4th APCAP Dec 5th 2008, NIAS Bangalore P āņ ini's Ash ţā dhy ā y ī : A Computer Scientist's...

4th APCAP Dec 5th 2008, NIAS Bangalore

Pāņini's Ashţādhyāyī: A Computer Scientist's Perspective

Amba KulkarniDepartment of Sanskrit Studies

University of HyderabadHyderabad

[email protected]


Pāņini's Ashţādhyāyī

Circa 500 B.C.E.

Extant Grammar of the then prevalent Sanskrit Language

Around 4000 sutras;

8 chapters 4 sections each


A Computer Scientist

Information Theory: Shannon

Computational Linguists:(Language: Means of coding the information.)Information Coding: How much, Where and How

Programming Languages: Concepts, Techniques and Models


Pāņini's Ashţādhyāyī

Pāņini's Ashţādhyāyī has something to offer to each of these fields


Information Coding

Claim:Panini was aware of the strength of language asan information coding device.

Evident from a) His style of presenting the information in sUtrab) His analysis of Sanskrit Language


Information Theory

BrevityKiparsky: Panini used Brevity to achieve

generalisation.

– Maximum Use of anuvŗtti

Ram went home.Ram ate an apple.----------------------------------------------Ram went home, ate an apple.


Anuvŗtti

upadeSe ac anunAsika it 1.3.2hal antyam 1.3.3na vibhaktau tusmA 1.3.4Adi ~nitudavAH 1.3.5.saH pratyayasya 1.3.6CutU 1.3.7laSaku ataddhite 1.3.8


upadeSe ac anunAsika (=it) 1.3.2 hal antyam 1.3.3 na vibhaktau tusmA (=it) 1.3.4 Adi ~nitudavAH (=it) 1.3.5 pratyayasya .saH (=it) 1.3.6 CutU (=it) 1.3.7 ataddhite laSaku (=it) 1.3.8

Anuvŗtti … contd


upadeSe(a) ac anunAsika(b) (=it)(c) 1.3.2 hal antyam(d) 1.3.3 na vibhaktau tusmA(e) (=it) 1.3.4 Adi(f) ~nitudavAH(g) (=it) 1.3.5 pratyaya(h)sya(i) .saH(j) (=it) 1.3.6 CutU(k) (=it) 1.3.7 ataddhite laSaku(l) (=it) 1.3.8

Anuvŗtti … contd


a b c d e c f g c h_i j c k c l c a (b + de + f [g + h_i{j + k + l }]) c

Anuvŗtti … contd


Anuvŗtti … contd

No Proper Nesting; MandUka pluti:Ad(a) guNaH(b) 6.1.84v.rddhiH(c) eci(d) {a} 6.1.85 etyedhatyUTsu (e) {a c d} 6.1.86upasargAt(f) ŗti(g) dhAtO(h) {a c} 6.1.87VA supyApiSale(i) {f g h a c} 6.1.88OtaH amSasoH(j) 6.1.89 e”ni(k) pararUpaM(l) { f h a} 6.1.90

a{b + c[d(1+e) + fh(g(1 + i)] + j + kl)}


Anuvŗtti … contd

Maximum advantage of features of Natural Language:

How are the complete phrases reconstructed?

AkAnksha (Expectancy): Major role in deciding the anuvŗtti


Anuvŗtti … contd

Example of borrowing from as many as 11 sūtras

Original sūtra: 3-3-65 क्वणः� व�णः�यां�� च

After anuvŗtti:3-3-65: क्वणः� व�णः�यां�� च प्रत्यांयां� परः� च आद्यु�दा�त्तः� च धा�तोः�� कृ� तोः� क्रि�यां�यां�� क्रि�यां�र्था��यां�म्� भा�व� अकृतोः�रिरः च कृ�रःकृ� सञ्ज्ञा�यां�म्�अप� उपसर्गे' व� नौ) (anuvŗtti from 11 different sūtras)


Anuvŗtti … ContdSome Statistics:

Total sūtras : (3984) 4000

Total Words (with sandhi): (7007) 7000

Total Sandhi split words: 9843Total words after repeating the words with anuvŗtti:

40,000Compression because of anuvŗtti: 1/6

In terms of byte size, compression is 1/3.


Information Theory

Normal Arrangement of Alphabet

a A i I u U ŗ ļ e E o O M H

k kh g gh “nc ch j jh ~nţ ţh .d .dh .n

t th d dh n p ph b bh m

y r l v S ş s h


ShivasUtra

Panini required several(42) subsets of thisalphabet to describe various operations.


ShivasUtra

Some of these subsets:

All vowelsAll consonantsAll vowels + semivowelsh y v r l + consonantsy v r l + consonantsv r l + consonantsr l + consonants


ShivasUtra

It is not advisable to give 42 names to these sets. It will be difficult to memorize the association.

These are Partially ordered sets.

Panini arranged them linearly in the form of 14 ShivasUtras.


a i u Nŗ ļ Ke o c

E O “Nh y v r T

l Nň m “n N n M

Jh bh Ňgh .dh dh Şj b g .d d S

kh ph ch .th th c .t t Vk p Y

SŞ s Rh L

SHIVASUTRAS


ShivasUtras .. contd

Optimality of these sUtras is proved independently by

Kiparsky (linguistically)and Petersen (mathematically)


ShivasUtras ... contd

Given a set of Partially Ordered sets, Now it is possible to tell

Whether the elements are Shivasutra encodable or not.

Ref: Petersen(2008)


Information Dynamics

Information Theory: Deals with

Measure of information, data compression, etc.

Information Dynamics: Focuses on flow of information in a language


Information Dynamics

For a Computer Scientist working in NLP

Where a language codes the informationHow it codes the informationHow much information it codes are important.


Information Dynamics … contd

Where a language codes information:

Useful to decide the parsing Strategy



How a language codes information:

Useful to decide whether the information can be passed on to other language without any efforts

or not



How much information a language codes:

Useful to decide whether the desired information can be extracted or not merely from a language

string without appealing to the extra linguistic knowledge.


Information Dynamics … Contd

Where: anabhihite 3.1.1

How much: svatantraH kartA 1.4.54

How (the manner): samAna kartŗkayoH pUrvakAle 3.4.21


Programming Languages

Data + Algorithm = Program

Algorithm: Around 4000 sUtras

Data: Shivasutra gaNapAtha DhAtupAtha uNAdi sUtra li”ngAnuSAsana


Programming Languages … contd

Data + Algorithm = Program

Object Oriented Programming:Encapsulation of data with the (markers to the)

functionsBhaj + (gh)a(~n) : Presence of gh => j->g



Ordering of rules:

Two meta rulesa) viprati.sedhe param kAryam 1.4.2(In case of conflict apply the later rule)

b) pUrvatra asiddham 8.2.1(Apply the rules in last 3 sections at the end and in linear order)



Typical VaiyAkara.na's view:

Event driven ProgrammingChanges in the Data spaces: Event

==> Triggers the rules



Typical vaiakara.nas view:



Control:Certain rules block certain other rules.

Blocking is of 3 different typesa) Partial blocking (asiddhavat)b) certain rules are not applicable (asiddhaH)c) only certain rules are applicable (asiddham)(direct implication on : passing of parameters)



Partial Blocking: Asiddhavat atra AbhAt



Ordering of the sUtras



Control:a) If X then Y (mA.thara kau.ndi.nya nyAya)b) If X then Y else Z (takra kau.ndi.nya nyAya)

c) If (not X) then Y (ni.sedha)d) if X then (Y and Z) (vibhA.sA)



Conflict Resolution:

Utsarga / apavAdaGeneral / special rule



Use of Special Features of Sanskrit

Use of Vibhaktis (case markers)Order of parameters in a function

IkaH ya.n aciIk ac → ya.n ac



Use of Special Features of Sanskrit

Use of Pronouns as variables

Tasmin iti nirdis.te pUrvasyaTasmAt iti uttarasya



Inheritance

Multiple inheritance → arranged as a linear inheritance

Taddhita pratyayaAshwini Deo 2007

4th APCAP Dec 5th 2008, NIAS Bangalore P āņ ini's Ash ţā dhy ā y ī : A Computer Scientist's...

Documents

Transcript of 4th APCAP Dec 5th 2008, NIAS Bangalore P āņ ini's Ash ţā dhy ā y ī : A Computer Scientist's...