# Logical Inference

Logical inference becomes Logic and Cause and Effect Analysis .

In the field of Data Science, "inference" often refers to "inference using Statistics< (statistical inference)" and " inference using Machine Learning (prediction / estimation / judgment)". The title of this page is "logical reasoning", but in the literature where logical reasoning is written, it is usually simply written as "reasoning".

In academics, statistical reasoning and logical reasoning are different, but in real-life reasoning, both theories are often combined as a countermeasure against the inconsistency between reality and theory.

In realistic reasoning, it is important not only the logical structure itself such as "If A is B", but also how to support "A" and "B" itself. The point seems to be how to make a judgment when a clear line cannot be drawn.

## Classification of logical inference

There seem to be various ways to divide logical inference, but here we use deduction, induction, abduction, and analogy.

• Deduction : Refer to general rules to derive results from what is actually happening.
• Induction : Collect facts and derive general rules.
• Abduction : Refer to the general law and derive the cause from the actual result.
• Analogy : Think of the fact that it consists of similar phenomena by applying it to the phenomenon you want to know.

### Induction in a broad sense

There is also a document that explains the induction method as "induction method is not deductive method" and "method included in conclusion is not included in the premise grounds".

Thinking in this way, the abduction and the analogy method can be considered as a kind of induction method.

## How to use deduction

Deduction cannot be used unless you understand the presupposed rules.

I think that it is normal to not understand something like a "law" about what happens in daily life and social life, so when you think about it, you have the opportunity to infer what happens in daily life and social life by deduction. Is rare.

### How to use deduction in a narrow sense

There are also literatures that explain deduction as "what can be handled by symbolic logic is deduction" or "a method that can be treated mathematically rigorously".

By declaring the correctness of the presupposed law as a "definition", we will be able to utilize the rich theory of symbolic logic .

### How to use deduction in a broad sense

If the general rule is linguistically "fruit if apple", deduction and abduction are different.

However, considering the general rule more broadly, in the case of a numerical value such as "If the value of A is large, the value of B is also large", it means that "If the value of B is large, the value of A is also large". Is true, so the distinction between deduction and abduction is not very important.

There are not many numerical rules that can be widely used for what happens in daily life and social life.

On the other hand, the laws of nature that have been studied in physics are numerical laws that can be widely used. Since it is applied as a theory of manufacturing in a factory, there are situations where deduction can be used to infer the phenomenon of a factory. Simulation by Mathematical Modeling is useful.

## Relationship with statistical inference

Logical reasoning can be used as a method of searching for Quality Way of Making Hypothesis . Statistical inference has become a method of searching for Quantity Way of Making Hypothesis . When using statistics when making inferences, it is assumed that they have happened many times in the past.

### Usage as an induction method for statistical inference

Statistical inference is used as a kind of induction when it is used to draw a general rule from the accumulation of facts. Associations Analysis is a typical way to find such a law.

### How to use statistical inference for deduction

It is also possible to derive a law from the accumulation of facts and infer on the premise of that law. In this case, use it as a preparation for performing the deduction method.

## Inference in the real

In the world of trial, there is only one target phenomenon. Since it is difficult to decide how to apply it to the law with only that one piece of information, it seems to refer to past precedents.

In real-life reasoning, in addition to statistical and logical reasoning, we also use information in areas in between. Since the conditions are different, it cannot be said to be "repeated", but since it may be a part, it is inferred by making full use of information on situations where there are similarities and information on the surrounding area. It also considers the variability in the range that the words you are dealing with mean. In the field I know, this is the case in Process Analysis for Abnormal Condition.

It would be nice to summarize the similar treatment a little more theoretically and systematically, but this site has not yet summarized it. There seems to be no good material in the world so far.

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