In early Indian philosophy, who is traditionally regarded as the author of the Nyaya Sutra, the foundational text of the Nyaya school of logic and epistemology?

Introduction / Context:
This question is from the domain of Indian philosophy and classical schools of thought known as the Darshanas. The Nyaya school is particularly famous for its systematic treatment of logic, reasoning and means of knowledge. Its basic doctrines are set out in a key text called the Nyaya Sutra. Knowing who composed this text helps you connect thinkers with the systems they founded.

Given Data / Assumptions:

• The philosophical text mentioned is the Nyaya Sutra.
• The Nyaya Sutra is the foundational text of the Nyaya school.
• The options list several ancient philosophers Gautama, Kanada, Kapila, Badarayana and Patanjali.
• The task is to identify which of these is traditionally regarded as the author of the Nyaya Sutra.

Concept / Approach:
The key idea is to match schools with their traditional authors. The Nyaya school focuses on logic and epistemology and its chief text is the Nyaya Sutra, ascribed to the sage Gautama, also known as Akshapada. Kanada is associated with the Vaisheshika school and its Vaisheshika Sutra. Kapila is linked with the Samkhya system. Badarayana is considered the author of the Brahma Sutra of the Vedanta school. Patanjali is associated with the Yoga Sutra. Therefore, among the options, only Gautama (Akshapada) fits correctly as the author of the Nyaya Sutra.

Step-by-Step Solution:
Step 1: Identify Nyaya as the school that deals mainly with logic and methods of correct reasoning.Step 2: Recall that the primary text of this school is the Nyaya Sutra.Step 3: Remember that traditional accounts of Indian philosophy attribute this work to sage Gautama, who is also called Akshapada.Step 4: Map the other names to their schools Kanada with Vaisheshika, Kapila with Samkhya, Badarayana with Vedanta, and Patanjali with Yoga.Step 5: Select Gautama (Akshapada) from the options as the only correct match for author of Nyaya Sutra.

Verification / Alternative check:

Why Other Options Are Wrong:

• Kanada: Founder of the Vaisheshika school, connected with the Vaisheshika Sutra, not the Nyaya Sutra.
• Kapila: Considered the founder of the Samkhya system, often associated with Samkhya Sutras or teachings, not with Nyaya.
• Badarayana: Traditionally associated with the Brahma Sutra, a core Vedanta text.
• Patanjali: Known for composing the Yoga Sutra, the classical text of the Yoga school.

Common Pitfalls:
Because there are many schools and many sages, students sometimes mix them up, especially Kapila, Kanada and Gautama. Another confusion arises from the fact that the name Gautama also appears in Buddhist contexts, which is a different figure. To avoid errors, always remember Nyaya logic equals Gautama Akshapada, Vaisheshika atoms equals Kanada, and Yoga equals Patanjali. This pairing method keeps the systems clearly separated in memory.

Final Answer:
The Nyaya Sutra, the foundational text of the Nyaya school of logic, is traditionally attributed to Gautama (Akshapada).