Last Updated
：2025/11/27
deduction theorem
Noun
(logic)
A
procedure
for
"discharging"
assumptions
from
an
inference,
causing
them
to
become
antecedents
of
the
conclusion;
or
vice
versa.
Symbolically,
the
conversion
of
an
inference
of
the
form
P,A⊢C
to
an
inference
of
the
form
P⊢A→C
or
vice
versa,
where
⊢
is
the
turnstile
symbol.
The
validity
of
the
procedure
is
a
metatheorem
of
the
given
logical
theory.
Japanese Meaning
論理学における定理の一種で、ある仮定を論証から解除し、その仮定を結論の前提条件（含意）として組み込む手続き、あるいはその逆の変換を示すもの。
Sense（1）
(logic)
A
procedure
for
"discharging"
assumptions
from
an
inference,
causing
them
to
become
antecedents
of
the
conclusion;
or
vice
versa.
Symbolically,
the
conversion
of
an
inference
of
the
form
P,A⊢C
to
an
inference
of
the
form
P⊢A→C
or
vice
versa,
where
⊢
is
the
turnstile
symbol.
The
validity
of
the
procedure
is
a
metatheorem
of
the
given
logical
theory.
（ plural ）
Quizzes for review
(logic) A procedure for discharging
assumptions from an inference, causing them to become antecedents of the conclusion; or vice versa. Symbolically, the conversion of an inference of the form P,A⊢C to an inference of the form P⊢A→C or vice versa, where ⊢ is the turnstile symbol. The validity of the procedure is a metatheorem of the given logical theory.
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See correct answer
deduction theorem
When teaching natural deduction, I emphasize how the deduction theorem allows us to discharge temporary assumptions and turn them into antecedents of the conclusion.
See correct answer
When teaching natural deduction, I emphasize how the deduction theorem allows us to discharge temporary assumptions and turn them into antecedents of the conclusion.
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