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- Astadhyayi of Panini

---Amrith KrishnaM.Tech -2nd Year

Guide : Dr. Pawan Goyal

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GrammarStructural rules governing the composition of clauses, phrases, & words in any given natural language, and this field includes morphology, syntax, and phonologyIngermann observed that the sutras have the samestructure as that of BNF and suggested to rename `Backus Naur Form'as `Paniini Backus Naur Form' (1967 ACM Communications). Formal GrammarSet of production rules for strings in a formal language. The rules describe how to form strings from the language's alphabet that are valid according to the language's syntax

CNeRG Reading GroupIIT KharagpurWhen choice your image, you must sent it to back! Right Click on Image->Send to Back ->Send Back

2padam(word) ::= subantam(nominal form) | ti_nantam(verbal form)(supti_nantam padam 1.4.14) ;subantam (nominal form) ::= pratipadikam (nom stem)sup(nom suff)pratipadikam(nominal stem) ::= krt (noun derived from a verb)| taddhita(noun derived from a noun)| samasa(compound)| underived pratipadikam(nominal stem) ;(krttaddhitasamasasca 1.2.46)

samasa(compound) ::= alaukika vigrahah. (Intermediate ling exp) ;alaukika vigrahah. ::= pratipadikam sup pratipadikam sup(sahasupa 2.1.4);In 2007, a work from Hyman (2007), which argued that the language generated by Paninis Grammar is mostly a regular LanguageCNeRG Reading GroupIIT KharagpurA -> B / C _ DCAD -> CBDA,B,C,D are strings or sets of strings (regular)

Generate RL with acyclicity restrictionJohnsons phonological rulesKiparsky & Penn 2012Given the specific, fixed grammar that Panini articulated in the Astadhyay, 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

Complete as it can generate any context-sensitive languageBrevity

Oral Traditionbuilt-in capacity for disambiguation

No Chomskyan system possesses this.Still RL-style analysis possible, by recasting the grammar*

Can accept any count languageCNeRG Reading GroupIIT Kharagpur. |. |. |. |. |

. |. |. |. |. |

. |. |. |. |Alphabets & Shiva SutrasWhere it all starts....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,CNeRG Reading GroupIIT Kharagpur

Buffet Managers Dilemma14 Sutras281 Pratyaharas42 Sets12 Million choices

Total list is of minimal lengthSound list is of minimal lengthAnubandha list is of minimal lengthOptimally arranged: no rearrangement results in a simpler one`n dishesWe take some dishes together (Set)People with different choices (veg/Nonveg)A person should find what he needs at a single stretchRepeated placement of a dish at different locations should be minimalMinimal markers for sets to be used

CNeRG Reading GroupIIT Kharagpur6The reasoning from economy goes like this. To be groupedtogether in a pratyahara, sounds must make up a continuoussegment of the list. Economy requires making the list asshort as possible, which means avoiding repetitions ofsounds, and using as few markers as possible.Consequently, if class A properly includes class B, theelements shared with B should be listed last in A; the markerthat follows can then be used to form pratyaharas for bothA and B. In this way the economy principle, by selecting theshortest grammar, determines both the ordering of soundsand the placement of markers among them.

- Kiparsky 1991CNeRG Reading GroupIIT KharagpurGrammar StructureRULESMETARULESLEXICAL LISTSGRAMMARAshtadhyayiUnadi SutrasDhatupathaGanapathaPHONOLOGICAL LISTSPanini Paribhasa sutrasAksharasamnayaCNeRG Reading GroupIIT Kharagpur8iko yan. aci (6.1.77)Ik{6} yan{1} ac{7}tasmin iti nirdiste purvasya (1.1.65)A word ending in locative case indicates `of the preeceding'.

sasthisthaneyoga (1.1.48)A word in genitive case undergoes change Ik{6} ac{7} ::= yan [1} ac{7}{i,u,r.,l.} {a,i,u,r.,l.,e,o,ai,au} -> {y,v,r,l} {a,i,u,r.,l.,e,o,ai,au}Grammar in Action{i,u,r.,l.} {y,v,r,l} {a,i,u,r.,l.,e,o,ai,au}A B/C _ D

W{5} W{6} W{7} ->W{5} W{1} W{7}

[iK] [yN.]/ _[aC]

CNeRG Reading GroupIIT KharagpurAnuvrttiJohn goes home. eats fruits.Johnupadese ac anunasik it 1.3.2hal antyam 1.3.3na vibhaktau tusmah. 1.3.4adih nitud avah 1.3.5sah pratyayasya 1.3.6cutu 1.3.7lasaku ataddhite 1.3.8upadese (a) it (c) ac anunasik ( = it)(b) hal antyam (d)na vibhaktau tusmah. (=it) (e) 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 ] ) cIf a == b step 1 step 2 step 3CNeRG Reading GroupIIT Kharagpur10Total Sutras: (3,984) 4,000Total Words: (7,007) 7,000Total Words after repeating the words with anuvrtti 40,000Compression due to anuvr.tti (40,000/7,000 ) 1/6

In terms of byte size, compression 1/3AnuvrttiCNeRG Reading GroupIIT KharagpurData EncapsulationDhatupathadhhrsa+ ktadhhrstaMethodniAttribute

CNeRG Reading GroupIIT Kharagpur12 deriving noun from nouns -- TaddhithaDhatus and pratipadikas are treated equally by Panini.Every rule contains Morphological Syntactic Semantic Specifications: (6th Case)RelationsSingle Inheritance

:

CNeRG Reading GroupIIT Kharagpur (, , ) 1.2.45

(,, , )

| 4.1.2 3.1.1. 3.1.2

(,, , , , root()) +

1.4.102 1.4.103

(,, , , , root()) + (,, , , , , root())CNeRG Reading GroupIIT Kharagpur 1.4.13 1.4.14

(,, , , , root()) + (,, , , , , root()) ()

| 1.4.18

(,, , , , , , root()) + (,, , , , , root()) ()

6.1.87 6.1.101 7.1.54 CNeRG Reading GroupIIT Kharagpur (,, , , , , , root()) + (,, , , , , (), - ,- ,root()) ()

6.4.3 7.3.102

(,, , , , , , root()) + (,, , , , , (), - ,- ,root() ()

1.4.110

(,, , , , , , root()) + (,, , , , , (), - ,- ,root() (, )

CNeRG Reading GroupIIT Kharagpur 8.4.2

(,, , , , , , root()) + (,, , , , , (), - ,- ,root() (, )CNeRG Reading GroupIIT Kharagpurperhaps the greatest difference between Paninis own formalism and the standard string-rewriting systems concomitant with Chomskys hierarchy, which is its built-in capacity for disambiguation. Paninis grammar, through its use of rule precedence and other meta-conventions, generates a single derivation for every grammatical sentence of Sanskrit.- PAUL KIPARSKY,2012

Paninis method of representing hierarchical information in a linear form is an interesting field of further investigations.-WIEBKE PETERSEN, 2004

Implement working systems.Doubles as a tool for learning the concepts of grammarCNeRG Reading GroupIIT KharagpurReferencesOn Pan.ini and the Generative Capacity of Contextualized Replacement Systems, Gerald Penn, Paul Kiparsky, COLING 2012,

A Mathematical Analysis of Paninis Sivasutras - Wiebke Petersen JoLLI. 13 (4), p. 471-489

Computer Simulation of Ashtadhyayi: Some insights, Pawan Goyal, Amba Kulkarni and Laxmidhar 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 1321.:CNeRG Reading GroupIIT Kharagpur