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Prakarana Panchika, a commentary on the siddhantas of Prabhakara Guru school of Mimamsa defines Arthaapatti as follows  <blockquote>अर्थापत्तिलक्षणम्। विना कल्पनयाऽर्थेन दृष्टेनाऽनुपपन्नताम्। नयताऽदृष्टमर्थं या साऽर्थापत्तिस्तु कल्पना।। 1 ।। इति। (Prak. Panc. Arthapatti Paricheda)<ref>Prakarana Panchika by Shalikanatha Mishra (Prabhakara Guru's School) [https://sa.wikisource.org/wiki/%E0%A4%AA%E0%A5%8D%E0%A4%B0%E0%A4%95%E0%A4%B0%E0%A4%A3%E0%A4%AA%E0%A4%9E%E0%A5%8D%E0%A4%9A%E0%A4%BF%E0%A4%95%E0%A4%BE#%E0%A4%85%E0%A4%B0%E0%A5%8D%E0%A4%A5%E0%A4%BE%E0%A4%AA%E0%A4%A4%E0%A5%8D%E0%A4%A4%E0%A4%BF%E0%A4%AA%E0%A4%B0%E0%A4%BF%E0%A4%9A%E0%A5%8D%E0%A4%9B%E0%A5%87%E0%A4%A6:%E0%A5%A4 Arthapatti Parichedha]</ref></blockquote><blockquote>दृष्टेनाऽर्थेनाऽदृष्टस्याऽर्थस्याऽर्थान्तरकल्पनायामसत्यामनुपपत्तिमापादयता याऽर्थान्तरकल्पना, साऽर्थापत्ति:। यथा - जीवतो देवदत्तस्य गृहाभावदर्शनेन बहिर्भावस्याऽदृष्टस्य कल्पना।  </blockquote>According to Dr. Jha the above sloka and bhashya are summarized as ''"In a case where the well-ascertained perception of a thing or things (artha) cannot be explained or reconciled without the presumption of another thing or things, then it is this presumption that constitutes Arthapatti. For instance, when we know that Devadatta is alive and perceive that he is not in the house, these two things - being alive and non-existence in the house cannot be reconciled unless we presume his existence somewhere outside the house; and the presumption of this external existence is what is called Arthapatti"'' (Page 70 of Reference <ref name=":2" />)

Prakarana Panchika, a commentary on the siddhantas of Prabhakara Guru school of Mimamsa defines Arthaapatti as follows  <blockquote>अर्थापत्तिलक्षणम्। विना कल्पनयाऽर्थेन दृष्टेनाऽनुपपन्नताम्। नयताऽदृष्टमर्थं या साऽर्थापत्तिस्तु कल्पना।। 1 ।। इति। (Prak. Panc. Arthapatti Paricheda)<ref>Prakarana Panchika by Shalikanatha Mishra (Prabhakara Guru's School) [https://sa.wikisource.org/wiki/%E0%A4%AA%E0%A5%8D%E0%A4%B0%E0%A4%95%E0%A4%B0%E0%A4%A3%E0%A4%AA%E0%A4%9E%E0%A5%8D%E0%A4%9A%E0%A4%BF%E0%A4%95%E0%A4%BE#%E0%A4%85%E0%A4%B0%E0%A5%8D%E0%A4%A5%E0%A4%BE%E0%A4%AA%E0%A4%A4%E0%A5%8D%E0%A4%A4%E0%A4%BF%E0%A4%AA%E0%A4%B0%E0%A4%BF%E0%A4%9A%E0%A5%8D%E0%A4%9B%E0%A5%87%E0%A4%A6:%E0%A5%A4 Arthapatti Parichedha]</ref></blockquote><blockquote>दृष्टेनाऽर्थेनाऽदृष्टस्याऽर्थस्याऽर्थान्तरकल्पनायामसत्यामनुपपत्तिमापादयता याऽर्थान्तरकल्पना, साऽर्थापत्ति:। यथा - जीवतो देवदत्तस्य गृहाभावदर्शनेन बहिर्भावस्याऽदृष्टस्य कल्पना।  </blockquote>According to Dr. Jha the above sloka and bhashya are summarized as ''"In a case where the well-ascertained perception of a thing or things (artha) cannot be explained or reconciled without the presumption of another thing or things, then it is this presumption that constitutes Arthapatti. For instance, when we know that Devadatta is alive and perceive that he is not in the house, these two things - being alive and non-existence in the house cannot be reconciled unless we presume his existence somewhere outside the house; and the presumption of this external existence is what is called Arthapatti"'' (Page 70 of Reference <ref name=":2" />)

Shabara Bhashya which is the authoritative commentary for Purva Mimamsa sutras Arthapatti is elaborated as follows<blockquote>औत्पत्तिकस्तु शब्दस्यार्थेन सम्बन्धस्तस्य ज्ञानमुपदेशोऽव्यतिरेकश्चार्थेऽनुपलब्धे तत् प्रमाणं सू.1.1.5 (Shab. Bhas. Sutr. 1.1.5)<ref>Shabara Bhashya For Sutra Purva Mimasa Sutra (1.1.5) ([https://sa.wikisource.org/wiki/%E0%A4%B6%E0%A4%AC%E0%A4%B0%E0%A4%AD%E0%A4%BE%E0%A4%B7%E0%A5%8D%E0%A4%AF%E0%A4%AE%E0%A5%8D/%E0%A4%AA%E0%A5%8D%E0%A4%B0%E0%A4%A5%E0%A4%AE%E0%A5%8B%E0%A4%BD%E0%A4%A7%E0%A5%8D%E0%A4%AF%E0%A4%BE%E0%A4%AF%E0%A4%83/%E0%A4%AA%E0%A5%8D%E0%A4%B0%E0%A4%A5%E0%A4%AE%E0%A4%83_%E0%A4%AA%E0%A4%BE%E0%A4%A6%E0%A4%83 Adhyaya 1 Pada 1 Adhikara 4])</ref></blockquote>Under this Mimamsa Sutra (1.1.5) Shabara Bhashya explanation for Arthapatti is as follows<blockquote>अर्थापत्तिरपि - दृष्टः, श्रुतो वार्थोऽन्यथा नोपपद्यते इत्यर्थकल्पना। यथा, जीवति देवदत्ते गृहाभावदर्शनेन बहिर्भावस्यादृष्टस्य कल्पना।। </blockquote>Arthapatti, "Presumption", also consists in the presuming of something not seen, on the ground that a fact already perceived or heard would not be possible without that presumption; for instance<ref>Mm. Ganganatha Jha () Shabara Bhasya [https://archive.org/details/ShabaraBhasyaTrByGanganathJha/page/n29 Translation] </ref>  

Shabara Bhashya which is the authoritative commentary for Purva Mimamsa sutras Arthapatti is elaborated as follows<blockquote>औत्पत्तिकस्तु शब्दस्यार्थेन सम्बन्धस्तस्य ज्ञानमुपदेशोऽव्यतिरेकश्चार्थेऽनुपलब्धे तत् प्रमाणं सू.1.1.5 (Shab. Bhas. Sutr. 1.1.5)<ref>Shabara Bhashya For Sutra Purva Mimasa Sutra (1.1.5) ([https://sa.wikisource.org/wiki/%E0%A4%B6%E0%A4%AC%E0%A4%B0%E0%A4%AD%E0%A4%BE%E0%A4%B7%E0%A5%8D%E0%A4%AF%E0%A4%AE%E0%A5%8D/%E0%A4%AA%E0%A5%8D%E0%A4%B0%E0%A4%A5%E0%A4%AE%E0%A5%8B%E0%A4%BD%E0%A4%A7%E0%A5%8D%E0%A4%AF%E0%A4%BE%E0%A4%AF%E0%A4%83/%E0%A4%AA%E0%A5%8D%E0%A4%B0%E0%A4%A5%E0%A4%AE%E0%A4%83_%E0%A4%AA%E0%A4%BE%E0%A4%A6%E0%A4%83 Adhyaya 1 Pada 1 Adhikara 4])</ref></blockquote>Under this Mimamsa Sutra (1.1.5) Shabara Bhashya explanation for Arthapatti is as follows<blockquote>अर्थापत्तिरपि - दृष्टः, श्रुतो वार्थोऽन्यथा नोपपद्यते इत्यर्थकल्पना। यथा, जीवति देवदत्ते गृहाभावदर्शनेन बहिर्भावस्यादृष्टस्य कल्पना।। </blockquote>Arthapatti, "Presumption", also consists in the presuming of something not seen, on the ground that a fact already perceived or heard would not be possible without that presumption; for instance Devadatta who is not in the house, and this non-existence in the house leads to the presumption that he is somewhere outside the house (as without this, the aforesaid fact of his being alive and not in the house could not be explained).<ref>Mm. Ganganatha Jha () Shabara Bhasya [https://archive.org/details/ShabaraBhasyaTrByGanganathJha/page/n29 Translation] </ref>  

==== Advaita Vedanta ====

==== Advaita Vedanta ====

अभाव is accepted by Naiyāyikas as a separate पदार्थ and not as a pramana.<ref name=":1">Paper Presentation by Prof. K. Subrahmanayam titled ''[https://groups.google.com/d/msg/bvparishat/xY1Y-wdPeSo/CKzUaFPABwAJ Pramāṇas in Indian Philosophy]''</ref> According to Kumarila Bhatta Mimamsa and Advaita Vedanta Anupalabdhi is an independent pramana.<ref name=":32" />

अभाव is accepted by Naiyāyikas as a separate पदार्थ and not as a pramana.<ref name=":1">Paper Presentation by Prof. K. Subrahmanayam titled ''[https://groups.google.com/d/msg/bvparishat/xY1Y-wdPeSo/CKzUaFPABwAJ Pramāṇas in Indian Philosophy]''</ref> According to Kumarila Bhatta Mimamsa and Advaita Vedanta Anupalabdhi is an independent pramana.<ref name=":32" />

In निरालम्बनवाद (श्लो^० १०७-११३) of श्लोकवार्त्तिक Kumārila clearly states that अलातचक्र etc. is बौद्धार्थ –<ref name=":1" /><blockquote>स्वप्नादिप्रत्यये बाह्यं सर्वथा न हि नेष्यते ॥ १०७ ॥</blockquote><blockquote>सर्वत्रालम्बनं बाह्यं देशकालान्यथात्मकम् । जन्मन्येकत्र भिन्ने वा तथा कालान्तरेऽपि वा ॥ १०८ ॥</blockquote><blockquote>तद्देशो वान्यदेशो वा स्वप्नज्ञानस्य गोचरः । अलातचक्रेऽलातं स्याच्छीघ्रभ्रमणसंस्कृतम् ॥ १०९ ॥</blockquote><blockquote>गन्धर्वनगरेऽभ्राणि पूर्वदृष्टं गृहादि च । पूर्वानुभूततोयं च रश्मितप्तोषरं तथा ॥ ११० ॥</blockquote><blockquote>मृगतोयस्य विज्ञाने कारणत्वेन कल्प्यते । द्रव्यान्तरे विषाणं च शशस्यत्मा च कारणम् ॥ १११ ॥</blockquote><blockquote>शशशृङ्गधियो मौण्ड्यं निषेधे शिरसोऽस्य च । वस्त्वन्तरैरसंसृष्टः पदार्थः शून्यताधियः ॥ ११२ ॥</blockquote><blockquote>कारणत्वं पदार्थानामसद्वाक्यार्थकल्पने । अत्यन्ताननुभूतोऽपि बुद्ध्या योऽर्थः प्रकल्प्यते ॥ ११३ ॥</blockquote>Patañjali says सतो बुद्धिविषयान् प्रकाशयन्ति (they express things that are there in the mind) which clearly supports ‘बौद्धार्थ’. ‘बुद्धौ कृत्वा सर्वाश्चेष्टाः कर्ता धीरस्तन्वन्नीतिः’ (the scholar, who has got an intellect that spreads, would imagine all the process, i.e. related to prior and latter, the relation etc. in the intellect) etc. is the statement of Patañjali which also establishes the सिद्धान्त of बौद्धार्थ. Words like शशशृङ्गम्, गगनकुसुमम् etc. express things that are बौद्ध (imaginary) rather than real.  

In निरालम्बनवाद (श्लो^० १०७-११३) of श्लोकवार्त्तिक Kumārila clearly states that अलातचक्र etc. is बौद्धार्थ –<ref name=":1" /><blockquote>स्वप्नादिप्रत्यये बाह्यं सर्वथा न हि नेष्यते ॥ १०७ ॥</blockquote><blockquote>सर्वत्रालम्बनं बाह्यं देशकालान्यथात्मकम् । जन्मन्येकत्र भिन्ने वा तथा कालान्तरेऽपि वा ॥ १०८ ॥</blockquote><blockquote>तद्देशो वान्यदेशो वा स्वप्नज्ञानस्य गोचरः । अलातचक्रेऽलातं स्याच्छीघ्रभ्रमणसंस्कृतम् ॥ १०९ ॥</blockquote><blockquote>गन्धर्वनगरेऽभ्राणि पूर्वदृष्टं गृहादि च । पूर्वानुभूततोयं च रश्मितप्तोषरं तथा ॥ ११० ॥</blockquote><blockquote>मृगतोयस्य विज्ञाने कारणत्वेन कल्प्यते । द्रव्यान्तरे विषाणं च शशस्यत्मा च कारणम् ॥ १११ ॥</blockquote><blockquote>शशशृङ्गधियो मौण्ड्यं निषेधे शिरसोऽस्य च । वस्त्वन्तरैरसंसृष्टः पदार्थः शून्यताधियः ॥ ११२ ॥</blockquote><blockquote>कारणत्वं पदार्थानामसद्वाक्यार्थकल्पने । अत्यन्ताननुभूतोऽपि बुद्ध्या योऽर्थः प्रकल्प्यते ॥ ११३ ॥</blockquote>[https://sa.wikisource.org/wiki/%E0%A4%B6%E0%A5%8D%E0%A4%B2%E0%A5%8B%E0%A4%95%E0%A4%B5%E0%A4%BE%E0%A4%B0%E0%A5%8D%E0%A4%A4%E0%A4%BF%E0%A4%95%E0%A4%AE%E0%A5%8D Slokavartika in Wikisource]

 

Patañjali says सतो बुद्धिविषयान् प्रकाशयन्ति (they express things that are there in the mind) which clearly supports ‘बौद्धार्थ’. ‘बुद्धौ कृत्वा सर्वाश्चेष्टाः कर्ता धीरस्तन्वन्नीतिः’ (the scholar, who has got an intellect that spreads, would imagine all the process, i.e. related to prior and latter, the relation etc. in the intellect) etc. is the statement of Patañjali which also establishes the सिद्धान्त of बौद्धार्थ. Words like शशशृङ्गम्, गगनकुसुमम् etc. express things that are बौद्ध (imaginary) rather than real.  

Patañjali advocates a third category, i.e., other than प्रमा and भ्रम, called विकल्प. प्रमा is यथार्थज्ञान (authoritative cognition) achieved through ''Pramāṇas'' whereas भ्रम or विपर्यय is the usage (and the connected cognition) that is borne from the usage and the cognition that follows but without the existence of the thing in question – शब्दज्ञानानुपाती वस्तुशून्यो विकल्पः (यौ^० सू^० १-९) is the ''sūtra'' of Patañjali. शशशृङ्गम् etc. are examples. Such a cognition is possible when there is बौद्धार्थ. There is no बाह्यार्थ (outside / real thing) but due to the capacity of ''Śabda'' the cognition is generated. The same is expressed by Kumārila in श्लोकवार्त्तिकम् (चोदनासूत्रम् – ६)   

Patañjali advocates a third category, i.e., other than प्रमा and भ्रम, called विकल्प. प्रमा is यथार्थज्ञान (authoritative cognition) achieved through ''Pramāṇas'' whereas भ्रम or विपर्यय is the usage (and the connected cognition) that is borne from the usage and the cognition that follows but without the existence of the thing in question – शब्दज्ञानानुपाती वस्तुशून्यो विकल्पः (यौ^० सू^० १-९) is the ''sūtra'' of Patañjali. शशशृङ्गम् etc. are examples. Such a cognition is possible when there is बौद्धार्थ. There is no बाह्यार्थ (outside / real thing) but due to the capacity of ''Śabda'' the cognition is generated. The same is expressed by Kumārila in श्लोकवार्त्तिकम् (चोदनासूत्रम् – ६)