21
Order and Logic
Another interesting fact about FOU R, which emerges from its truth table
and its Hasse diagram, is the following result.
1.3.8 Proposition Relative to the truth ordering ≤ t on FOU R, we have
t 1 ∨ t 2 = {t 1 , t 2 } and t 1 ∧ t 2 =
n
{t 1 , t 2 } for all truth values t 1 and t 2 . In
particular, in classical two-valued logic and Kleene’s strong three-valued logic
relative to ≤ t , we have t 1 ∨ t 2 = max{t 1 , t 2 } and t 1 ∧ t 2 = min{t 1 , t 2 } for all
truth values t 1 and t 2 .
Order and Logic
Another interesting fact about FOU R, which emerges from its truth table
and its Hasse diagram, is the following result.
1.3.8 Proposition Relative to the truth ordering ≤ t on FOU R, we have
t 1 ∨ t 2 = {t 1 , t 2 } and t 1 ∧ t 2 =
n
{t 1 , t 2 } for all truth values t 1 and t 2 . In
particular, in classical two-valued logic and Kleene’s strong three-valued logic
relative to ≤ t , we have t 1 ∨ t 2 = max{t 1 , t 2 } and t 1 ∧ t 2 = min{t 1 , t 2 } for all
truth values t 1 and t 2 .