Buddhist Logic, the categorical nomenclature modern Western discourse has extended to Buddhadharma traditions of 'Hetuvidya' (Sanskrit) and 'Pramanavada' (Sanskrit), which arose circa 500, is a particular development, application and lineage of continuity of 'Indian Logic', from which it seceded. Indian logic, and Buddhist Logic—in main heralded by Dignāga (c 480-540 CE)—are both primarily studies of 'inference'-patterns, where ‘inference’ is a gloss of anumāna (Sanskrit).
Sadhukhan, et al. (1994: p. 7) frames the centrality of 'syllogism' to Buddhist Logic and foregrounds its indivisibility as an investigative, authenticating and proofing tool instituted to establish the valid cognitive insights of the Buddhadharma:
Buddhist logic obviously contains the forms and nature of syllogism, the essence of judgement, etc. for which it deserves the name of logic. But that logic is not only logic it also establishes the doctrines of the Buddhists. Thus the philosophical tenets were the fulcrum and the logic developed as tools to establish those.
Following the work of Tucci (1929) and the critique of Anacker (2005, rev.ed.) upon the collation of Frauwallner (1957), it is now understood that Vasubandhu's Vāda-vidhi ("A Method for Argumentation") refined the five argument logic of the Nyāya-sūtra to a three argument form and not his pupil Dignāga. In addition to pruning the two redundant arguments from the syllogism, Vasubandhu tendered a further qualification: he posited that a sound relationship, a 'logical pervasion' (vyāpti) needs to be defined between the first and second arguments, a relationship between the 'Demonstrandum' (pratijna) and the 'Justification' (hetu) that is assumed in the Nyāya-sūtra and other literature of the Nyāya school. This logical pervasion is required to fashion sound arguments. Vasubandhu's Vāda-vidhi was reconstructed by Frauwallner from embedded quotations harvested from the works of Dignāga, amongst others. Dignāga as the oft-cited wellspring of the logical triune in the Buddhadharma is now invalidated.
Read more about Buddhist Logic: Qualifications of What Is Signified By The Lexical Signifier 'Logic' in The Dharmic Context, Antecedents and Secession, Pramana Sets As Determining Traditions of Dharma, Early Buddhism and The Rise of Nagarjuna, Indian Transmission Lineages To Tibet and Concomitant Translations, Vasubandhu: Avinābhāva, Doctrine of Trairūpya, Dignāga's, Dharmakirti's Theory of Inference, Doctrine of Anyapoha, Lexicon
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