Last Updated
：2025/11/26
Heyting algebra
Noun
(algebra,
order
theory)
A
bounded
lattice,
L,
modified
to
serve
as
a
model
for
a
logical
calculus
by
being
equipped
with
a
binary
operation
called
"implies",
denoted
→
(sometimes
⊃
or
⇒),
defined
such
that
(a→b)∧a
≤
b
and,
moreover,
that
x
=
a→b
is
the
greatest
element
such
that
x∧a
≤
b
(in
the
sense
that
if
c∧a
≤
b
then
c
≤
a→b).
Japanese Meaning
ヒーティング代数：論理計算のモデルとして利用される有界格子であり、二項演算「含意」（→、または⊃や⇒）を備える。具体的には、(a→b)∧a ≤ bを満たし、さらにx = a→bがx∧a ≤ bとなるような最大の元となるように定義される代数構造。
Sense（1）
(algebra,
order
theory)
A
bounded
lattice,
L,
modified
to
serve
as
a
model
for
a
logical
calculus
by
being
equipped
with
a
binary
operation
called
"implies",
denoted
→
(sometimes
⊃
or
⇒),
defined
such
that
(a→b)∧a
≤
b
and,
moreover,
that
x
=
a→b
is
the
greatest
element
such
that
x∧a
≤
b
(in
the
sense
that
if
c∧a
≤
b
then
c
≤
a→b).
（ plural ）
Quizzes for review
(algebra, order theory) A bounded lattice, L, modified to serve as a model for a logical calculus by being equipped with a binary operation called implies
, denoted → (sometimes ⊃ or ⇒), defined such that (a→b)∧a ≤ b and, moreover, that x = a→b is the greatest element such that x∧a ≤ b (in the sense that if c∧a ≤ b then c ≤ a→b).
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See correct answer
Heyting algebra
A Heyting algebra provides a semantic model for intuitionistic logic by interpreting implication as the greatest element x such that x ∧ a ≤ b.
See correct answer
A Heyting algebra provides a semantic model for intuitionistic logic by interpreting implication as the greatest element x such that x ∧ a ≤ b.
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