Indian Logic For Ai System Design : Presented At Vigyan Bharati Seminar At Iisc- Bangalore In 2006

Indian Logic and AI System Design Dr Ananda Mohan Ghosh, Former Prof and HOD Computer Science, Bengal Engineering College (DU), INDIA [email protected] Dr Ashok Banerji, Faculty and Content Expert, Jones International University, USA [email protected] Monisha Electronic Education Trust Abstract The importance of Logic and its mathematical formulation can hardly be overstated in the modern age of Information Technology. Design, implementation and innovations of both computer hardware and software systems are dependent on Logic in different forms and formats. Digital logic is mainly used for hardware design. Symbolic logic and Propositional Calculus are essentially required for the design of Artificial Intelligence (AI) applications. Given the current level of understanding there is a need to review Logic from the perspective ancient wisdom. Can Indian Logic, both old and new systems, known as Puratana Nyaya (PN) and Nabya Nyaya (NN), help more efficient AI design process? This paper is an attempt in that direction. It will first review the origin of the concept of logic and thereafter it will propose the possible areas of application in modern context. Before an answer to the actual question of AI design is sought, we need to remove a common misconception. It is commonly believed that the concept Logic was first introduced by Greek philosopher Aristotle around 300 years BC. However, Indian Shastras and Puranas clearly indicate that India's Gautam Muni introduced Logic concepts during Ramanaya period which will be not less than 3000 years old before Christ. This means that Logic System was introduced in India some 5000 years before from now, much earlier than Aristotle. Modern Encyclopedia names, India, Greece and China, as the probable place of origination of the logic system. It will be worth to trace the history of its origin. Based on historical facts and figures it can now be claimed that the logic concept was introduced in India first through the Nyaya Shastra. Thereafter the knowledge went to China around 500 years BC, through Buddhist and Jaina monks, and through Alexander the Great, reached to Aristotle of Greece. Sarma (2005) has given a very nice description of the Indian Logic Systems and indicated how those concepts can be mapped to solve computer science problems. He has shown how better knowledge representation is possible using Indian logic systems [11]. This paper shows how the inference mechanism can be improved using Indian Logic Systems. This can be used for design of Inference Engine of an Expert System. Further, the explanation mechanism can also be improved utilizing the ancient concept that originated in India but hardly known to the current day academia.

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1. Introduction Both computer hardware and software make use of different logic systems. Although hardware circuits depend much more on digital logic, software, according to application requirements, depends on various types of logic systems like predicate logic, fuzzy logic, default reasoning and inference mechanisms. Careful study shows that the logic, argumentation and inference techniques used in Artificial Intelligence (AI) systems today are mostly modifications of the methods originally proposed by Indian scholars some 5000 years before from now. There are many other valuable Indian logic and argumentation methods available which have a good scope for improving existing AI and Expert System (ES) packages, specially in the area of medical diagnosis and legal judgement where case base reasoning [3] is inevitable. This paper is an attempt to explore that possibility. 2. Historical Perspective of Logic Systems Indian Logic in the form of Nyaya Shastra was first introduced by Gautama Muni (husband of Devi Ahalya who was rescued by Ram as described in the Ramanaya) [8]. Even in the Vedic age logic concept was very much present as evidenced from the Rigveda hymn 10.129 [1, 9] where ‘reality’ is said to be represented in the form of [A, Not A, A and Not A, Not A and Not Not A]. These are similar to the current Boolean logic formulations. The first proper compilation of scattered Indian logical concepts (in the name of Nyaya Sutras) was done by Medhatithi Gautama and Aksapada Gautama around 550—150 BCE [5, 10]. Kallisthenes (370—327BCE), a friend of Aristotle and court historian to Alexander the Great, collected all the texts of Nyaya Sutras and handed over all of them to Aristotle who is regarded as the father of western logic, mathematics and science. In fact, the 3-step Greek logical reasoning (syllogism) is a simplified formal representation of the 5-step Indian method of reasoning originally proposed by Gautama. 3. Growth of Different Reasoning & Logical Systems It will be useful to review the growth of different reasoning and logic systems proposed by different systems. Therefore in this section we will review the (a) Indian logic system, (b) Buddhist logic systems, (c) Western logic, and (d) Jaina Logic. 3.1 Indian logic systems- 11 aspects of logic The modern scientific world came to know about Indian contributions to Reasoning and Logical methods through Henry Colebrooker (1824) who mentioned the eleven specific logical points that are present in the Indian logic systems. These are shown in Table 1. As commented by Glashoff [13], western logic is more mathematics based whereas Indian logic is more analogy and epistemology based. However, Nabya Nyaya tried to introduce the concept of predicate calculus in the process of reasoning maintaining the traditional 5step syllogism – Pratijna, hetu, vyapti, upanaya, nigamana [Schayer, 1933]. The third step udaharana is modified by vyapti to take care of ‘for-all’, ‘some or none’ propositions.

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Table 1: Eleven specific logical points present in the Indian logic systems (Colebrooke, 1824). (1) 5-Step Well-formed

Indian Syllogism : a) Statement of the thesis to be proved; (pratijna), b) Citation of a reason ( hetu ); c) Mention of an example ( case or instance); (udaharana), d) Application of reason to explain the case in hand; (upanaya), e) Final inference. (niganama). (2) 16 Rules and Principles of Debate. (3) General issues on epistemology and metaphysics. (4) The concept of Multi-valued logic and propositional calculus as introduced by Dinnaga & Dharmakirti. (5) Negation, Logical consequences and quantification as introduced by Nabya Nyaya (NN) school. (6) Case based argumentation and Rule based Inference. (7) Similarity and dissimilarity based Schematic inference. (8) Transformed inference from case based to rule based. (as used in Machine learning systems ). (9) Class-object or Set-member relationship. (10)Causal-predicative – past experiences help predicting future. ( Similar to extrapolation technique of to-day) (11)Non-monotonic Reasoning. 3.2 Buddhist logic systems - 5 temporal steps and reason-thesis Buddhist logicians were of the opinion that a reason must satisfy 3-conditions: i) Reason Property (F) occurs in a; ii) F occurs in some homologue (eva meaning “only”); iii) F occurs in no heterologue [i.e. F never occurs without G]. All F are G; Fa; therefore Ga. Indian Buddhist monk Dignaga is regarded as the Indian Aristotle [14]. Buddhist logic, as proposed by him, follows the following 5 temporal steps:i) Formulation of a formal rule for syllogism; ii) Development of formal syllogistic using the wheel of reasoning ( hetucakradamaru); iii) Simplification of the syllogism; iv) Introduction of the word “eva” [from general to specific]; v) Refinement or minimization of the general rule. Hetucakra stands for reason-thesis combinations. The reason must have relevance to the thesis. It must support the thesis. It must not support the anti-thesis. Indian Logic and AI System Design. Ghosh and Banerji, 2006

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“The wheel of reason provides an aid for determining the validity of a given argument. It gives the criteria for the choice of possible premises for the valid inference. It lists the possible relations between three different types of reasons in a combinatorial form. Each of the resulting combinations is evaluated asking whether it is valid, invalid or doubtful.” [14] 3.3 Western logic - 3-step syllogistic logic The father of western logic, Aristotle, defined 3-step syllogistic logic where every syllogism is a sequence of three propositions; the first two imply the third. Three basic syllogisms are: i) ii) iii)

modus ponens [if p then q; p; therefore q]; modus tollens [p or q; ~q; therefore p ]; and categorical [ all x are y; no x is y; some x is y; some x is not y ].

John Venn (1880) introduced Venn diagram for analyzing categorical syllogism [one circle for each term]. 3.4 Jaina Logic - 7-predicate approach The Indian Jaina Logic made use of 7-predicate approach [12]. Those 7- predicates can be described as follows:-i) ii) iii) iv) v) vi) vii)

The first predicate pertains to an assertion. The second predicate pertains to a denial. The third predicate pertains to successive assertion and denial. The fourth predicate pertains to simultaneous assertion and denial. The fifth predicate pertains to an assertion and a simultaneous assertion and denial. The sixth predicate pertains to a denial and a simultaneous assertion and denial. The seventh predicate pertains to a successive assertion and denial and a simultaneous assertion and denial.

Thus a predicate may assume any one of the three truth values --- true (T), false (F), and non-assertible (U). So it is an extension of the conventional two truth values (T & F) assertions. Such multi-valued assertions will be able to cope up many imprecise decision and diagnostic problems solved by Fuzzy logic at present. In fact, this 7-predicate approach can guide Fuzzy system designers in a much better way. 4. Comparing Indian Logic with Western Logic As already mentioned, Indian Logic started with the Nyaya Shastra to find out proper inference patterns, rules of debate, and acquisition of knowledge [11]. Caraka Samhita applied those Nyaya’s method of logical reasoning for the development of new medicine and medical diagnosis [6, 11]. “Pramanas (Epistemology) form the basis of Indian Logic” [11] and “A pramana is the means leading to a knowledge episode (prama) at its end” [Motilal]. Therefore, finding the fact and truth (both in real and abstract form) from Indian Logic and AI System Design. Ghosh and Banerji, 2006

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perceptions, observations and seeking Experts’ opinions (including Vedas) is considered to be the basis of Indian logic systems. In Puratana Nyaya (PN), a 3-step pramana method is adopted – i) ii) iii)

Doubt ( whether p or not-p); Proof of the thesis or anti-thesis; 5-limbed syllogism to demonstrate proper reasoning.

In Aristotelian Logic [5], a higher stress on demonstrative reasoning using mathematical model is given. “Aristotle presumed that all ...... knowledge must be derived from what is already known.” Thus, the process of reasoning by syllogism employs a formal definition of validity that permits the deduction of new truths from established principles. The goal is to provide an account of why things happen the way they do, based solely upon what we already know [15]. 4.1 Application advantages There are some distinct advantages in using Indian logic systems. These are given below: (a)

Indian logic is better to apply in situations where available facts and rules are insufficient to apply proper reasoning. In contrast, Aristotelian logic will be better when available knowledge base is quite rich and strong.

(b)

Indian logic gives more emphasis on experience, belief and hearsay, whereas Aristotelian logic puts more faith on mathematical reasoning. Although mathematical reasoning is more precise, but may not cope up truly with all real life situations. To tackle imprecise and ill-defined real life problems, Indian logic may be found more suitable.

(c)

In designing Expert Systems, Indian logic will be more helpful than Aristotelian logic as experts seldom can give mathematical justification to the decisions or choices taken by them. Experts often apply analogy or case based reasoning.

(d)

The knowledge acquired and represented through Indian logic can be stored in a Knowledge Base (KB) with additional slots or links which can help accelerating both forward and backward chaining mechanism used in Inference Engines.

4.2 Fuzzy reasoning Reasoning with possibilities (syadvada) was first proposed by Jaina Logician Samantabhadra [600AD] and in modern times those concepts have given rise to fuzzy and multi-valued logical systems. However, the 7-valued logical theory can be applied to separate members of a fuzzy set into 7- sub groups according to the true(t), false(f), uncertain(u), tf, tu, fu and tfu value ranges with respect to which goal seeking search space can be minimized. Indian Logic and AI System Design. Ghosh and Banerji, 2006

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4.3 Frame based knowledge representation The concept of dharma-dharmin or property- location, as introduced by Navya Nyaya (NN), can enrich frame based knowledge representation. The presence, absence and differences in slots or attribute values will be able to control the path of search in a more deterministic way. According to Dharmakirti [6, 14] a relation should have any of the following characteristics [11]: i) Dependency is a relation (aRb). ii) Amalgamation or contact is a relation. iii) Expectancy is a relation. iv) Cause-effect is a relation. v) The common feature that exists between two things is a relation. In data and knowledge base schema design, the above mentioned aspects can be included to make reasoning more efficient. 4.4 Relational database In a relational database, all tables are having a flat structure. By joining different tables a complex query is processed. When many tables are involved, the processing time and memory requirements (for storing intermediate results) may be quite large and unacceptable. If the table schema of the knowledge base of an Expert System can be designed according to NN logic, relational algebraic operations can be avoided and search can remain confined to slot accessing and link-chaining mainly. This will ensure faster search. According to NN, use of both table and frame as a direct (sakshat) relation and table or frame/slot chaining as chain relations (paramapara) can be used for Knowledge manipulation in Expert systems. 5. Knowledge Based Expert System and Indian Logic Let us first have an overview of an Expert System (Figure 1) which can be built by choosing one from various representations and reasoning systems [7].

Figure 1: Architecture of an Expert System Indian Logic and AI System Design. Ghosh and Banerji, 2006

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The ‘knowledge base’ stores facts and knowledge acquired from observations, models and different domain specific experts. Knowledge can be represented in different forms like – facts, rules, semantic net, frames, objects, etc. The ‘inference engine’ provides control and navigation mechanism to search through the knowledge base and help arriving at a proper decision. Three most popular inference drawing techniques are – ‘forward chaining’ (generating new assertions from existing rules), ‘backward chaining’ (most suitable for medical diagnosis and fault finding) and ‘tree searches’ (suitable when knowledge base is represented as a network or tree or forest structure). When knowledge is represented in the form of frames or objects and relationships, on which Navya Nyaya has given much stress, frame and semantic network model will be most suitable and inference engine will be able to work on tree search technique. Frame or object based knowledge representation can take care of dharma-dharmin or contact and co-locusness type relationships as described in Navya Nyaya. By such inclusion the process of search can be made more converging and accurate. In fact, Frame based knowledge representation can also take care of case based and nonmonotonic reasoning [2, 3] for which Indian logic is most famous. Horn clause or first order predicate based reasoning is found applicable mostly for monotonic knowledge bases. User Interface (UI) is another important component of an Expert System. UI can collect additional information which can influence a search process to arrive at a better decision. More over, a user can ask for explanation in support of the decisions taken. Of course, Indian logic embedded frame based knowledge representation can make UI design more efficient. Let us now examine how Indian logic can be embedded in a frame based Expert System. 6. Indian Logic Embedded Frame Based Knowledge Engineering A knowledge engineer first collects facts, different attributes and their values, procedures, if any, and rules from domain experts. Then he/she tries to store them in the knowledge base in the structure of a ‘frame’ as shown in figure 2. A frame is a generalized record structure which has a ‘name’ and ‘various slots’ – like relationship slot, attribute slot 1, attribute slot 2, ..... attribute slot N. Each attribute slot can be specified with range of possible values, default value, etc. Procedures to manipulate relationships and attribute values for different slots can also be included within the frame structure. Such a frame structure can be used to accommodate Indian style of logical reasoning. The 5-step Indian syllogism starts with the problem in question (1st step) and ends with the final decision or inference (5th step). The second step – hetu – can be taken care of by the rules in the conventional way. The 3rd step – udarahana or vyapti – can be accommodated by adding a new slot in the frame structure and case based reasoning can be triggered as and when Indian Logic and AI System Design. Ghosh and Banerji, 2006

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required. The 4th step – upanaya -- is nothing but conventional search mechanism adopted by the IE component of ES. Slot attribute values can take care of uncertainties and impreciseness by 7-predicate fuzzy logic based implementation. Frame :: Name

Frame :: Car

Inheritance Slot : IS_A

IS_A : Vehicle

Attribute Slot : value vvvalueValue Attribute Slot : value

Engine : {Pet, Dsl} Cylinder : { 2,3,4,6}

(a) (b) Figure 2: A general Frame Structure (a) with an example – Car(b) Such a frame structure can be used to accommodate Indian style of logical reasoning. The 5-step Indian syllogism starts with the problem in question (1st step) and ends with the final decision or inference (5th step). The second step – hetu – can be taken care of by the rules in the conventional way. The 3rd step – udarahana or vyapti – can be accommodated by adding a new slot in the frame structure and case based reasoning can be triggered as and when required. The 4th step – upanaya -- is nothing but conventional search mechanism adopted by the IE component of ES. Slot attribute values can take care of uncertainties and impreciseness by 7-predicate fuzzy logic based implementation. The property-location or dharma-dharmin concept of Navya Nyaya can also be incorporated in the frame structure using additional slot(s) and adding pointers, if necessary. The ‘potness property’ and ‘pot-contact-hood’ table or ground locations [11] can be included in a frame by adding sub-fields, called ‘facets’ [4] in appropriate slots. In fact, all Indian logic concepts can be included in a frame which is regarded as a superset of semantic network representation. To accommodate Indian logic concepts in a frame structure, addition of slots and facets in those slots may be necessary. With such enhanced frames, the processing speed and inference accuracy can be improved easily. So far as User Interface is concerned, inclusion of 3rd logic syllogism -- udarahana or vyapti – will help initiating the search process in a more deterministic way. After accepting the problem statement, ES may ask the user to cite an example or case related to the problem being solved. When such an example is fed in, the matching slot or facet values can be compared. The unspecified attribute slots with probable values may be displayed on the screen for choice or confirmation by the user. This is another advantage an ES designer will have if Indian logic concept is adopted. Indian Logic and AI System Design. Ghosh and Banerji, 2006

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Manipulation of frames can be carried out by using a language like LISP or any objectoriented programming language. Available reasoning tools like Automated Reasoning Tool (ART) can easily be used. There will be no change in the structure of the AI Shell, changes will be there by addition of slots, facets and links in the frame structure only if Indian Logic concepts are included. Future researchers are invited to explore further possibilities of using Indian logic embedded frames and ART like tools for improving the performance of AI based software. 7. Conclusion This paper tried to trace out the history and growth of Indian logic and the most valuable contributions made by Indian scholars even before the emergence of Aristotelian logic in Greece. Example or case based Indian logical reasoning has some advantages over first order predicate calculus based formal reasoning as real-life reality can never be fully expressed in mathematical forms. To improve decision making search processes and to ensure quicker convergence, both Indian and Western logical methods are to be combined and that can be made possible easily if frame based knowledge representation is adopted. Such a combined approach is proposed here for further exploration by the future researchers who will be able to trace out many more valuable but forgotten areas of Indian logic. References [1]Ganeri, J. (2002). Ancient Indian Logic as a Theory of Case-Based Reasoning. Journal of Indian Philosophy, 33–45. Accessed from http://pcwww.liv.ac.uk/~jonardon/pdf/casebasedreasoning.pdf. [2]Oetke, C. (1996). Ancient Indian Logic as a Theory of Non-Monotonic Reasoning. J. of Indian Philosophy, 24. [3]Kolodner, J.L. (1992). An Introduction to Case-based Reasoning. AI Review, 6. [4]Padhy, N.P. (2005). Artificial Intelligence and Intelligent Systems. Oxford University Press. [5]Kak, S. (2005). Aristotle and Gautama on Logic and Physics. S. Louisiana State University, ArXiv: Physics / 0505172 v1, accessed from http://arxiv.org/abs/physics/0505172. [6]Sarma, V.V.S. (2003). Indian Logic and AI , BiswaBharat@tdil, Technology Watch. Accessed from http://www.tdil.mit.gov.in/TDIL-OCT2003/indian%20logic%20&%20artificial%20intelligence.pdf. [7]Poole, D., Mackworth, A. and Goebel, R. (1998).Computational Intelligence: a logical approach. Oxford University Press. [8]http://en.wikipedia.org/../../ [9]Ganeri, J. (ed) (2001). Indian Logic: A Reader. Routledge, London, ISBN 0700713298. [10]Kak, S. (2003). Indian Physics: Outline of Early History. ArXiv Physics :0310001. Accessed from http://arxiv.org/PS_cache/physics/pdf/0310/0310001.pdf. [11]Sarma, V.V.S. (2005). Indian Systems of Logic (Nyaya): A Survey. IIT Bombay

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[12]Ganeri,

J. (2002). Jaina Logic and the Philosophical Basis of Pluralism. History and Philosophy of Logic, 23, Taylor & Francis Ltd. ISSN 1464-5149, accessed from http://pcwww.liv.ac.uk/~jonardon/pdf/jaina%20logic.pdf. [13]Glashoff, K. (n.d.). Using Formulas for the Interpretation of Ancient Indian Logic. Modern Interpretation of Ancient Logics by Klaus Glashoff, Accessed from http://www.logic.glashoff.net/Texte/Formalismus_final.pdf. [14]Peckhaus, V. (2001). Dignaga’s Logic of Invention. Lecture at First International Conference of the New Millennium on History of Mathematical Sciences, 22-122001, INSA, Delhi. [15]http://www.philosophypages.com/../../ [16]Colebrooke, H. T. (1824). On the Philosophy of the Hindus: [Part II]: On the Nyâya and Vaioeeshika systems’. Transactions of the Royal Asiatic Society (1824) 1: 92–118. Reprinted in GANERI (2001c: 26–58), referred in ‘Ancient Indian Logic As A Theory Of Case-Based Reasoning’ Jonardon Ganeri, Journal of Indian Philosophy, 33–45, 2002. [17]Schayer, Stanislaw (1933). Über die Methode der Nyâya-Forschung, in O. Stein and W. Gambert (eds.) Festschrift für Moritz Winternitz, Leipzig 1933: 247–257. Translated by Joerg Tuske in GANERI (2001c: 102–109), referred in ‘Ancient Indian Logic As A Theory Of Case-Based Reasoning’ Jonardon Ganeri, Journal of Indian Philosophy, 33–45, 2002.

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