Last Updated：2025/11/27
(logic) A Kripke frame together with either one of the following: (1) a function associating each of the frame's worlds to a set of prime formulae which are true
for the given world, (2) a function associating each prime formula to a set of worlds for which the prime formula is true
, (3) a forcing relation between worlds and prime formulae. Additionally, there is a set of rules for deducing (from the given function or relation) what formulae are forced to be true by a given world. (The set of rules depends on which logic the Kripke model is being applied to, whether one of several modal logics or intuitionistic logic).
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Kripke model
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Source Word
Kripke model
Noun
(logic)
A
Kripke
frame
together
with
either
one
of
the
following:
(1)
a
function
associating
each
of
the
frame's
worlds
to
a
set
of
prime
formulae
which
are
"true"
for
the
given
world,
(2)
a
function
associating
each
prime
formula
to
a
set
of
worlds
for
which
the
prime
formula
is
"true",
(3)
a
forcing
relation
between
worlds
and
prime
formulae.
Additionally,
there
is
a
set
of
rules
for
deducing
(from
the
given
function
or
relation)
what
formulae
are
forced
to
be
true
by
a
given
world.
(The
set
of
rules
depends
on
which
logic
the
Kripke
model
is
being
applied
to,
whether
one
of
several
modal
logics
or
intuitionistic
logic).
Japanese Meaning
論理学において、Kripkeモデルとは、Kripkeフレームに加え、次のうちのいずれかを付加したものを指します。1) 各世界に対して、その世界で真とされる原始公式（素公式）の集合を割り当てる関数、2) 各原始公式に対して、その公式が真となる世界の集合を割り当てる関数、または3) 世界と原始公式の間の強制関係です。さらに、これらの関数または関係から、各世界で真とされる公式を導出する規則の集合が定められ、適用される論理体系（例えば、複数のモーダル論理や直観主義論理など）に依存します。
Sense（1）
(logic)
A
Kripke
frame
together
with
either
one
of
the
following:
(1)
a
function
associating
each
of
the
frame's
worlds
to
a
set
of
prime
formulae
which
are
"true"
for
the
given
world,
(2)
a
function
associating
each
prime
formula
to
a
set
of
worlds
for
which
the
prime
formula
is
"true",
(3)
a
forcing
relation
between
worlds
and
prime
formulae.
Additionally,
there
is
a
set
of
rules
for
deducing
(from
the
given
function
or
relation)
what
formulae
are
forced
to
be
true
by
a
given
world.
(The
set
of
rules
depends
on
which
logic
the
Kripke
model
is
being
applied
to,
whether
one
of
several
modal
logics
or
intuitionistic
logic).
（ plural ）
