# Logical reasoning

<https://en.wikipedia.org/wiki/Logical_reasoning>

There are 3 kinds of logical reasoning: deductive, on one side, and inductive and abductive on the other. Each method is studied in the eponymously named kind of logic.

Within the context of a *mathematical model*, the 3 kinds of reasoning can be described as follows:

* The construction/creation of the structure of the model is *abduction*
* Assigning values (or probability distributions) to the parameters of the model is *induction*
* Executing/running the model is *deduction*

In short, the conclusion of inductive argument **may follow**, while in deductive logic it **must follow** (may vs must).

Given one or more premises (preconditions), a conclusion (logical consequence), and an inference rule (material conditional) that implies the conclusion given the premises, one can explain the following:

## Deductive reasoning

*Deductive reasoning* determines whether the truth of the conclusion can be determined for that rule, based solely on the truth of the premises.

Example: "When it rains, things outside get wet. The grass is outside, therefore: when it rains, the grass gets wet."

Mathematical logic and philosophical logic are commonly associated with this type of reasoning.

## Inductive reasoning

<https://en.wikipedia.org/wiki/Inductive_reasoning>

*Inductive reasoning* attempts to support a determination of the rule. It hypothesizes a rule after numerous examples are taken to be a conclusion that follows from a precondition in terms of such a rule.

Example: "The grass got wet numerous times when it rained, therefore: the grass always gets wet when it rains."

While they may be persuasive, these arguments are not deductively valid (see the problem of induction). Science is associated with this type of reasoning.

*Inductive reasoning* and its method, *induction*, is studied in the *inductive logics*.

**Induction** is a method of reasoning in which the premises contribute some justification for the truth of the conclusion. The truth of the conclusion of an inductive argument is never certain because it is generally based on the previous experience and the likelihood of it repeating.

In inductive logic, if the argument is good, the conclusion will *probably* follow from the hypotheses. This is probable because inductive logic is based on the observation and previous experience, so it can never make claims with absolute certainty.

The argument is inductive because the premises are based on the past experience and past observations. The conclusion does not only depend on the truth of the premises, but the whole argument is based on the assumption that no other outcome then the one previously observed is possible (probable). Under rigorous scrutiny, induction is a type of prediction, an educated guess.

This type of reasoning is sometimes used in science.

Note that *inductive reasoning* or *inductive logic* can sometimes be referred to as just *induction*, which is also the case for *mathematical induction*, but these two induction methods (logical vs mathematical) are completely separate things.

## Abductive reasoning

<https://en.wikipedia.org/wiki/Abductive_reasoning>

*Abductive reasoning* and its method, *abduction*, is studied in the *abductive logics*.

**Abduction** is a form of logical inference that starts with observations, then proceeds to find the most likely explanation for the observed events. It begins by forming a hypothesis, which is then put under thorough scrutiny.

Diagnosticians, detectives and scientists often use this type of reasoning.

Abductive reasoning (best explanation) works in reverse: given a (true) conclusion, it attempts to select a cogent set of (true) premises that support the conclusion (possibly not uniquely).

Example: When it rains, the grass gets wet.\
The grass is wet.\
Therefore, it might have rained.

This kind of reasoning can be used to develop a hypothesis, which in turn can be tested by additional reasoning or data.
