Short answers, pulled from the story.
Dignaga, who lived approximately from 480 to 540 CE, is the founder of the pramānavāda or epistemological school of Buddhist logic. His magnum opus, the Pramana-samuccaya, established the tradition that Dharmakirti later extended in the 7th century.
Pramana refers to a valid means or instrument of knowledge. The school of Dignaga recognized only two pramanas: perception and inference. This differed from the Nyaya school, which accepted four, including comparison and testimony.
Dharmakirti added the requirement that a valid cognition must confirm causal efficacy, meaning the cognition must comply with the object's capacity to perform a function. He also developed Buddhist atomism, holding that only momentary particulars are ultimately real, with everything else being conventional.
The Buddha rejected both scriptural authority and pure rationalism as sole sources of knowledge, favoring verification through personal experience. He also divided questions into those that could be resolved through analysis and those he set aside as unanswerable, called avyakatas. His view combined elements of empiricism, pragmatism, and coherentism according to scholars like K.N. Jayatilleke.
Dharmakirti's Pramanavarttika became the central text on epistemology in Tibet, secured in that role by Sakya Pandita's Tshad-ma rigs-gter written in the 13th century. The Gelug school built its logical curriculum around Dharmakirti's pramana texts, and the debate between the realist tradition of Chapa Chogyi Sengge and the anti-realist tradition of Sakya Pandita became a defining topic in Tibetan Buddhist philosophy.
Apoha, or exclusion, is Dignaga's theory of how words convey meaning. For Dignaga, a word does not directly refer to a positive entity but gives its meaning by excluding everything it is not. The word 'cow' conveys meaning through the exclusion of all non-cows.