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... A proof is the record of operation of a sound inference procedure An inference procedure is complete if it can find a proof for any sentence that is entailed. Sound reasoning is called logical inference or deduction. A reasoning system should be able to draw conclusions that follow from the premises ...
Lecture_ai_3 - WordPress.com
Lecture_ai_3 - WordPress.com

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Nyaya

Nyāya (Sanskrit: न्याय, ny-āyá), literally means ""rules"", ""method"" or ""judgment"". It is also the name of one of the six orthodox (astika) schools of Hinduism. This school's most significant contributions to Indian philosophy was systematic development of the theory of logic, methodology, and its treatises on epistemology.Nyaya school's epistemology accepts four out of six Pramanas as reliable means of gaining knowledge – Pratyakṣa (perception), Anumāṇa (inference), Upamāṇa (comparison and analogy) and Śabda (word, testimony of past or present reliable experts).In its metaphysics, Nyaya school is closer to Vaisheshika school of Hinduism than others. It holds that human suffering results from mistakes/defects produced by activity under wrong knowledge (notions and ignorance). Moksha (liberation), it states, is gained through right knowledge. This premise led Nyaya to concern itself with epistemology, that is the reliable means to gain correct knowledge and to remove wrong notions. False knowledge is not merely ignorance to Naiyayikas, it includes delusion. Correct knowledge is discovering and overcoming one's delusions, and understanding true nature of soul, self and reality.Naiyayika scholars approached philosophy as a form of direct realism, stating that anything that really exists is in principle humanly knowable. To them, correct knowledge and understanding is different than simple, reflexive cognition; it requires Anuvyavasaya (अनुव्यवसाय, cross-examination of cognition, reflective cognition of what one thinks one knows). An influential collection of texts on logic and reason is the Nyayasutras, written by Aksapada Gautama about 2nd century CE.Nyaya school shares some of its methodology and human suffering foundations with Buddhism; however, a key difference between the two is that Buddhism believes that there is neither a soul nor self; Nyaya school like other schools of Hinduism believes that there is a soul and self, with liberation (moksha) as a state of removal of ignorance, wrong knowledge, the gain of correct knowledge and unimpeded continuation of self.
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