The Four Valued Logic

The law

The contradiction

｛P∧-P∧(P⇔-P)∧-(P⇔-P)｝=T2

Four value logic has the law of the contradiction .

This is most different from Lukasiewicz's "Three valued logic" and his "Many-valued logic"

This law in this four valued logic is the expansion of the contradiction of 2-valued logic.

Because every propositions have either of four truth values which can exist only in exclusive,

this logical rule is natural in this logic. So, this logic is the extended logic from 2-valued logic.

The excluded middle

｛P∨-P∨(P⇔-P)∨-(P⇔-P)｝=T1

Four valued logic has the law of the excluded middle.

This law is the extension of the excluded middle of the binary logic.

Every proposition have either value of four truth values which can exist only exclusively.

If all propositions have either of four truth values, the proposition with the middle between 4 truth values can not exist.

So,the excluded middle have to be defined naturally in this logic.

The tautology

｛P≡P｝=T1,T3,T4

The tautology of four valued logic is the extension of the tautology of the binary logic.

This is very different from 2-valued logic and very important for our communication.