# Dictionary Definition

inference n : the reasoning involved in drawing a
conclusion or making a logical judgment on the basis of
circumstantial evidence and prior conclusions rather than on the
basis of direct observation [syn: illation]

# User Contributed Dictionary

## English

### Noun

- The act or process of inferring by deduction or induction.
- That which is inferred; a truth or proposition drawn from another which is admitted or supposed to be true; a conclusion; a deduction.

#### Translations

the act or process of inferring by deduction or
induction

- Finnish: päättely

that which is inferred

- Finnish: päätelmä

# Extensive Definition

expert-subject Logic

Inference is the act or process of deriving a
conclusion based
solely on what one already knows.

Inference is studied within several different
fields.

- Human inference (i.e. how humans draw conclusions) is traditionally studied within the field of cognitive psychology.
- Logic studies the laws of valid inference.
- Statisticians have developed formal rules for inference from quantitative data.
- Artificial intelligence researchers develop automated inference systems.

## The accuracy of inductive and deductive inferences

The process by which a conclusion is inferred from multiple observations is called inductive reasoning. The conclusion may be correct or incorrect, or partially correct, 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.Inductive inference is the method of science. A theory is proposed
based on multiple observations, usually observations carried out
with great care, using measurement. The theory is
then tested many times, by independent investigators, using their
own multiple observations. If the theory proves correct to within
the accuracy of those observations, then it is provisionally
accepted. Any scientific theory is subject to additional testing,
and may be modified or overthrown based on additional evidence. For
example, the Germ Theory of Disease required modification when
viruses and also deficiency diseases were discovered.

Scientific theories arrived at by inductive
inference have proved stable enough over long periods of time to
revolutionize the way human beings live. A scientific theory can be
overthrown only by carefully recorded repeated observations,
carried out independently by a large number of investigators. They
cannot be overthrown by revelation, authority, ignorance, or
doubt.

The process by which a conclusion is logically
inferred from certain premises is called deductive
reasoning. Deductive inference is the method of mathematics. Certain
definitions and
axioms are taken as a
starting point, and from these certain theorems are deduced using pure
reasoning. The idea for a theorem may have many sources: analogy,
pattern recognition, and experiment are examples of where the
inspiration for a theorem comes from. However, a conjecture is not
granted the status of theorem until it has a deductive proof. This method of inference is
even more accurate than the scientific method. While
mathematicians, like all human beings, make mistakes, these
mistakes are usually quickly detected by other mathematicians and
corrected. The proofs of Euclid, for example,
have mistakes in them that have been caught and corrected, but the
theorems of Euclid, all of them without exception, have stood the
test of time for more than two thousand years.

From a pragmatic viewpoint, the inferences
arrived at by the methods of science and mathematics have proved
much more successful than the inferences arrived at by any other
method. This has given rise to the popular saying, when a
conclusion is challenged, "Do the math."

## Valid inferences

Inferences are either valid or invalid, but not
both. Philosophical
logic has attempted to define the rules of proper inference,
i.e. the formal rules that, when correctly applied to true
premises, lead to true conclusions. Aristotle has
given one of the most famous statements of those rules in his
Organon.
Modern mathematical
logic, beginning in the 19th century, has built numerous
formal
systems that embody Aristotelian
logic (or variants thereof).

## 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'll begin with the most famous of them all:

All men are mortal Socrates is a man
------------------ Therefore Socrates is mortal.

The reader can check that the premises and
conclusion are true. The Greek name for this form was Modus
Ponens

The validity of an inference depends on the form
of the inference. That is, the word "valid" does not refer to the
truth of the premises or the 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 Modus
Ponens:

All A are B C is A ---------- Therefore C is
B

The form remains valid even if all three parts
are false:

All apples are blue. A banana is an apple.
Therefore bananas are blue

For the conclusion to be necessarily true, the
premises need to be true.

Now we turn to an invalid form.

All A are B. C is a B. 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.

All apples are fruit. (true) Bananas are fruit.
(true) Therefore bananas are apples. (false)

But false premises may, by accident, lead to a
true conclusion.

All fat people are fish John Lennon was fat
------------------- Therefore John Lennon was a fish

where a valid inference is used to derive a false
conclusion from false premises. The inference is valid because it
follows the form of a correct inference. However, inference can
also be used to derive true conclusions from false premises: All
fat people are musicians John Lennon was fat -------------------
Therefore John Lennon was a musician

In this case we have two false premises that
imply a true conclusion.

## 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.

## 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.

### An example: inference using Prolog

Prolog (for
"Programming in Logic") is a 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:

?- mortal(socrates). (where ?- signifies a query:
Can mortal(socrates). be deduced from the KB using the rules) gives
the answer "Yes".

On the other hand, asking the Prolog system the
following:

?- mortal(plato).

gives the answer "No".

This is because Prolog does not know
anything about Plato, and hence
defaults to any property about Plato being false (the so-called
closed
world assumption). Finally ?- mortal(X) (Is anything mortal)
would result in "Yes" (and in some implemenations: "Yes":
X=socrates) Prolog can be used
for vastly more complicated inference tasks. See the corresponding
article for further examples.

### Automatic inference and the semantic web

Recently automatic reasoners found in semantic web a new field of application. Being based upon first-order logic, knowledge expressed using one variant of OWL can be logically processed, i.e., inference can be made upon it.## Inference and uncertainty

Traditional logic is only concerned with certainty - one progresses from premises to a conclusion, where all the premises and the concusion are declarative sentences that are either true or false. There are several motivations for extending logic to deal with uncertain "propositions" and weaker modes of reasoning.- Philosophical motivations
- A large part of our everyday reasoning does not follow the strict rules of logic, but is nevertheless effective in many cases
- Science itself is not deductive, but largely inductive, and its process cannot be captured by standard logic (see problem of induction).

- Technical motivations
- Statisticians and scientists wish to be able to infer parameters or test hypothesis on statistical data in a rigorous, quantified way.
- Artificial intelligence systems need to reason efficiently about uncertain quantities.

### Common sense and uncertain reasoning

The reason most examples of applying deductive
logic, such as the one above, seem artificial is because they are
rarely encountered outside fields such as mathematics. Most of our
everyday reasoning is of a less "pure" nature.

To take an example: suppose you live in a flat.
Late at night, you are awakened by creaking sounds in the ceiling.
You infer from these sounds that your neighbour upstairs is having
another bout of insomnia and is pacing in his room,
sleepless.

Although that reasoning seems sound, it does not
fit in the logical framework described above. First, the reasoning
is based on uncertain facts: what you heard were creaks, not
necessarily footsteps. But even if those facts were certain, the
inference is of an inductive nature: perhaps you have often heard
your neighbour at night, and the best explanation you have found is
that he or she is an insomniac. Hence tonight's footsteps.

It is easy to see that this line of reasoning
does not necessarily lead to true conclusions: perhaps your
neighbour had a very early plane to catch, which would explain the
footsteps just as well. Uncertain reasoning can only find the best
explanation among many alternatives.

### Bayesian statistics and probability logic

Philosophers and scientists who follow the
Bayesian
framework for inference use the mathematical rules of probability to find this
best explanation. The Bayesian view has a number of desirable
features - one of them is that it embeds deductive (certain) logic
as a subset (this prompts some writers to call Bayesian probability
"probability logic", following E. T.
Jaynes).

Bayesianists identify probabilities with degrees
of beliefs, with certainly true propositions having probability 1,
and certainly false propositions having probability 0. To say that
"it's going to rain tomorrow" has a 0.9 probability is to say that
you consider the possibility of rain tomorrow as extremely
likely.

Through the rules of probability, the probability
of a conclusion and of alternatives can be calculated. The best
explanation is most often identified with the most probable (see
Bayesian
decision theory). A central rule of Bayesian inference is
Bayes'
theorem, which gave its name to the field.

See Bayesian
inference for examples.

### Nonmonotonic logic

Source: Article of André Fuhrmann about
"Nonmonotonic Logic"

A relation of inference is monotonic if the
addition of premises does not undermine previously reached
conclusions; otherwise the relation is nonmonotonic.
Deductive inference, at least according to the canons of classical
logic, is monotonic: if a conclusion is reached on the basis of a
certain set of premisses, then that conclusion still holds if more
premisses are added.

By contrast, everyday reasoning is mostly
nonmonotonic because it involves risk: we jump to conclusions from
deductively insufficient premises. We know when it is worth or even
necessary (e.g. in medical diagnosis) to take the risk. Yet we are
also aware that such inference is defeasible—that new information
may undermine old conclusions. Various kinds of defeasible but
remarkably successful inference have traditionally captured the
attention of philosophers (theories of induction, Peirce’s theory
of abduction, inference to the best explanation, etc.). More
recently logicians have begun to approach the phenomenon from a
formal point of view. The result is a large body of theories at the
interface of philosophy, logic and artificial intelligence.

## Three types of logical inference

There are three types of inference:- Deductive reasoning, finding the effect with the cause and the rule.
- Abductive reasoning, finding the cause with the rule and the effect.
- Inductive reasoning, finding the rule with the cause and the effect.

### An example

Hooke's law is the rule that gives the elongation of a beam (that's an effect) when a force (that's the cause) is acting on a beam.- If the force and Hooke's law are known, the elongation of the beam can be deduced.
- If the elongation and Hooke's law are known, the force acting on the beam can be abduced.
- If the elongation and the force are known, Hooke's law can be induced.

## References

- Ian Hacking. An Introduction to Probability and Inductive Logic. Cambridge University Press, (2000).
- Edwin Thompson Jaynes. Probability Theory: The Logic of Science. Cambridge University Press, (2003). ISBN 0-521-59271-2.
- David J.C. McKay. Information Theory, Inference, and Learning Algorithms. Cambridge University Press, (2003).
- Henk Tijms. Understanding Probability. Cambridge University Press, (2004).
- André Fuhrmann: Nonmonotonic Logic.

## See also

- Reasoning
- Analogy
- Axiom
- Bayesian inference
- Business rule
- Business rules engine
- Expert system
- Fuzzy logic
- Inference engine
- Inquiry
- Logic
- Logic of information
- Logical assertion
- Logical graph
- Nonmonotonic logic
- Rule of inference
- List of rules of inference
- Theorem
- Portals

inference in Arabic: استدلال

inference in Bulgarian: Умозаключение

inference in Catalan: Inferència

inference in German: Schlussfolgerung

inference in Spanish: Inferencia

inference in Esperanto: Inferenco

inference in French: Inférence

inference in Korean: 추론

inference in Croatian: Zaključak

inference in Italian: Inferenza

inference in Dutch: Gevolgtrekking

inference in Japanese: 推論

inference in Polish: Wnioskowanie

inference in Portuguese: Inferência

inference in Romanian: Inferenţă

inference in Russian: Умозаключение

# Synonyms, Antonyms and Related Words

Baconian method, a fortiori reasoning, a
posteriori reasoning, a priori reasoning, allegory, allusion, analysis, arcane meaning,
assumption, axiom, coloration, conclusion, conjecture, connotation, consequence, consequent, corollary, deduction, deductive
reasoning, derivation, epagoge, generalization, guess, guessing, guesswork, hint, hypothesis, hypothesis and
verification, illation,
implication, implied
meaning, import, induction, inductive
reasoning, innuendo,
intimation, ironic
suggestion, judgment,
meaning, metaphorical
sense, nuance, occult
meaning, overtone,
particularization,
philosophical induction, postulate, postulation, postulatum, premise, presumption, presupposal, presupposition, proposition, ratiocination, reckoning, sequitur, set of postulates,
subsense, subsidiary
sense, suggestion,
supposal, supposing, supposition, surmise, syllogism, syllogistic
reasoning, symbolism,
synthesis, thesis, tinge, touch, undercurrent, undermeaning, understanding, undertone, working
hypothesis