Indian logic is primarily concerned with the study of formal inference and argumentation, seeking to establish rules and principles for determining the validity and soundness of arguments.

Gautama, also known as Akshapada Gautama, is credited with authoring the Nyaya Sutras, a foundational text in Indian logic that laid the groundwork for subsequent developments in the field.

The syllogism, a deductive argument consisting of a major premise, a minor premise, and a conclusion, is the central concept in Gautama's Nyaya system, serving as the primary tool for logical reasoning and inference.

Indian logic influenced the development of logic in the West through multiple channels, including the translation of Indian logical texts into Greek and Arabic, the travels of Indian scholars to Europe, and the exchange of ideas between Indian and Western philosophers.

Gottfried Wilhelm Leibniz, a prominent 17th-century German philosopher and mathematician, was significantly influenced by Indian logic, particularly the Nyaya system, which he studied and incorporated into his own philosophical and logical theories.

Indian logic continues to be relevant in contemporary philosophical discourse, offering a unique perspective on logical reasoning and argumentation, providing insights into the nature of language and meaning, and challenging traditional Western notions of logic and rationality.

The Nyaya school of Indian logic is renowned for its focus on the theory of inference, developing a sophisticated framework for analyzing and evaluating different types of arguments and inferences.

The Vaisheshika school of Indian logic is primarily concerned with investigating metaphysical and epistemological questions, seeking to understand the nature of reality and the process of knowledge acquisition.

The Mimamsa school of Indian logic is renowned for its focus on the interpretation of Vedic texts, seeking to establish the correct understanding and application of Vedic injunctions and rituals.

The Vedanta school of Indian logic centers around the doctrine of Brahman, the ultimate reality and the source of all existence, seeking to understand the relationship between Brahman and the individual soul.

Indian logic made significant contributions to the development of mathematics in India by providing a framework for mathematical reasoning and proof, developing new mathematical concepts and techniques, and fostering a culture of mathematical inquiry and exploration.

Brahmagupta, an influential Indian mathematician and astronomer, is credited with developing the concept of zero and incorporating it into the Indian number system, revolutionizing mathematical calculations and paving the way for advancements in mathematics.

Indian logic has significant implications in the field of computer science, providing a foundation for the development of logical reasoning systems, offering insights into the nature of computation and algorithms, and contributing to the design and implementation of programming languages.

Indian logic has influenced the study of artificial intelligence in multiple ways, including providing a framework for representing and reasoning with knowledge, contributing to the development of logical inference engines, and inspiring the creation of new AI algorithms and techniques.

Studying Indian logic today presents several challenges, including the scarcity of available texts and manuscripts, the difficulty in interpreting ancient Sanskrit texts, and the lack of scholarly research and analysis.