

Now let's look at the theorems. If P has a truth value x, then the negation of the negation of P has the truth value x. If the assumption that P has a truth value x implies a contradiction, then P does not have the truth value x. If P has a truth value x and Q has a truth value y, then the conjunction P and Q has the lowest truth value amongat truth values ​​x and y. If P has a truth value x, then we can introduce the disjunction P has the truth value x or Q has a truth value y. If P does not have a truth value x or Q has a truth value y, then if P has the truth value x, Q has the truth value y. If P has a truth value x or Q has a truth value y, then if P does not have the truth value x, Q has the truth value y. If, when P has a truth value x, Q has a truth value y and P has the truth value x, then Q has the truth value y. If, when P has a truth value x, Q has a truth value y and Q does not have the truth value y, then P does not have thr truth value x.