Short answers, pulled from the story.
Medhatithi Gautama founded the anviksiki school of logic around the 6th century BCE. This school became a central pillar for early Indian logical inquiry and influenced subsequent philosophical developments.
Jain philosophers contributed unique epistemological doctrines including Anekantavada, Syadvada, and Nayavada from the 6th century BCE through the 17th century CE. Key figures such as Kundakunda and Umāsvāti authored foundational texts during the 2nd century CE to establish these views.
Dignaga created the doctrine of Trairūpya and the Hetucakra Wheel of Reasons scheme between 480 and 540 CE. Dharmakirti lived from 600 to 660 CE and contributed significantly to theoretical achievements in inference within this tradition.
Gangesha Upadhyaya founded the Navya-Nyaya school in Mithila during the 13th century CE. His book Tattvacintāmaņi addressed criticisms from Śrīharśa's Khandanakhandakhādya while examining Nyaya thought more rigorously himself.
Henry T. Colebrooke published The Philosophy of the Hindus: On the Nyaya and Vaisesika Systems in 1824 analyzing inference compared to Aristotelian logic. This work marked a significant moment in Western engagement with Indian logical traditions.