## Types of Inference

This document explains different types of inference, which are processes of drawing conclusions based on available information.

**1. Deduction:**

Deduction is the process of deriving a specific conclusion from general principles or observations. It involves drawing new truths from already established and known truths (continuity). In deduction, if a statement is considered true or at least likely to be true, it implies certain specific and specific statements that can be derived from it. This reasoning in logic requires the conclusion to follow directly from the premises.

**2. Induction:**

Induction is a form of inference that draws general conclusions from specific observations. It moves from specific instances to broader generalizations.

**3. Intuition:**

Intuition is a type of inference that occurs without conscious reasoning or theoretical basis. Conclusions emerge from unconsciously observed patterns.

**4. Heuristic:**

Heuristic inference is based on past experience and knowledge. It uses rules of thumb or shortcuts to reach conclusions.

**5. Generate & Test:**

Generate and test involves a trial and error approach to reach conclusions. Solutions are proposed and tested to see if they meet all the requirements. If a solution is satisfactory, the process stops; otherwise, a new solution is generated and tested again.

**6. Abduction:**

Abduction is a form of inference that moves from an observed conclusion to a possible explanation. It is similar to modus ponens, but not a valid deductive argument. Abduction is useful as a heuristic inference rule. 

**Modus Ponens:**

```
p -> q
p
∴ q
```

**Abduction:**

```
p -> q
q
∴ p
```

- Abduction is not a valid deductive argument.
- It is useful as a heuristic inference method.
- Analogy, generate and test, and abduction are non-deductive methods. These methods cannot guarantee the truth of the conclusion even with true premises.

**7. Default:**

Default reasoning uses general knowledge as default assumptions. This knowledge is used unless contradicted by specific evidence.

**8. Autoepistemic:**

Autoepistemic logic is a formal logic used to represent and reason about knowledge of knowledge. While propositional logic can only express facts, autoepistemic logic can express knowledge and knowledge about facts.

**9. Nonmonotonic:**

- Previously acquired knowledge might be incorrect when new evidence is obtained. In logic systems, adding new axioms can lead to the provability of many theorems.
- The increase in theorems with increased axioms is known as a monotonic system.
- Issues arise when introducing partial or complete new axioms that contradict previously established axioms.
- In non-monotonic systems, the increase in theorems does not necessarily correspond with the increase in axioms.

**10. Analogy:**

- Analogy-based inference draws conclusions based on similarities to other situations. It attempts to use past situations as guides for new ones.
- Example: medical diagnosis (symptoms experienced by a patient are similar to those experienced by another patient).
- Analogical reasoning is related to induction. While induction makes inferences from specific to general in the same situation, analogy makes inferences from different situations. 

Using these inference steps, answer this question:
In the town of Meowington, Whiskers Purr-ot, the cat detective, is investigating the mysterious disappearance of Lady Tabby's diamond collar. There are three suspects: Mittens, Clawdia, and Tigger. Only one suspect tells the truth, and the thief must be among them.
The premises are as follows:
If Mittens was in the garden, then Clawdia was in the parlor.
Tigger or Clawdia has the diamond collar, but they both claim not to have it.
Tigger says that he was sleeping in the attic when the collar went missing.
If Clawdia has the diamond collar, she must have been in the parlor.
Mittens claims that if he had taken the collar, he would not be hiding in the bushes.
It is known that the cat with the collar was not sleeping.
Determine who took Lady Tabby's diamond collar using the premises given.