The extended law of 4-valued logic plain text version 1998.4

1. contradiction

[ p&-p&(p<=>-p)&-(p<=>-p) ] =T2

This 4-valued logic has the law of the contradiction. This is the extended law of contradiction of 2-valued logic. This is most different to the Lukasiewicz's "3-valued logic" and his "many-valued logic". Because every proposition have either of four truth values in the four valued logic, which can exist only in exclusive, this logical rule is natural law in this logic.

2. excluded middle

[ pV-pV(p<=>-p)V-(p<=>-p) ] =T1

This is extended law of excluded middle of 2-valued logic,too. Every proposition have either value of four truth values which can exist only exclusively. If all propositions have either of four truth values in this logic, the proposition with the middle value between 4 truth values can not exist. So,the excluded middle have to be defined naturally in this logic.

3. tautology

[ p=p ] =T1,T3,T4

This is extended law of tautology of 2-valued logic.This tautology of four valued logic have three truth values, because tautology of the 3rd and 4th truth valued propositions have a same truth value to this propositions. This is very different character from 2-valued logic.

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