アポーハ代数・アポーハ論理・アポーハ比量

抄録

In his Apoha Theory, Dignāga argues that when two words stand in a hyper-hyponym relationship (sāmānya-viśeṣa relationship), each word does not exclude the other, and that the meaning (artha) of the hyponym includes the meaning of the hypernym. Using symbolic logic, the author of the present paper has formalized the meaning of a word on a given group of words each of which has a definite extension. A result of formalization is that the negation in the negative compound behaves like a negation in intuitionistic logic, rather than a negation in classical logic, in which the law of double negation holds.

The present paper introduces two implication-free propositional subsystems of Gentzen’s LK (classical logic), one of which is equivalent with Gentzen’s LJ (intuitionistic logic), and names both systems “Apoha logic”. The present paper shows that in relation to Dignāga’s three-part-inference, we can, under some logical conditions, deduce in Apoha logic the double negation of the proposition (pratijñā) from the premises–––the inferential reason (hetu) and the negative concomitance (vyatireka)–––whereas in Apoha logic we cannot necessarily deduce the proposition from the premises.