A review of some concepts and terms from nyAya is in order before we proceed further. Please see "Materials for the study of Navya Nyaya Logic" by Ingalls or "The Navya-Nyaya doctrine of negation" by Bimal Krishna Matilal for more details.
Process of inference:
Every noneternal entity, according to nyAya, must be a result of an instrumental cause (karaNa) and an operation (vyApAra). An inference (anumAna), that is a means to knowledge of man and hence noneternal, must have an instrumental cause and an operation by which the cause brings about the inference.
In the process of inference, the operation is called parAmarsha or consideration, and the instrumental cause is the knowledge of invariable concomitance (vyApti), also called pervasion. This vyApti corresponds very roughly to logical implication in Western logic.
In the inference, "the mountain possesses fire because it has smoke", the instrumental cause, karaNa is the knowledge of the invariable concomitance, "smoke is the invariable concomitant of fire", vahni-vyApyo dhUmaH, ie. where there is smoke there is fire. The operation, vyApAra is the consideration (parAmarsha) that is a knowledge of the occurrence of the concomitant in the subject (pakshha) where the inference is being made. In the inference, "the mountain possesses fire because it has smoke", the parAmarsha will be of the form, "the mountain possesses smoke which is an invariable concomitant of fire" - parvato vahni-vyApya-dhUmavAn.h
In polemical treatises and debates, an inference is stated tersely by listing the inference (conclusion) followed by a single word representing the application of the consideration and the invariable concomitance. For example, parvato vahnimAn.h dhUmAt.h, "the mountain possesses fire because of smoke."
In every inference, there are evident three terms, called 1) sAdhya or that which is to be proved, 2) the hetu or linga, the concomitant, and 3) the subject or pakshha, that in which the hetu is known to occur. In the inference, parvato vahnimAn.h dhUmAt.h, "the mountain has fire because of smoke", the sAdhya is vahni (fire), the hetu is smoke, and the pakshha is parvata (mountain).
In the standard form of inference, the three terms are placed as follows:
pakshha sAdhya-with-possessive-suffix hetu-in-ablative-case
For example, parvato vahnimAn.h dhUmAt.h, "the mountain has fire because of smoke."
The definition of vyApti is very important. It is defined by the bhAshhA-parichchheda (of VishvanAtha) as:
vyAptiH sAdhyavadanyasminn-asaMbandha udAhR^itaH |
Invariable concomitance is said to be the absence of relation of the (hetu) to anything other than what possesses the sAdhya.
Here the relation should be the same as the relation under consideration for the vyApti. As per this definition of vyApti, smoke is an invariable concomitant of fire (or smoke is "pervaded" by fire) because it is not the case that there is something that has smoke but not fire. However, fire is not an invariable concomitant of smoke. There are things such as a red-hot iron rod that has fire but no smoke. So fire is not an invariable concomitant of smoke.
A relation between two entities is often explained as the superimposition of one entity on the other. Here, the entity that is superimposed is called the superstratum or Adheya. The entity on which the Adheya is superimposed is called substratum or locus. Sanskrit names for "substratum" is AdhAra or Ashraya or adhikaraNa. In the example, bhUtale ghaTo vartate, "there is a pot on the ground", the superstratum is the pot (ghaTa), the ground (bhUtalam.h) is the substratum or locus, and the relation is "contact", saMyoga.
Another way of looking at relations (saMbandha) is to differentiate between what Ingalls calls "occurrence-exacting" and "non occurrence exacting" relations. Relations such as inherence (samavAya) are always occurrence exacting. samavAya or inherence is the relation between a whole and its parts, a genus or class (jAti) and a particular instance of the class, etc. Contact (saMyoga) can sometimes be occurrence exacting but sometimes not.
In relation between two entities, one of the entities is an adjunct or pratiyogin, and the other is a subjunct or anuyogin. If a relation is such that one entity is a locus or substratum (AdhAra) of the other which must be the superstratum (Adheya), then the AdhAra is the subjunct or anuyogin. The Adheya is the adjunct or pratiyogin. In the example, bhUtale ghaTaH, "there is a pot on the ground", ghaTa is the pratiyogin while bhUtalam.h is the anuyogin.
Two types of absences (abhAva) are distinguished in navya-nyAya. One is called anyonya-abhAva that is essentially a denial of identity between to entities. The other is saMsarga-abhAva or relational absence. Here, there are three kinds: 1) prAgabhAva, the absence of a thing before it is brought into being, 2) dhvamsAbhAva, the absence of a thing after it is destroyed, and 3) atyanta-abhAva, eternal absence.
The terms pratiyogin and anuyogin are also used in the context of absences. When we say "bhUtale ghaTo nAsti", "there is no pot on the ground", the pratiyogin of the absence is "ghaTa", pot, and the anuyogin is "bhUtalam.h", ground. The pratiyogin of this type should be called "abhAvIya-pratiyogin" to distinguish it from the relational adjunct, but naiyAyikas often write "pratiyogin" for both relational and absential adjuncts.