## What is deduction?

Deduction is a term from logic and comes from the Latin word deductiowhich means "derivation" or "derivation". It denotes a logical conclusion from the general to the particular. It is also understood as theory to empiricism.

The basis is the inheritance of properties of higher-level elements to their subsets. Through a general theory, statements can thus be made about concrete individual cases. The precondition or assumption is also called premise. From one or more premises, the logical consequence follows with the help of inference rules, which is compellingly or deductively valid. The truth of the premise leads to the truth of the conclusion. No false conclusion may arise from a true premise.

Deductive inferences, like other scientific methods, are not verifiable, but only falsifiable. That is, their validity is assumed as long as there is no counter-evidence or new knowledge. In the field of artificial intelligence deduction plays an essential role in logic programming and automatic proof.

## What are examples of deduction?

A classic example of deductive reasoning comes from Aristotle:

All human beings are mortal. Socrates is a human being. It follows that Socrates is mortal.

The premises "all human beings are mortal" and "Socrates is a human being" are true. The property "mortal" of the superordinate category human being is transferred to the concrete example of Socrates.

Another example of deductive reasoning is:

Pilots have a quick reaction time. He is a pilot. He has a quick reaction time.

The premise here is that the characteristic of a quick reaction time applies to pilots in general. According to the premise, a concrete representative of the category therefore possesses a fast reaction capability, otherwise he would not be a pilot. The statement is therefore true.

Also in the detective stories Sherlock Holmes the deductive method is present. In The blue carbuncle Holmes estimates the socio-economic background of the wearer of an old hat based on general phenomena. The size and quality of the found hat indicate an intellectual and wealthy person. However, since the hat is aging and full of dust, Holmes logically assumes that the owner is no longer financially well off and rarely leaves the house.

## What are the differences between induction and abduction?

### Deduction vs. induction

Induction (lat. inducere "bring about") is the reverse process to deduction. Here, a general conclusion is formed from a concrete observation or phenomenon. The path is therefore from empiricism to theory. Collecting data on individual elements leads to the realisation of properties that all representatives of a group or category possess.

Example:

The little sparrow lays eggs. The sparrow is a bird. All birds lay eggs.

The specific premise here is the egg-laying sparrow, which belongs to the group of birds. From the observation of the sparrow follows the abstract conclusion about the behaviour of all birds.

Induction and deduction never occur in pure form. The premises used in deductive reasoning are closely linked to empirical findings and induction to already established theory. The procedures differ essentially in the question of whether a regularity is to be verified (deduction) or a new one formed (induction).

### Deduction vs. abduction

A third method of logical reasoning is the Abduction (lat. abducere "to lead away"). The term was introduced by the American philosopher Charles Sanders Peirce. It differs from induction and deduction in that it extends knowledge. An unknown cause is derived from two known conclusions.

Example:

These apples are red. All the apples from this basket are red. These apples are from this basket.

From the result, the rule "all apples from this basket are red" is used to infer the case "these apples are from this basket". Abductive reasoning is a presumption based on circumstantial evidence.