- -of-Panini Astadhyayi Amrith Krishna M.Tech -2nd Year Guide : Dr. Pawan Goyal
Grammar
Formal Grammar
Structural rules governing the
Set of production rules for strings in a
composition of clauses, phrases, &
formal language. The rules describe
words in any given natural language,
how to form strings from the
and this field includes morphology,
language's alphabet that are valid
syntax, and phonology
according to the language's syntax
::= __expression__
Ingermann observed that the sutras have the same
structure as that of ::=
BNF and suggested to rename `Backus Naur Form'
::= as `Paniini Backus Naur Form' ::= ","
(1967 ACM Communications).
padam(word) padam(word)
::= subantam(nominal subantam(nominal form) | form) | ti_nantam(verbal ti_nantam(verbal form)
(supti_nantam padam 1.4.14) ; subantam (nominal form)
::= pratipadikam (nom stem)sup stem)sup(nom (nom suff)
pratipadikam(nominal pratipadikam(nominal stem) ::= krt (noun derived from a verb) | taddhita(noun taddhita(noun derived from a noun) | samasa(compound) samasa(compound) | underived pratipadikam(nominal pratipadikam (nominal stem) ; In 2007, a work from Hyman (2007), which argued that the language generated by Panini’s (krttaddhitasamasasca 1.2.46) Grammar is mostly a regular Language samasa(compound) samasa(compound)
::= alaukika vigrahah. (Intermediate ling exp) ;
alaukika vigrahah.
::= pratipadikam sup pratipadikam sup
(sahasupa 2.1.4) ;
Kiparsky & Penn 2012 Given the specific, fixed grammar that Panini articulated in the Astadhyay ı, which formal language class(es) does it belong to? Given the grammar formalism that Panini used for this grammar, what kind of grammars can we write in general? That is to say, where does the class of Paninian languages fit within the Chomsky hierarchy?
Powerful than RL and CFL
Brevity
A -> B / C _ D CAD -> CBD
Complete as it can generate Oral Tradition A,B,C,D are strings any context-sensitive language Still RL-style analysis possible, by recasting the grammar* Can accept language
any
count
built-in
or sets of strings (regular)
capacity
for
UL CSL CFL
Generate RL with acyclicity restriction disambiguation Johnson’s Johnson ’s phonological phonological rules
No Chomskyan possesses this.
system
RL
Alphabets & Shiva Sutras Where it all starts…..
अ
आ
इ
ई
उ
च
ऊ ख छ
ऋ
क ग ज
ऌ
ए घ झ
ऐ
ओ
औ
अं
अ
ङ ञ
……..
Not only Panini was by far the first linguist in recorded history, but I claim he was the first informaticien, 24 centuries before computers came into existence.
Prof. Gerard Huet, Computer Scientist, Inria,
Paris,
१. २. ३. ४. ५.
अ इ उ ण ् | ऋ ऌ ् | एओ| ऐ औ च ् | हमवय
|
६. र ण ण ् | ७. ञ भ ङ ण न भ ् | ८. झ ब ञ ञ ् | ९. घ ढ ध ष ् | १०. ज फ ग ड द श ् |
११. ख प छ ठ च ट त व ् | १२. ऩ म म ् | १३. श ष स य ् | १४. ह र ् |
अ इ उ ण च ् ह म व य र ण ण ् ण ् ऋ ऌ ् ए ओ ऐ औ च ञ भ ङ ण न भ भ ् झ ब ञ ् घ ढ ध ष ् ज फ ग ड द श ् ख प छ ठ च ट त व ् ऩ म ् श ष स य ् ह र ् `
Buffet Manager’s Dilemma
The reasoning from economy goes like this. To be grouped together in a pratyahara, sounds must make up a continuous segment of the list. Economy requires making the list as short as possible, which means avoiding repetitions of sounds, and using as few markers as possible. Consequently, if class A properly includes class B, the elements shared with B should be listed last in A; the marker that follows can then be used to form pratyaharas for both A and B. In this way the economy principle, by selecting the shortest grammar, determines both the ordering of sounds and the placement of markers among them.
- Kiparsky 1991
Grammar Structure
Ashtadhyayi RULES Unadi Sutras GRAMMAR
METARULES
Panini Paribhasa sutras Dhatupatha
LEXICAL LISTS Ganapatha PHONOLOGICAL LISTS
Aksharasamnaya
Grammar in Action in Action Ik{6} yan{1} ac{7}
A
{i,u,r.,l.} {y,v,r,l} {a,i,u,r.,l.,e,o,ai,au}
W{5} W{6} W{7} ->
tasmin iti nirdiste purvasya (1.1.65) A word ending in locative case indicates `of the preeceding'. sasthisthaneyoga (1.1.48)
W{5} W{1} W{7}
[iK]
A word in genitive case undergoes change
Ik{6} {i,u,r.,l.}
ac{7}
::=
{a,i,u,r.,l.,e,o,ai,au} ->
B/C _ D
→
yan [1} {y,v,r,l}
ac{7} {a,i,u,r.,l.,e,o,ai,au}
[yN.]/
→
_[aC]
Anuvrtti John goes home. John eats fruits. upadese (a) it (c)
upadese ac anunasik it 1.3.2 hal antyam 1.3.3
ac anunasik ( = it)(b)
na vibhaktau tusmah. 1.3.4
hal antyam (d) na vibhaktau tusmah. (=it) (e)
adih nitud avah 1.3.5 sah pratyayasya 1.3.6 cutu 1.3.7 lasaku ataddhite 1.3.8
If a == b step 1 step 2 step 3
adih (f) nitudavah (=it) (g) pratyayasya (h) sah. (=it) (i) cutu (=it) (j) lasaku (=it) ataddhite (k)
a (b + de + f [ g + h f i + j + k g ] ) c
Anuvrtti
Total Sutras:
(3,984) 4,000
Total Words:
(7,007) 7,000
Total Words after repeating the words with anuvrtti
40,000
Compression due to anuvr.tti (40,000/7,000 )
1/6
In terms of byte size, compression
1/3
Data Encapsulation
Dhatupatha
="A.8.3.23"/>
nidhhrsa
+ kta
dhhrsta
< %(semivowel($1))"/> /function>
deriving noun from nouns -- Taddhitha
Dhatus and pratipadikas are treated equally by Panini.
Every rule contains Morphological
उऩगो : अऩमभ ् उऩग ु
Syntactic
(6th Case)
Semantic Specifications
अऩमभ ्
Relations Single Inheritance
उऩग ु
अऩमभ ्
औऩगव :
याभ ( (फह ु वचन वचन, षठ , ऩ ुलरङ लरङ)
अथवदधात वदधात ुयमम यमम ातऩदभ । ्
1.2.45
याभ ( वचन , षठ , ऩ ुलरङ लरङ ) (ातऩदभ , ्फह ु वचन वौजसभौछटामाबङेमामङसमामङसोसामोस ऩ ऩु ् 4.1.2 मम । 3.1.1. ऩयच । 3.1.2 याभ ( वचन , षठ , ऩ ुलरङ लरङ , अायात , root(याभ )) + स ऩ ऩु ् (ातऩदभ , ् फह ु वचन तामेवचनववचनफह ु वचनामे वचनामेश ।1.4.102 स ुऩ ऩ ।1.4.103
याभ (ातऩदभ ातऩदभ , ् फह ु वचन वचन , षठ , ऩ ुलरङ लरङ , अायात , ऩु , ्उऩदेश, मम, वबत , फह ु वचन वचन , षठ , root(आभ आभ )) ् (स ऩ
याभ )) आभ ् )) + आभ
root(
मभात ् ममवधतदाद ममेऽगभ । ् 1.4.13 मभात स तङतं ु तङतं ऩदभ । ् 1.4.14 याभ ( वचन , षठ , ऩ ुलरङ लरङ , अायात , अग root(याभ )) (ातऩदभ , ् फह ु वचन )) आभ ् (स ऩ आभ ऩु , ् उऩदेश, मम , वबत , फह ु वचन वचन , षठ , root(आभ आभ )) ् (ऩद )
+
मच बभ | ् 1.4.18 याभ ( वचन , षठ , ऩ ुलरङ लरङ , अायात , अग , ब , (ातऩदभ , ् फह ु वचन root(याभ )) आभ ् (स ऩ ऩु , ् उऩदेश , मम , वबत , फह ु वचन वचन , षठ , )) + आभ आभ )) ् (ऩद ) root(आभ आग ण ण ु ।6.1.87 अ सवण दीघथ । 6.1.101 वनमाऩो न ु । 7.1.54
याभ (ातऩदभ , ् फह ु वचन वचन , षठ , ऩ ुलरङ लरङ , अायात , अग , ब , आभ ् (स ुऩ ऩ, ् उऩदेश, मम , वबत , फह ु वचन वचन , षठ , )) + आभ root(याभ )) आगभ (न ु ),), -इत , ् उ -इत ,root( नाभ ) ् ) (ऩद ) ् नाभ नाभ । 6.4.3 स ुऩ ऩ च । 7.3.102 याभा ( वचन , षठ , ऩ ुलरङ लरङ , अायात , अग , ब , (ातऩदभ , ् फह ु वचन आभ ् (स ुऩ ऩ, ् उऩदेश, मम , वबत , फह ु वचन वचन , षठ , )) + आभ root(याभ )) आगभ (न ु ),), -इत इत ् ,उ -इत इत ् ,root(नाभ नाभ ) ् (ऩद ) वयाभोऽवसानभ । ् याभा (ातऩदभ , ् फह ु वचन वचन , षठ , ऩ ुलरङ लरङ , अायात , अग , ब , root(याभ )) आभ ् (स ुऩ ऩ, ् उऩदेश , मम , वबत , फह ु वचन वचन , षठ , )) + आभ आगभ (न ु ),), -इत इत ् ,उ -इत इत ् ,root(नाभ नाभ ) ् (ऩद , अवसान )
1.4.110
अ ु वान ुमवामे मवामेऽऩ । 8.4.2
याभाणाभ ् याभा (ातऩदभ ातऩदभ , ् फह ु वचन वचन , षठ , ऩ ुलरङ लरङ , अायात , अग , ब , आभ ् (स ुऩ ऩ, ् उऩदेश, मम , वबत , फह ु वचन वचन , षठ , )) + आभ root(याभ )) आगभ (न ु ),), -इत इत ् ,उ -इत इत ् ,root(नाभ नाभ ) ् (ऩद , अवसान )
perhaps the greatest difference between Panini’s own formalism and the standard stringrewriting systems concomitant with Chomsky’s hierarchy , which is its built-in capacity
for disambiguation. Panini’s grammar, through its use of rule precedence and other meta-conventions, generates a single derivation for every grammatical sentence of Sanskrit. -
•
Implement working systems.
•
Doubles as a tool for learning the concepts of o f grammar
Panini’s method of representing hierarchical information in a linear form is an
interesting field of further investigations. -
References On Pan.ini and the Generative Capacity of Contextualized Cont extualized Replacement Systems, Gerald Penn, Paul Kiparsky, COLING 2012, A Mathematical Analysis of Panini’s Sivasutras - Wiebke Petersen JoLLI. 13 (4), p. 471-489 Computer Simulation of Ashtadhyayi: Some insights, Pawan Goyal, Amba Kulkarni and Laxmidhar Laxmid har
धमवाद :
Behera. Sanskrit Computational Linguistics: Revised, Selected and Invited Papers, Springer -Verlag. pp. 139-160. (2009)
Modeling Paninian Grammar, Peter M. Scharf, Sanskrit Computational Linguistics: Revised, Selected and Invited Papers, Springer-Verlag. Pp 95-126 Hyman, M. D. (2007). From Paninian sandhi to finite state calculus. In Huet, G. and Kulkarni, A., editors, Proceedings of the First International Symposium on Sanskrit Computational Linguistics, pages 13–21.
