最終更新日：2025/11/21
(algebra) An algebraic structure (𝛴,∨,∧,∼,0,1) where ∨ and ∧ are idempotent binary operators, ∼ is a unary involutory operator (called complement
), and 0 and 1 are nullary operators (i.e., constants), such that (𝛴,∨,0) is a commutative monoid, (𝛴,∧,1) is a commutative monoid, ∧ and ∨ distribute with respect to each other, and such that combining two complementary elements through one binary operator yields the identity of the other binary operator. (See Boolean algebra (structure)#Axiomatics.)
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Boolean algebra
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元となった辞書の項目
Boolean algebra
名詞
(algebra)
An
algebraic
structure
(𝛴,∨,∧,∼,0,1)
where
∨
and
∧
are
idempotent
binary
operators,
∼
is
a
unary
involutory
operator
(called
"complement"),
and
0
and
1
are
nullary
operators
(i.e.,
constants),
such
that
(𝛴,∨,0)
is
a
commutative
monoid,
(𝛴,∧,1)
is
a
commutative
monoid,
∧
and
∨
distribute
with
respect
to
each
other,
and
such
that
combining
two
complementary
elements
through
one
binary
operator
yields
the
identity
of
the
other
binary
operator.
(See
Boolean
algebra
(structure)#Axiomatics.)
日本語の意味
ブール代数：論理演算（論理和、論理積、補集合など）により定義される代数的構造。集合や論理回路、計算理論などで用いられ、0や1を含む定数や、分配法則、冪等性など特有の公理系に基づいた体系である。
意味（1）
(algebra)
An
algebraic
structure
(𝛴,∨,∧,∼,0,1)
where
∨
and
∧
are
idempotent
binary
operators,
∼
is
a
unary
involutory
operator
(called
"complement"),
and
0
and
1
are
nullary
operators
(i.e.,
constants),
such
that
(𝛴,∨,0)
is
a
commutative
monoid,
(𝛴,∧,1)
is
a
commutative
monoid,
∧
and
∨
distribute
with
respect
to
each
other,
and
such
that
combining
two
complementary
elements
through
one
binary
operator
yields
the
identity
of
the
other
binary
operator.
(See
Boolean
algebra
(structure)#Axiomatics.)
意味（2）
（ plural ）
