Boolean algebras are Heyting algebras with the additional
constraint that the law of the excluded middle is true
(equivalently, double-negation is true).
This means that in addition to the laws Heyting algebras obey,
boolean algebras also obey the following:
(a ∨ ¬a) = 1
¬¬a = a
Boolean algebras generalize classical logic: one is equivalent to
"true" and zero is equivalent to "false". Boolean algebras provide
additional logical operators such as xor, nand, nor, and
nxor which are commonly used.
Every boolean algebras has a dual algebra, which involves reversing
true/false as well as and/or.
Boolean algebras are Heyting algebras with the additional constraint that the law of the excluded middle is true (equivalently, double-negation is true).
This means that in addition to the laws Heyting algebras obey, boolean algebras also obey the following:
Boolean algebras generalize classical logic: one is equivalent to "true" and zero is equivalent to "false". Boolean algebras provide additional logical operators such as
xor,nand,nor, andnxorwhich are commonly used.Every boolean algebras has a dual algebra, which involves reversing true/false as well as and/or.