Explain Nyaya theory of inference.

The Nyāya school of Indian philosophy is renowned for its rigorous epistemological framework, particularly its theory of inference (anumāna). Anumāna is one of the pramāṇas (means of valid knowledge) accepted by the Nyāya system. Rooted in logic and rational analysis, the Nyāya theory of inference has significantly influenced Indian philosophical discourse.

### Definition and Components of Inference
In the Nyāya tradition, inference is defined as knowledge derived from reasoning, following a connection between a middle term (hetu) and a major term (sādhya). Inference involves the cognition of a relationship, generally causal or concomitant, based on previously known observations.

The Nyāya theory identifies three key components in the process of inference:
1. Pratijñā (Proposition): The statement or claim to be established.
2. Hetu (Reason): The logical ground or reason supporting the claim.
3. Udāharaṇa (Example): An illustration that demonstrates the invariable relationship between the middle term and the major term, often cited with both positive and negative examples.
4. Upanaya (Application): The application of the general rule (stated in the example) to the specific case at hand.
5. Nigamana (Conclusion): The final inference drawn from the preceding steps.

These five steps constitute what is termed as the "pañcāvayava" or five-membered syllogism of Nyāya, which is unique compared to the three-step syllogism of Aristotelian logic.

### Types of Inference
Nyāya classifies inference into different types based on distinct criteria:

#### 1. Based on Nature of Inference:
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