Relations In Knowledge Representation (An Interdisciplinary Study in Nyaya, Mimamsa, Vyakarna, Tantra, Modern Linguistics, and Artificial Intelligence in Computer Application)

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The logic of consciousness belongs to certain conceptual formulations that give a valid basis for on expression to be crystallized on a relational scale. The relations are found to be developed as functional elements in internal representation of an expression. While framing a model of representational analysis we take notice of relations as an intermediate point between an expression and its structured content. This model aims at disambiguating the expression in all its possible levels and converting it to a particular logical form as specified by internal representation.

The present book studies the artificial intelligence of computer researches that specifically relate to Sanskrit and Sastras. The undertone of this study is to understand the problems that invariably involves semantic specifications and conceptual clarity in the context of different theories of knowledge representation and such other allied theories. This is an interdisciplinary study in Nyaya, Mimamsa, Vyakarana, Tantra, Modern Linguistics, and artifical Intelligence in computer application.

The book is divided into 16 chapters Ch.1 Introduction; Ch.2 An Analytical Survey of relations ch.3 identity in identification Ch.4 difference A relational analysis Ch.5 identifying a number Ch.6 Qualifier and qualificand; ch.7 is vocative a qulificand Ch. 8 Mimamsa theory of knowledge representation Ch.9 Tantric Formula and concept of sentence Ch.10. Tantric theory of knowledge representation Ch.11 Representation of an indeclinable Ch.12 knowledge representations a Study on cross point Ch. 13 Nyaya Padartha and conceptual graph. Ch.14 Nyaya technique and manipulation of quantifier in knowledge representation Ch. 15 I Philosophy A Representative identification ch.16 Indian theories of knowledge representation a postscript.

The book contains diagrams for illustrating the theories.

Dr. K.C Dash is head of Department of Navya Nyaya Sri Jagannath Sanskrit University Puri.

The logic of consciousness belongs to certain conceptual formulations that give a valid basis for an expression to be crystallized on a relational scale. The relations are found to be developed as functional elements in internal representation of an expression. While framing a model of representational analysis we take notice of relations as an intermediate point between an expression and its structured content. This model aims at disambiguating the expression in all its possible levels and converting it to a particular logical form as specified by internal representation.

The present study is an outcome of my interest in artificial intelligence of computer researches that specifically relate to Sanskrit and Sastras. The undertone of this study is to understand the problems that invariably involves semantic specifications and conceptual clarity in the context of different theories of knowledge representation and such other allied theories. My observations provide here a concise description of interrelation ships amongst representational constituents.

The study in its essence is a set of speculations on a particular aspect of interdisciplinary research on knowledge representation.

I have been benefited from the inspirations of many people. At the very outset I express my debt of gratitude to late Kaviraj Kulamani Mishra, my revered guru who initiated me first to study the ancient lore. I express my indeptedness to Prof. V.N. Jha Director C.A.S.S. University of Poona who framed the background of all my subsequent thinkings.

I am immensely grateful to Pandit Professor T.S. Srinivas Shastri, Poona, Professor Satyavrat Shastri, Ex-vice-Chancellor, Shir Jagannath Sanskrit Vishvavidyalaya, Puri, Professor N.S.R Tatacharya, Vice-Chancellor, R.S.V. Tirupati, Prof. N. Vizenathan University of Madras and many others who directly and indirectly stand before me as different sources of inspirations.

I wish to place specially on record my gratitude to Prof. Radha Vallabh Tripathy, Sagar University Sagar (M.P) who appears before me as a constant source of inspiration. On the same line I record my special thanks to Dr. Sadananda Dixit the General Secretary Lokabhasha Prachara Samiti, Puri and a friend of mine for his encouragement and genuine interest in my scholastic and literary works.

I take this opportunity of acknowledging my obligations to Prof. G.C. Nayak, Vice Chancellor and Shri S.K. Dash Choudhury, Comptroller of Finance Shri jagannath Sanskrit Vishvavidyalaya puri for their warm encouragement.

I also like to take this opportunity to note that I have been considerably helped by my wife Smt. Subhadra Dash in bringing this work to the present shape. I enjoy my feelings of thankfulness to her.

Much importance has been attached to the authority of sabda ‘expression’ as a source of knowledge. This is accepted as ‘testimony’ on the basis of both scriptural and non-scriptural attestation relatively consistent with the trustworthy source. Since it remains as an authoritative means in harmony with our experience and reason the analysis centers around certain linguistic structure. Although it is subsumed under the term ’discourse’ in modern linguistics the representation of knowledge of a concerned structure is termed as sabdabodha in Indian philosophical systems. In other words, it is a technical stretch of integrated sequences of both linguistic and extra-linguistic elements in a discrete form.

Form of Expression
An expression is designated as a vakya ’sentence’ if it maintains grammatical as well as semantic appropriateness. This, more or the less, is the representative view of the Logicians who hold that a verbal form is less important for designating a collection of words as a sentence. This shows that the Logicians do not lay stress on the formal aspect of an expression. However, they do not discard altogether the view of the Grammarians who hold that a verbal form is a necessity for an expression which is given the designation of vakya. The point of difference lies in the fact that the Logicians define an expression as a sentence on the basis of semantic consideration whereas the Grammarians define it in terms of formal criterion. Nyayakosa (p. 730) records the view of Gangesa who holds that vakyatvam ca visistartha para-sabdatvam that which causes a qualificative reference is a sentence. Annambhatta Sticks to the formal definition as pada samuho vakyam whereas kesava Misra is more exhaustive in giving the definition as vakyam tu akamka yogyata sannidhimatian padanam samuhah a collection of words with expectancy, compatibility and continguity constitutes a sentence'. This definition categorically shows the grouping of expressions into three major sections. A collection of words may consist of) finished forms showing nominal or noun-noun relationship, viz., trayah kalah Three times,

ii) Finished forms showing verbal or verb-verb relationship, viz., pacati bhavati ’cooking takes place', and

(iii) finished forms showing nominal-verbal or noun—verb relationship, viz., caitrah pacati catira cooks.

The Logician's theory of language is based on a principle of direct relationship between word and its referent. Consider, for example, the expression bhur it is vyaharat ’he (the creator)’uttered bhuh. This expression owes its origin to the occasion when there was no ’earth'. The question is, how to establish a direct relation between the word bhuh and its referent ’external earth' which was not created till the time of utterance. In such a situation, the Grammarians point out that the term bhuh, refers to a mental construction of ’earth' without having any external existence. The Logicians do not subscribe to this view. They say that the earth was correspondingly created when the creator uttered the very word bhuh. Thus, there is a direct relationship.

It is clear from the above point that there is a fundamental distinction of levels for establishing relationship. These two levels may be called as non physical and physical respectively. When an utterance comes to the knowledge of the addressee it represents its form as well as the object referred to by it. This object may be a physical entity or a conceptual approximation. Further, the addressee is able to pick out some thing from the field of his perception and he also knows that there are things beyond his perception. Here the question of identification comes. The idea may be more clear from the passage of Searle (1969).

"... .... in an utterance of a sentence, ’The man robbed me was over six feet tall', I can be said to refer to the man who robbed me, even though in one sense of "identify". I may not be able to identify the man who robbed me. I may not be able, e.g., to pick him out of a police line• up or say any thing more about him. Still assuming one and only one man robbed me, I do succeed in making an identifying reference in an utterance of above sentence". In this case, since the physical identification of ‘the man who robbed him' is impracticable he refers to ’that man' making an identifying reference as to the fact before his addressee. This means that the speaker possesses identifying knowledge of that man who is not physically present and thus he makes anon—physical identification which is referential one.

The identifying knowledge bears importance in both physical and non-physical identification. Straw son (1971:79) makes the point clear saying that "identifying knowledge is the knowledge of the existence of a particular item distinguished, in one or another sense, by the audience from any other. The appropriate stretch of identifying knowledge to be invoked by the use of an expression deemed adequate by the speaker, in the total circumstances of utterance, to indicate the audience which of all the items, within the scope of the audience’s identifying knowledge, is being declared, in the utterance as a whole, to be thus and so".

It is to be noted that the logician’s idea of padarthadhih recollection of the meaning of words and word elements’ stands in close relation to the notion of identifying knowledge. Moreover, since speaker and addressee are accustomed to the varieties of expression in a given language they are never misled by an utterance. The Logicians, therefore, hold that abhidheyatvain ca padajanya pratiti vsiayatvam expressibility means identifiably of what is caused through words. in other words, the knowable is expressible. The idea is that some are identified physically whereas the others take recourse to linguistic identification which is essentially referential and holds good incase of abhava ’absence’ which is treated as a separate category.

Referential Mode of Absence
Abhava ’absence’ and bhava ’the object itself’ stand on one and the same level of reality. But their perception requires a supplementation of linguistic element for further specification. In Indian philosophy we come across various linguistic forms such as abhava, asat, alika avustu, asadatanan, na, nirupdkhya nissvabhava, nirupa and tuccha etc., in terms of negation, absence, and denial etc.. All such terms fall into two major categories namely minus (-) and zero (0). When it is minus it points to a straight relation and when zero, it is the physical incordinate in terms of specific relation.

Whatever it may be, absence is made explicit and identified by means of abstraction from its substratum. It is represented with the help of its counter positive. The representational form rests on certain distinction in its scope determined by the inner model and surface structure of an expression in which the term na 'no/not' as a nominal prefix or an adverbial qualifier forms an important part. The form of expression is regularized on are presentational base in which the inner model accords with the reality. The linguistic element no ness never correspond to bareness. On the other hand, it points to referential perceptibility.

Representation The theory of representation takes its basis from the inner and outer model of an expression. It is also connected with rhetorical stance as far as a work of art is concerned. Simply, it is not just an uptake of presentational elements. For instance, a flag does not represent itself as a flag made of a piece of cloth, but it represents a nation and the like. Similarly, the theory of representation shows how an expression differs from what it represents and takes some additional signification which fits the criteria of linguistic validity and truth. This also accounts for the hierarchical organization of relationship.

The scheme of knowledge representation aims at a scrutiny of explicitness. This involves the knowledge of generic nature abiding in each constituent of a given structure. Moreover, the scheme resorts to a process that internalizes the hierarchical such as:

(i) Cognition of words and word-elements,

(ii) Recollection of the meaning of the same,

(iii) Knowledge of relation (vrtti) resulting from elemental recollection,

(iv) Intentionality and finally

(v) The relational structure in a qualifier - qualificand set up

Identity and Non-identity
The Logicians postulate two major kinds of relational factors namely ’identity’ and ’non-identity’ or ’difference’ in all possible levels of an expression. When there is a co referential situation’ identity’ is understood as the intermediate of two counter-co>relates. Similarly, the differential relation is realized as a denial or non identity. Since an expression is explained in terms of relationship the wholesome meaning is not attributed to separate word units. As far as the syntactic and semantic agreement is concerned the Grammarians speak of ’identity’ between nominative case and the verbal suffix. In the same way, the Mimamsakas accept ’identity’ between the presumed or implied agent and the nominative case. The Logicians also accept the same between a nominal base and the nominative suffix. The differential relation is a relation of two non-co occur rent relata.

Logical Grammar
The Logician’s procedure of analysis is intimately connected with the grammatical theories and issues. The Grammarians formulate their theories mostly on formal aspect of the Language. The Logicians, however, reconstruct the grammatical system correspondingly alternative to the formal tendencies. They hold that a valid expression yield a determinate structure. Himilarly, a valid word (sargajasabda) is considered significant no generate a valid cognition. A word is valid if it is meaningful in collaboration with other syntactically related constituents. An expression, in the same way, is to be treated as valid.

As far as the aspect of knowledge representation is concerned the logical grammar determines the categories which are semantically acceptable in an expression. The cognition arises from a well-formed relational structure in which representational elements are interrelated in accordance with the rules of logical grammar.

Philosophical Semantics the Logician’s defining procedure essentially involves the generic characteristics of a thing, which, in other words, serves as the indemnificatory basis. Even a word is described in terms of Tits determinant nature and cognitive aspect. The items presented in an expression are regarded as a structure of thought from hearer’s point of view. This is represented as a structured content. The content is scrutinized in a relation-determined frame. For instance, a state of consciousness as an event is supposed to occur by certain relation in the soul which is its causal substrate. Similarly, the relation ’inherence’ combines the generic property with particular existent. This model is a logical construct.

Since the aim of the Logicians to study the sarthaka 'valid’ expression they stick to the extent of knowledge of the embedded expression. They, therefore, carefully avoid the intricacy of natural language and take account of quite different aspects of the structure. The semantic representation, in this context, points to a process in which something that an expression means, is displayed. This acts as an intermediate stage between syntactic structure and semantic interpretation. Moreover, it is the disambiguated form of meaning.

Controversy in knowledge Representation
It is true that there are different schools who deal with the theories of knowledge representation. It is also a point to note that they are at variance with each other. But we cannot take their theories as rival theories. In spite of controversies they seem to be mutually contributory and conducive to the development of respective thoughts in point of clarity and disambiguation.

The whole controversy is based on the primary element of an expression which serves as the main qualificand. The Grammarians hold that the primary qualificand is vyapara action whereas the Mimamsakas lay stress on bhavana' efficient force' or ’productive urge' as the prominent element. The 4Logicians are of the opinion that it is the prathamanta ‘nominative agent' that stands prominent. It also comes to notice that the Logicians have referred to the primacy of an indeclinable in certain cases which gains support from Tantric texts. Besides, there are some points which appear to be the bases of disputes. Attempts have been launched upon to resolve those which seem to be the cases of emphasis and indiscriminate choice.

Reconciliation
I A process of reconciliation is suggested by some scholars to accommodate all these theories in a form in which karta agent and karma action’ appear as main qualificand in active and .passive voice respectively. This is called - akhyatartha—kartr—karma-mukhya—visesyaka—sabdabodha ’a form of knowledge representation in which agent and action as the meaning of verb—structure stand prominent'. Thus the expression caitrah gacchati ’Caitra goes’ is represented as caitrabhinna gamana karta the going—agent is non different from Caitra’. Similarly the expression caitra bhinnaim gamana karma the going action is non different from Caitra. In this way a logico grammatic pattern of knowledge representation may be recognized for more correct syntactic and semantic parallelism.

A case for Artificial Intelligence
Recently there is a claim that Sanskrit has several applications in modern computers. The area of Artificial Intelligence has encouraged an emphasis on knowledge engineering in which sabdabodha procedure forms an important part. As we know Artificial intelligence involves the computational models of mental features. The sabdabodha procedure stands on the similar line. Because it takes its basis from the very nature of an utterance and the cognition it generates. This is semantic extraction of internal representation which displays clarity correctness and disambiguation. The representation is the actual meaning and disambiguation. The representation is the actual meaning of an expression which points to a complete set of conceptual constituents. Moreover it provides a minute description of the inter relationship among the constituents.

Adequate details and appropriate technique are available with the Indian theories of knowledge representation to meet the ambiguous situation and contextual variations. As fat as the natural language processing in computer is concerned the sabdabodha models can be used profitably to represent the sense of a word phrase clause and sentence unambiguously.