In Logic, inference or deduction is an intellectual operation by which the truth of a proposition is affirmed as a consequence of its connection with other propositions already recognized as true. It consists, therefore, in deriving conclusions from known or decidedly true premises. The conclusion is also called idiomatic.

The process by which a conclusion is inferred from multiple observations is called a deductive or inductive , depending on the context. The conclusion may be correct, incorrect, correct within a certain degree of accuracy, or correct in certain situations. Conclusions inferred from multiple observations can be tested by additional observations.

Examples of Inference

Aristotle defined a series of syllogisms , which can be used as building blocks for more complex reasoning. We begin with the most famous of them all:

• All men are mortal.
• Socrates is a man
• Therefore, Socrates is mortal.

The process described above is called deductive.

The premises and the conclusion are true, but logic follows along with inference. However, the truth of the conclusion does not always follow from the truth of the premises. 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 it can be false even if the parts are true. But a valid form with true premises will always have a true conclusion.

Consider the following example:

• A – All fruits are sweet.
• B – A banana is a fruit.
• C – Therefore, the banana is sweet.

Now we return to an invalid form:

• All A is B.
• C is a B.
• Therefore, C is an A.

To show that this method is invalid, we seek to demonstrate how it can lead from true premises to a false conclusion.

• All apples are fruits. (Correct)
• Bananas are fruits. (Correct)
• Therefore, bananas are apples. (Wrong)

A valid argument with false premises can lead to a false conclusion.

• All fat people are Greek.
• John Lennon was fat.
• 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:

• 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 numerous cases where we tend to reach erroneous conclusions, especially on more counterintuitive issues.

Automatic logical inference

AI systems first provided "automatic logical inference." Since these were already extremely popular research topics, they led to industrial applications in the form of expert systems and later "business rule engines."

The job of an inference system is to automatically extend a knowledge . The knowledge base (KB) is a set of propositions that represent what the system knows about the world. Various techniques can be used by the system to extend the KB through valid inferences.