-
Inference
is
the
act
of
drawing
a
conclusion
by
deductive
reasoning
from
given facts. The conclusion drawn is
also called an inference. The laws
of
valid inference are studied in the field of logic.
Human inference (i.e. how humans draw
conclusions) is traditionally
studied
within
the
field
of
cognitive
psychology
;
artificial
intelligence
researchers develop automated inference
systems to emulate human
inference.
Statistical
inference
allows
for
inference
from
quantitative
data.
Contents
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1 Accuracy of inductive
inferences
2 Examples of
deductive inference
3
Incorrect inference
4
Automatic logical inference
o
4.1 Example
using Prolog
o
4.2 Use with the semantic
web
o
4.3 Bayesian statistics and probability
logic
[1]
o
4.4 Nonmonotonic logic
5 See also
6
References
[
edit
] Accuracy
of inductive inferences
The
process
by
which
a
conclusion
is
inferred
from
multiple
observations
is
called
inductive
reasoning
.
The
conclusion
may
be
correct
or
incorrect,
or correct to
within a
certain
degree of
accuracy, or correct
in
certain
situations.
Conclusions
inferred
from
multiple
observations
may
be
tested
by
additional observations.
[
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] Examples
of deductive inference
Greek
philosophers
defined a number of
syllogisms
, correct three
part
inferences,
that
can
be
used
as
building
blocks
for
more
complex
reasoning.
We begin with the most famous of them
all:
1.
All men
are mortal
2.
Socrates is a man
3.
Therefore,
Socrates is mortal.
The
reader
can
check
that
the
premises
and
conclusion
are
true,
but
Logic
is
concerned
with
inference:
does
the
truth
of
the
conclusion
follow
from
that
of the premises?
The validity of an
inference depends on the form of the inference.
That
is, the word
conclusion, but rather
to
the form
of
the
inference. An
inference can be
valid even if the parts are false, and
can be invalid even if the parts
are
true. But a valid form with true premises will
always have a true
conclusion.
For example, consider the form of the
following
symbological
track:
1.
All
apples are blue.
2.
A banana is an apple.
3.
Therefore, a
banana is blue.
For the conclusion to
be necessarily true,
the
premises need
to be true.
Now we turn to an invalid form.
1.
All A are B.
2.
C is a B.
3.
Therefore, C
is an A.
To show that this form is
invalid, we demonstrate how it can lead from
true premises to a false conclusion.
1.
All apples are
fruit. (True)
2.
Bananas are fruit. (True)
3.
Therefore,
bananas are apples. (False)
A valid
argument with false premises may lead to a false
conclusion:
1.
All fat people are Greek.
2.
John Lennon
was fat.
3.
Therefore, John Lennon was Greek.
When a valid argument is used to derive
a false conclusion from false
premises,
the
inference
is
valid
because
it
follows
the
form
of
a
correct
inference.
A valid argument
can also be used to derive a true conclusion from
false
premises:
1.
All fat people
are musicians
2.
John Lennon was fat
3.
Therefore,
John Lennon was a musician
In this
case we have two false premises that imply a true
conclusion.
[
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] Incorrect
inference
An incorrect inference is
known as a
fallacy
.
Philosophers who study
informal
logic
have compiled large lists of
them, and cognitive
psychologists have
documented many
biases in human
reasoning
that favor
incorrect reasoning.
[
edit
] Automatic
logical inference
AI
systems
first
provided
automated
logical
inference
and
these
were
once
extremely popular research topics,
leading to industrial applications
under the form of
expert
systems
and later
business
rule engines
.
An inference
system's job is to extend a knowledge base
automatically.
The knowledge base (KB)
is a set
of propositions
that
represent what the
system
knows
about
the
world.
Several
techniques
can
be
used
by
that
system
to extend KB by means of valid
inferences. An additional requirement is
that the conclusions the system arrives
at are
relevant
to its task.
[
edit
] Example
using Prolog
Prolog
(for
programming language
based
on
a
subset
of
predicate
calculus
.
Its
main
job
is
to
check
whether
a
certain
proposition
can
be
inferred
from
a
KB
(knowledge
base)
using
an
algorithm
called
backward chaining
.
Let
us
return
to
our
Socrates
syllogism
.
We
enter
into
our
Knowledge
Base
the following piece of code:
mortal(X) :- man(X).
man(socrates).
(
Here
:-
can
be
read
as
if.
Generally,
if
P
Q
(if
P
then
Q)
then
in
Prolog
we would code
Q
:-
P
(Q if P).)
This states that all men are
mortal and that Socrates is a man. Now we
can ask the Prolog system about
Socrates: