Editing Many-valued logic (section)

=== Bochvar's internal three-valued logic ===

Another logic is Dmitry Bochvar's "internal" three-valued logic <math>B_3^I</math>, also called Kleene's weak three-valued logic. Except for negation and biconditional, its truth tables are all different from the above.<ref name="Bergmann 2008 80">{{harv|Bergmann|2008|p=80}}</ref>

{|
|
{| class="wikitable" style="text-align: center;"
|-
! width="25" | {{underset|+|∧}}
! width="25" | {{math|T}} 
! width="25" | {{math|I}} 
! width="25" | {{math|F}}
|-
! {{math|T}} 
| {{math|T}} || {{math|I}} || {{math|F}}
|-
! {{math|I}} 
| {{math|I}} || {{math|I}} || {{math|I}}
|-
! {{math|F}} 
| {{math|F}} || {{math|I}} || {{math|F}}
|}
||
||
||
{| class="wikitable" style="text-align: center;"
! width="25" | {{underset|+|∨}}
! width="25" | {{math|T}}  
! width="25" | {{math|I}} 
! width="25" | {{math|F}}
|-
! {{math|T}}  
| {{math|T}} || {{math|I}} || {{math|T}}
|-
! {{math|I}} 
| {{math|I}} || {{math|I}} || {{math|I}}
|-
! {{math|F}} 
| {{math|T}} || {{math|I}} || {{math|F}}
|}
||
||
||
{| class="wikitable" style="text-align: center;"
|-
! width="25" | {{underset|+|→}}
! width="25" | {{math|T}}  
! width="25" | {{math|I}} 
! width="25" | {{math|F}}
|-
! {{math|T}} 
| {{math|T}} || {{math|I}} || {{math|F}}
|-
! {{math|I}} 
| {{math|I}} || {{math|I}} || {{math|I}}
|-
! {{math|F}} 
| {{math|T}} || {{math|I}} || {{math|T}}
|}
|}

The intermediate truth value in Bochvar's "internal" logic can be described as "contagious" because it propagates in a formula regardless of the value of any other variable.<ref name="Bergmann 2008 80"/>