What kinds of fallacious middle terms did Nyaya logicians identify?

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History of logic Zeno's paradox, illustrated by Achilles' racing a tortoise.

In the Nyaya school of logic, the middle term (hetu) is essential for establishing a valid inference. To ensure both formal validity and material truth, Nyaya logicians identified five specific types of fallacious middle terms:1

Inconclusive (savyabhichara): A middle term that is too broad, leading to multiple, conflicting conclusions.1
Contradictory (viruddha): A middle term that opposes or negates the very conclusion it is intended to establish.1
Controversial (prakaranasama): A middle term that fails to settle the issue, instead provoking the same question it was meant to resolve.1
Counterquestioned (sadhyasama): A middle term that is itself unproved or requires further evidence, failing to provide a firm foundation for the argument.1
Mistimed (kalatita): A middle term that is applied outside of its relevant temporal context, rendering it inapplicable to the case at hand.1

These classifications reflect the Nyaya emphasis on ensuring that logical reasoning remains grounded in verifiable examples and accurate premises.1