Hetu is the Sanskrit term for 'reason' or 'evidence' in Nyaya philosophy. It is one of the three components of a valid syllogism, along with the paksa (subject) and the sadhya (conclusion).

There are three types of hetus in Nyaya philosophy: 1. Svabhava Hetu (Inherent Reason) - This type of hetu is based on the inherent nature or characteristics of the subject. 2. Karya Hetu (Effect Reason) - This type of hetu is based on the effect or result of the subject. 3. Asatkarya Hetu (Absence of Effect Reason) - This type of hetu is based on the absence of an effect or result that would be expected if the subject were true.

Svabhava Hetu is based on the inherent nature or characteristics of the subject. For example, if we say that 'fire is hot' because it has the inherent property of heat, then 'heat' is the Svabhava Hetu.

Karya Hetu is based on the effect or result of the subject. For example, if we say that 'fire is hot' because it causes things to burn, then 'burning' is the Karya Hetu.

Asatkarya Hetu is based on the absence of an effect or result that would be expected if the subject were true. For example, if we say that 'fire is not cold' because it does not cause things to freeze, then 'freezing' is the Asatkarya Hetu.

The purpose of using hetus in Nyaya philosophy is to establish the validity of a syllogism, to prove the truth of a conclusion, and to refute an opponent's argument.

Fire is hot because it burns things is an example of a Svabhava Hetu because it is based on the inherent nature or characteristics of fire.

Smoke is a sign of fire because it is always produced by fire is an example of a Karya Hetu because it is based on the effect or result of fire.

The absence of smoke is a sign of the absence of fire is an example of an Asatkarya Hetu because it is based on the absence of an effect or result that would be expected if fire were present.

The difference between a Svabhava Hetu and a Karya Hetu is that Svabhava Hetu is based on the inherent nature of the subject, while Karya Hetu is based on the effect or result of the subject.

The difference between a Karya Hetu and an Asatkarya Hetu is that Karya Hetu is based on the presence of an effect or result, while Asatkarya Hetu is based on the absence of an effect or result.

All fire is hot because it burns things is an example of a valid syllogism using a Svabhava Hetu because the hetu (burning things) is inherent in the nature of fire.

All smoke is a sign of fire because it is always produced by fire is an example of a valid syllogism using a Karya Hetu because the hetu (being produced by fire) is an effect or result of fire.

The absence of smoke is a sign of the absence of fire is an example of a valid syllogism using an Asatkarya Hetu because the hetu (absence of smoke) is the absence of an effect or result that would be expected if fire were present.