Relation (सम्बन्धः)

Relation or Sambandha (Samskrit: सम्बन्धः) refers to the logic of relations developed in Nyaya shastra.

Nyaya rests to a great extent on the concept of sambandha or relation. This concept is an all- pervasive one on account of which Navya-Nyaya can be termed relational logic. It has potential benefits for realizing new and deep knowledge representation schemes superior to semantic nets and conceptual graphs used in AI. Relations also play a significant role in the process of cognition. The concept is also complex because it involves difficulties of various types, ontological, logical and epistemological.

Introduction

Nyaya rests to a great extent on the concept of sambandha or relation. This concept is an all- pervasive one on account of which Navya-Nyaya can be termed relational logic. It has potential benefits for realizing new and deep knowledge representation schemes superior to semantic nets and conceptual graphs used in AI. Relations also play a significant role in the process of cognition. The concept is also complex because it involves difficulties of various types, ontological, logical and epistemological.

Characteristics of a Relation

According to Dharmaklrti (Sambandha Panksa, c. 600 ce), a relation will have any of the following characteristics:

1. Dependency is a relation.

2. Amalgamation or contact is a relation.

3. Expectancy is a relation.

4. Cause-Effect is a relation.

5. That which exists in two things is a relation.

What is a relation? An obvious answer is that a relation connects two entities. A relation that readily comes to mind between two objects is contact (samyoga). Navya-Nyaya regards all relations as dyadic relations between two terms; the first is called anuyogin or referend and the second, the pratiyogin or referent. The Navya Nyaya theory is that a relation is always a property resident in the referend. The relation R between two things a and b can be represented by aRb, where a is the referend, b is the referent and R is the relation. In the knowledge fire (is) on (the) mountain (parvato vahniman — the mountain (is) fire-possessing), the mountain is called anuyogin and fire is called pratiyogin.

Classification of Relations

Relations in Navya-Nyaya can be classified based on different criteria. According to one criterion, the relations are classified into saksat (direct) and paramapara (chain) relations. A relation not involving other relations is termed direct; while one which involves other relations is a chain relation. For example, samyoga (contact) is a direct relation while samanadhikarana (co- locusness) is a chain relation. Fig. 1 shows the types of direct and chain relations.

The second criterion is based on whether the relation is occurrence-exacting or non-occurrence-exacting. In this "exacting" (niydmaka) means "limiting" (avacchedaka). An occurrence-exacting (vrtti-niyamaka) relation is one wherein the occurrence is regulated/limited in an entity. The relation involves the notion of substratum-superstratum (iadhara-adheya), between two distinct objects otherwise unconnected. Paryapti is a vrtti-niyamaka relation. Non-occurrence-exacting (vrtti- aniyamaka) is the opposite. Examples of non-occurrence-exacting relations are pervasion (vyapti), essential identity (abheda), and describerness-describedness (nirupakatva-nirupyatva).

The third category is for locus-pervading and non-locus- pervading relations. The relations are governed by pervasion (vyapti). The former is generally known as complete occurrence (vyapya-vrtti) while the latter, incomplete occurrence (avyapya- vrtti). Sarityoga between two material objects is usually an incomplete occurrence relation.

Concepts for Understanding Relations

1. A sentence in Sanskrit is often a qualificative cognitive state (visista jnana). An observer cognizes any object as qualified by a property or a qualifier.

2. According to some Navya-Naiyayikas, knowledge having for its content a qualified object is called a relation {visista-pratlti-niyamaka-visesasyaiva-sambandhatvat). The idea underlying this definition is that in a qualified knowledge entity three things become primarily the content of knowledge — the qualificand (znsesya), the qualifier (visesana) and the relation (sambandha) between the two. For Example, in the knowledge dandl-purusa (a man with a stick) the qualificand is the man, and the qualifier is the stick. When a qualificand has two qualifiers one expressed in the subject and one in the predicate, that expressed in the predicate is distin¬ guished as the prakara or the cheif qualifier.

3. When two entities are related one may often conceive of one as superimposed on the other. The entity that is superimposed is called the superstratum or adjunct (iadheya) and the element on which it rests is called the substratum or subjunct (adhara). The adhara is also called locus (adhikarana) or abode (asraya). The term avacchedaka is used in two senses: limitor and resident limitor. It denotes that property which by itself being one of the primary meanings of a term differentiates that term from terms denoting other objects. In some cases, the substratum is considered as the avacchedaka of the property residing in the object. Yet in some other cases, the adjective of the substratum of a particular property is called the avachchedaka of that property. The term avacchinna means "limited."

4. When jnana is analysed in Navya-Nyaya its content- ness, i.e., visayata becomes important. The visayata is subdivided into three categories: visesyata, prakarata and samsargata. Samsargata refers to the relation between the qualifier and the qualificand. The meaning of samsarga in this context is the point of intersection.

In several philosophical systems there is some ambiguity associated with words such as "is" and "exist." In normal usage the same word may be used in an existential sense as in "God is" in the sense of God exists and in the predicational sense as in "God is perfect." In Indian philosophy two words satta and bhava are the words for existence. The Naiyayikas carefully distinguish between these two words. Satta means existence or reality. It is traditionally defined as a generic character. Presence is denoted by bhava and its opposite abhava denotes absence.

Types of Relations

Samyoga

(a) Samyoga : Contact is one type of direct relation, e.g., bhutale ghatah asti (the pot is on the floor). This could have been said as ghatasya samyogah bhutale asti (the ground possesses the contact of the pot). In this example ghatah is the visesana. In the language of the Naiyayika this cognition is expressed as bhutalatvavacchinnaprakdraka samyogasamsargaka ghatatvd- vacchinnavisesya jhanam. In English, the qualifierness is limited by the jarness and by the relation of contact determining the qualificandness, limited by groundness. Samyoga is also vrtti- niydmaka (occurrence-exacting) relation, from the notion of the adhara-adheya bhava (locus-locatee relationship). The Naiyayika interprets this as bhutalatvavacchinnanista adharata nirupita samyogasambandhavacchina ghatatvdvacchina cidheyatavan ghatah. That is, the pot is the superstratum, supported by the ground limited by groundness, through samyoga relation. So, there is adharata bhava in the ground and adheyatd bhava in the pot. This occurrence-exacting relation between the pot and the ground is generally known as a relation of incomplete occurrence (avyapya-vrtti) because when a contact takes place between two substances (dravyas) it has to occur only in a part of them (point of contact), provided the two substances have parts.

Samavaya

Samavdya is considered as one of the seven fundamental categories (padartha) of the classical Vaisesika school, while samyoga (contact or conjunction) and vibhdga (disjunction) are considered as types of a second category guna (quality). Samavdya or inherence is an example of a direct relation and is also an occurrence-exacting relation. For example, in the knowledge of ghatah asti, ghatatva is visesana existing in the ghata by samavdya (inherence) relation. In nllah ghatah asti there is a blue jar, the blueness and the potness are inherent in the pot. Samavdya can be known by the sense-organs and hence through perception. This relation can also be easily seen as a vyapya vrtti relation. Navya-Nyaya distinguishes between two awarnesses such as a blue pot and a pot. To explain this difference Navya-Nyaya introduces the important concept of a limitor (avacchedaka). In a single word "pot" the potness (ghatatva) is the avacchedaka. In the relation aRb, a is the pot, R is inherence (samavaya) and b is the universal ghatatva which is cognized directly. Here b is the limitor of the property of being the qualificand and resident in a. A limitor is thus a qualifier in this case but all qualifiers are not limitors. In the phrase "blue jar" (nlla ghata) there are two avacchedakas residing in nllatva, even though the objects ghatah and mlah ghatah are one and the same.

Svarupa

It is not always the case that R is either contact or inherence. For example, R may represent a cause and effect relationship. What is this cause and effect relationship? The standard answer of the Naiyayika is that this relationship is not a distinct entity but merely the property of being either the cause or the effect. Under this category of relations a whole range of relationships exist from pitr-putra bhava to sambandhf- sambandha bhava. These relations are called svarupa or self¬ linking relations.

Examples : In the knowledge "This is a man," the qualifier of "man" is the generic character "man-ness" by which every member of the class "man" is recognized. In the same situation, if one's knowledge is "This is Devadatta," the qualifier of Devadatta is the Devadatta-ness. Man-ness inheres in every man (samavaya). The Devadatta-ness resides in Devadatta not by relation samavaya, but a particular qualification relation, at which is a visesanata-visesa-sambandha. The Devadatta-ness becomes an imposed property (upadhi) and the relation is a svarupa sambandha. This relation is also a vyapya vrtti relation. So far as the svarupa sambandha is concerned, it can be either a occurrence-exacting relation or a non-occurrence-exacting relation.

Tadatmya or Abheda

This is also one of the types of direct relations. This denotes essential identity or non¬ separateness. Navya-Nyaya recognizes this as a self-linking relation. The terms abheda and tadatmya have been used as synonymous terms in Navya-Nyaya. The term abheda would mean the constant absence (atyantabhdva) of bheda. Tadatmya is the uncommon property (asadharana dharma) existing in the self (sva). When defined in this way tadatmya exists in one and only one entity, being the essence of that entity.

Sadrsya

The Navya-Naiyayikas use the term pratiyogin normally in the situation of similarity (sadrsya), e.g., candra iva mukham (the face is like the moon). Candra is pratiyogin and mukha is anuyogin for the similarity relation. This is also a direct relation of the self-linking type.

Kalika

This denotes a temporal relation. This is of two sorts: direct (saksat) and indirect (parampara). Time is considered to be a single, formless, eternal substance. Everything resides directly in time through a temporal relation. Time is a substratum for all entities. For example, asmin mase varsa and vahgadese varsa have a similar syntactical relation. Direct temporal relation is of two sorts. In the first, all entities reside directly in universal time (mahakala). The second is the more important relation to logic wherein all non-eternal entities reside directly in a portion of time. This is the relation between rain and a particular month. Now a portion of time is an imposed property (upadhi) on time. While time itself is eternal, its imposed properties are calibrations furnished by actions, contacts and disjunction. For example, these are set by the (apparent) motion of the Sun across a line.

Avacchedakatva

An especially difficult and important relation is that of limitorness, i.e., avacchedakatva and its converse, limitedness (avacchedyatva). Raghunatha Siromani makes this relation an important tool in Navya-Nyaya analysis. When someone says bhutale ghato nasti (there is no pot on the ground), the following questions arise in the listener's mind:

1. Whether the pratiyogin is any particular pot.

2. Whether it implies all pots.

3. Does the pratiyogita exist only in pots and not in something else such as cloth.

4. Whether this absence of pot is with respect to the full pot or parts of it.

5. Or is it the denial of the relation of the pot with the ground.

The Navya-Naiyayikas attempt to answer these questions with the concept of avacchedaka. The delimitor of the counter¬ positiveness can be stated as either tadghatatva or simply ghatatva. The former refers to a particular pot while the latter, to all pots. Ghatatva as delimitor also implies that there cannot be anything else other than pots. As regards issues (4) and (5), Navya-Naiyayikas utilize the concept of a relational delimitorness (pratiyogita-avacchedaka-sambandha). Navya-Nyaya literature gives a large number of examples where an avacchedaka may be used for the sake of avoiding ambiguity. We give some examples to illustrate different applications of avacchedaka.

1. Pratiyogita-avacchedaka: In the case of the absence of the form ghato nasti, the ghata is the pratiyogf (counter¬ positive) of the absence of ghata and ghatatva is the pratiyogita-avacchedaka.

2. Visayata-avacchedaka: If the ghata becomes the content (visaya) of knowledge, then the same ghatatva could be the visayata-avacchedaka (limitor of contentness).

3. Visayita-avacchedaka: The corresponding knowledge which is the container (visayi) of the content (visaya) has got the generic charcater jhanatva (knowledgeness) which is visayita-avacchedaka in this case.

4. Prakarata-avacchedaka: In the case of the knowledge of the form of ghatavat bhutalam (the ground is jar- possessing), the ghata is the prakara of bhutala and ghatava is the prakarata-avacchedaka.

5. Karyata-avacchedaka: In the case of the ghata being the effect of a stick (danda) ghatatva is the limitor of the effectness (ikaryata-avacchedaka), while dandatva (stickness) is the karanata-avacchedaka (the limitor of the causeness).

Abhava

Abhava is one of the seven categories under the Vaisesika system. Where R is a self-linking connector (svariipa sambandha) there are only two entities involved, although the situation is still triadic in form. The absence of a known entity denotes a case where there is no contact. For example, the relation between the place where something is absent (abhava) and the absence in bhutale ghato nasti or to be precise bhutale ghatabhava asti (there is absence of pot on the ground). The pot is said to be the pratiyogin or counter-positive of the absence of pot and the ground is said to be the anuyogin. This relation is called absential qualification (abhavtya visesanata). This can be represented as "ground-(R-absence of pot)." The ground is characterized by (svarupa) the absence of a pot. Here R does not designate a third thing beyond its relation; the ground is functioning as its own relation. Relational absences are denials of relations other than that of identity. These are said to be of three kinds:

1. Prior absence (pragabhava) denotes the absence of a thing somewhere before it is created. For example, prior to making a pot there is only clay and the pot is absent.

2. Posterior absence (pradhvamsabhava) denotes the absence of an existing thing after it has been destroyed. For example, if the pot is broken it ceases to exist.

3. Constant absence (atyantabhava) denotes the absence of a thing somewhere when this absence is not time- bound. For example, there is no fire in a lake. This may be expressed by "a lake is the locus of constant absence of fire."

In the knowledge of the constant absence of fire in a lake, the fire may be called pratiyogin and the lake, the anuyogin of an absence. Literally, the name for an adjunct in such a case is absential adjunct (abhaviya pratiyogin). This is also frequently referred to as counter-positive. In every counter-positive there exists counter-positiveness (pratiyogita).

Samyukta - samavaya

This is an indirect relation which is formed by a combination of two relations, contact (samyoga) and inherence (samavaya). In producing the perception of a quality {guna) or any other object which inheres in a subject (dravya) this relation comes into operation. As the quality inheres in a substance and the substance comes in contact with the sense-organ the sense-organ is said to be associated with the quality through this relation. This is a compound relation between the sense-organ and the form (rupa) of the object.

Samyukta - samaveta - samavaya

This indirect relation comes into effect if the perception by contact of the generic character jdti which inheres in a guna which again in turn inheres in a substance dravya.

Samaveta - samavaya

It is a compound of two samavayis. This relation is one where a is related to c through b in the form inherence of c in that which is inhered in, viz., b, by the subject a. Colour of the threads is related to the cloth by this relation. Here, c = cloth, b = threads and a = colour.

Svasamavayi - samavetatva

This is another type of indirect relation wherein samavdya, samyoga and svarupa are involved. For example, pate tanturupam — means thread-form in the cloth. Here, tantu = thread, is the co-locus for both pata = cloth and rupa = form. In this relation there exists co-locus-ness.

Modern Information Technology Applications of Indian Logic

The concepts of Indian logic have never been used for modern applications as the IT and AI systems. Therefore, there is a need to familiarize these concepts to make them useful in today's application context.

The cognitive and linguistic sciences offer scope for a multidisciplinary study of the mind or what might be called "natural intelligence." Cognitive science seeks an under¬ standing of such mental abilities as perception, recognition, categorization, memory, reasoning and problem-solving, motor control, speech, language, and communication. Linguistics focuses on the nature of human language — its theoretical, descriptive, behavioural, and evolutionary bases. It also serves as a window into human cognition. The approaches of a variety of disciplines, including cognitive psychology, linguistics, artificial intelligence, neuroscience, philosophy, and anthropology, are all brought to bear on common problems of mind, brain, and language. The future of the cognitive and linguistic sciences lies in crossing these traditional disciplinary boundaries. In linguistics and language processing, theories of phonology, syntax and semantics are increasingly enmeshed with the results of formal, compu¬ tational, and experimental studies. It is in this context we believe that a serious exploration of Indian philosophical views on logic and language is helpful to integrate the classical ideas with the present-day thinking. Indian Logic may be used to develop IT tools and products for conducting administration, business and educational activities in Indian multilingual environment through contextualizing Indie knowledge.

KNOWLEDGE ENGINEERING

Some possible applications for Indian logic are the following:

• Development of methods for knowledge acquisition, representation and validation using the deeper notion of knowledge in Indian logic. (Example: Use of Petri Nets for Indian Logic.)

• Development of a Sanskrit Word-net that would lead to Sanskrit as an Indian Link Language (ILL) to support machine translation from one Indian language to the other.

• Formalization of the methodology of hierarchical semantic analysis of sentences of ordinary (laukika) language using several layers of knowledge such as lexicons (kosa), grammar (vyakarana), logic (nyaya), and exegesis (mimamsa).

• Formalization of the methodology of semantic analysis of literary language (alarikara, vyanjanci, dhvani aspects) that would facilitate machine translation and know¬ ledge interpretation.

• Exploration of the methodology of parartha-anumana in tarka to train a researcher to defend a thesis, and to respond to the arguments of critics.