Short answers, pulled from the story.
Indian logic is one of three original traditions of logical inquiry developed independently in human history, alongside Greek and Chinese logic. Its origins trace to the anviksiki school founded by Medhatithi Gautama around the 6th century BCE, making it approximately 2,500 years old. The tradition continued developing into the modern era through the Navya-Nyaya school.
Gotama founded the Nyaya school of Hindu philosophy and composed the Nyaya Sutras around the 2nd century CE. The school identified four valid sources of knowledge: perception, inference, comparison, and testimony. Its methodology was subsequently adopted by most other Indian philosophical schools.
Navya-Nyaya, or Neo-Logical philosophy, was founded in the 13th century CE by Gangesha Upadhyaya of Mithila. His central work, the Tattvacintamani, covered logic, set theory, and epistemology. The school developed theories anticipating aspects of modern set theory and Gottlob Frege's distinction between the sense and reference of proper names.
George Boole (1815-1864) and Augustus De Morgan (1806-1871) made their pioneering applications of algebraic ideas to logic during a period when British scholars were actively studying Indian logic. Mary Everest Boole confirmed the Indian influence on Boole in her 1901 open letter titled "Indian Thought and Western Science in the Nineteenth Century." De Morgan himself wrote in 1860 that Sanskrit and Greek speakers were the two peoples who had independently formed systems of logic.
Jain logic rests on three doctrines: anekantavada, the theory of relative pluralism or manifoldness; syadvada, the theory of conditioned predication; and nayavada, the theory of partial standpoints. Jain logic flourished from the 6th century BCE to the 17th century CE.
Akalanka was an 8th-century CE Jain logician whose Sanskrit works are regarded as landmarks in Indian logic. He has been called the "Master of Jain logic." His writings contributed to the broader Jain logical tradition that spanned from the 6th century BCE to the 17th century CE.