Indian Logic for AI system Design
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Indian Logic and AI System Design

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.
Indian Logic and AI System Design. Ghosh and Banerji, 2006 1
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
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 Ëœrealityâ„¢ 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, © 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 5-
step syllogism “ Pratijna, hetu, vyapti, upanaya, nigamana [Schayer,
1933]. The third step
udaharana is modified by vyapti to take care of Ëœfor-allâ„¢, Ëœsome or
noneâ„¢ propositions.
Indian Logic and AI System Design. Ghosh and Banerji, 2006 2
Table 1: Eleven specific logical points present in the Indian logic
(Colebrooke, 1824).
3.2 Buddhist logic systems - 5 temporal steps and reason-thesis
Buddhist logicians were of the opinion that a reason must satisfy 3-
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 3
(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
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.
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.
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) modus ponens [if p then q; p; therefore q];
ii) modus tollens [p or q; ~q; therefore p ]; and
iii) 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) The first predicate pertains to an assertion.
ii) The second predicate pertains to a denial.
iii) The third predicate pertains to successive assertion and denial.
iv) The fourth predicate pertains to simultaneous assertion and
v) The fifth predicate pertains to an assertion and a simultaneous
and denial.
vi) The sixth predicate pertains to a denial and a simultaneous
assertion and
vii) 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 Nyayaâ„¢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 4
perceptions, observations and seeking Expertsâ„¢ 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) Doubt ( whether p or not-p);
ii) Proof of the thesis or anti-thesis;
iii) 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.
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.
© 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
(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
both forward and backward chaining mechanism used in Inference
4.2 Fuzzy reasoning
Reasoning with possibilities (syadvada) was first proposed by Jaina
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 5
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
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
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 6
The Ëœknowledge baseâ„¢ 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 Ëœinference engineâ„¢ 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),
Ëœbackward chainingâ„¢ (most suitable for medical diagnosis and fault
finding) and Ëœtree
searchesâ„¢ (suitable when knowledge base is represented as a network
or tree or forest
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
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
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 Ëœframeâ„¢ 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 7
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.
(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 Ëœpotness
propertyâ„¢ and Ëœpot-contact-hoodâ„¢ table or ground locations [11] can
be included in a
frame by adding sub-fields, called Ëœfacetsâ„¢ [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
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 8
Frame :: Name
Inheritance Slot : IS_A
Attribute Slot : value
Attribute Slot : value
Frame :: Car
IS_A : Vehicle
Engine : {Pet, Dsl}
Cylinder : { 2,3,4,6}
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.
[1]Ganeri, J. (2002). Ancient Indian Logic as a Theory of Case-Based
Journal of Indian Philosophy, 33“45. Accessed from
[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
[6]Sarma, V.V.S. (2003). Indian Logic and AI , BiswaBharat@tdil,
Technology Watch.
Accessed from
[7]Poole, D., Mackworth, A. and Goebel, R. (1998).Computational
Intelligence: a
logical approach. Oxford University Press.
[8] en.wikipedia../../
[9]Ganeri, J. (ed) (2001). Indian Logic: A Reader. Routledge, London,
[10]Kak, S. (2003). Indian Physics: Outline of Early History. ArXiv
Physics :0310001. Accessed from
[11]Sarma, V.V.S. (2005). Indian Systems of Logic (Nyaya): A Survey.
IIT Bombay
Logic Conference, 8-1-2005.
Indian Logic and AI System Design. Ghosh and Banerji, 2006 9
[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
[13]Glashoff, K. (n.d.). Using Formulas for the Interpretation of
Ancient Indian Logic.
Modern Interpretation of Ancient Logics by Klaus Glashoff, Accessed
[14]Peckhaus, V. (2001). Dignagaâ„¢s Logic of Invention. Lecture at
First International
Conference of the New Millennium on History of Mathematical Sciences,
2001, INSA, Delhi.
[15] philosophypages../../
[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 Reasoningâ„¢ Jonardon Ganeri, Journal of Indian
Philosophy, 33“45, 2002.
[17]Schayer, Stanislaw (1933). Ãber 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
Indian Logic As A Theory Of Case-Based Reasoningâ„¢ Jonardon Ganeri,
Journal of
Indian Philosophy, 33“45, 2002.
Indian Logic and AI System Design. Ghosh and Banerji, 2006 10
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