Truth tables of 4-valued logic plain text version 1998.4

1. negation -p (corrected at 1999.03)

This is the same rule as the negation of 2-valued logic , which denies the excluded proposition.(Q&A20)

p　 -p -p  -p  -p

T1　    T2 T3  T4

T2  T1      T3  T4

T3  T1 T2       T4

T4  T1 T2 T3　

2. equivalence p=q

This is the same rule as the equivalence of 2-valued logic. But,in case of 3rd and 4th valued proposition, the truth value of equivalence is the same as the value of proposition. This case is different from 2-valued logic,because the identity of 3rd valued proposition is defined that it is not same but is not different, and the identity of 4th valued proposition is defined that it is not itself.

= T1 T2 T3 T4

T1 T1 T2 T2 T2

T2 T2 T1 T2 T2

T3 T2 T2 T3 T2

T4 T2 T2 T2 T4

3. implication p=>q

This is the most important rule of this logic. This implication has considerably complex shape compared with that of binary logic. However, this law of implication contains that of the binary logic as it is. It is important and famous case in science that the 3rd valued proposition as a former implies the 1st valued proposition as a later. Especially, it is important for logic of Buddhism that 4th valued proposition implies a 3rd valued proposition.

=> T1 T2 T3 T4

T1 T1 T2 T3 T4

T2 T1 T1 T3 T4

T3 T1 T2 T3 T4

T4 T1 T2 T3 T4

4. conjunction p&q

This is constructed by the same generative rule as the conjunction of 2-valued logic. So,this conjunction has considerably similar shape compared with that of 2-valued logic, and this conjunction contains the conjunction of the binary logic as it is. It is most important and useful that this logic has the contradiction different from Lukasiewicz's 3-valued logic. So, this logic is the extension of 2-valued logic.

&  T1 T2 T3 T4

T1 T1 T2 T2 T2

T2 T2 T2 T2 T2

T3 T2 T2 T3 T4

T4 T2 T2 T4 T4

5. disjunction pVq

This disjunction has considerably different and complex shape compared with that of 2-valued logic. It is important in law or science that the 3rd valued proposition is disjunctive to the 1st valued proposition, because its disjunction has the 3rd truth value. Especially, for logic of Buddhism, it is important that 4th valued proposition is disjunctive to the 1st valued proposition, because its disjunction has the 4th truth value. This is most important and useful logical rule for our communication. But this disjunction is same generative rule as that of 2-valued logic, so, this logic is the extension of 2-valued logic.

V  T1 T2 T3 T4

T1 T1 T1 T3 T4

T2 T1 T2 T3 T4

T3 T3 T3 T3 T3

T4 T4 T4 T3 T4

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