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Computational Structure of Aṣṭādhyāyī and Conflict Resolution Techniques

Computational Structure of Aṣṭādhyāyī and Conflict Resolution Techniques. By Sridhar S Varakhedi Srinivasa. Topics. A brief introduction to Aṣtādhyāyī Computational structure of Aṣtādhyāyī Illustrations Representation of sutras Mathematical formulae Limitations of this structure.

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Computational Structure of Aṣṭādhyāyī and Conflict Resolution Techniques

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  1. Computational Structure of Aṣṭādhyāyī andConflict Resolution Techniques By Sridhar S Varakhedi Srinivasa Third International Symposium on Sanskrit Computational Linguistics, HCU, Hyderabad. 15-17 Jan 2009

  2. Topics • A brief introduction to Aṣtādhyāyī • Computational structure of Aṣtādhyāyī • Illustrations • Representation of sutras • Mathematical formulae • Limitations of this structure. • Enriched Model • Summary Third International Symposium on Sanskrit Computational Linguistics, HCU, Hyderabad. 15-17 Jan 2009

  3. A brief introduction to Aṣtādhyāyī • Aṣtādhyāyī describes the fundamentals of Sanskrit language in terms of phonology, morphology and syntax in about 4000 sutras. • Consists of definitions, prescribing rules and meta-rules that are context-sensitive and operative in sequence or recursion. • Design of Aṣtādhyāyī has a crucial role in the process of language generation. Third International Symposium on Sanskrit Computational Linguistics, HCU, Hyderabad. 15-17 Jan 2009

  4. Input Input Siddha Siddha Block Block A B A A Asiddhavat Asiddhavat Block Block Legend Legend Legend Asiddha Asiddha Block Block Sutra group A, B A, B A, B – – – Environment Environment Environment C C C – – – Final state/result Final state/result Final state/result C C Computational Structure of Aṣtādhyāyī • Siddha block contains sutras belonging to sapādasaptādhyāyī (SA) excluding asiddhavat sutras • Asiddhavat block contains sutras from 6.4.22 to 6.4.175. • Asiddha block contains tripādī(TP) sutras.(8.2.1 till the end) Third International Symposium on Sanskrit Computational Linguistics, HCU, Hyderabad. 15-17 Jan 2009

  5. Input Input Siddha Siddha Block Block A B A A Asiddhavat Asiddhavat Block Block Legend Legend Legend Asiddha Asiddha Block Block Sutra group A, B A, B A, B – – – Environment Environment Environment C C C – – – Final state/result Final state/result Final state/result C C Computational Structure of Aṣtādhyāyī • Each small circle represents a group of sutras that are grouped in the form of tree based on topics. • A, B represent different states of input (environment). • Inward arrows towards circles indicate environment is observed by sutras. Outward arrows indicate modification of the environment on application of sutras. • C represents the final state. Third International Symposium on Sanskrit Computational Linguistics, HCU, Hyderabad. 15-17 Jan 2009

  6. Input Input Siddha Siddha Block Block A B A A Asiddhavat Asiddhavat Block Block Legend Legend Legend Asiddha Asiddha Block Block Sutra group A, B A, B A, B – – – Environment Environment Environment C C C – – – Final state/result Final state/result Final state/result C C Illustration – Siddha Block • Let A = [vana ṭā] is present state. • The sutra ‘ṭā ṅasiṅasāminātsyāḥ’ , in the siddha block finds the condition for its application. • This sutra is applied and A gets changed to [vana ina]. • Sutra ‘ādgunaḥ’, in the siddha block finds the condition and is applied. • A now reads as [vanena] • Further, no sutra in any block finds condition. Hence, A is passed to C. • Now C has the final form [vanena] Third International Symposium on Sanskrit Computational Linguistics, HCU, Hyderabad. 15-17 Jan 2009

  7. Input Input Siddha Siddha Block Block A B A A Asiddhavat Asiddhavat Block Block Legend Legend Legend Asiddha Asiddha Block Block Sutra group A, B A, B A, B – – – Environment Environment Environment C C C – – – Final state/result Final state/result Final state/result C C Illustration – Asiddhavat Block • Let A = [śās hi] • Two Sutras namely ‘śā hau’ and ‘hujhalbhyo herdhiḥ’ in the Asiddhavat block finds their condition. • A is duplicated in B. • Sutra ‘śā hau’ is applied to B that is changed to [śā hi]. • Sutra ‘hujhalbhyo herdhiḥ’ also finds its condition in A and gets applied to B that is changed to [śā dhi]. • Further no more sutras in this block find condition, Now, A is overwritten with B. • None of the sutras either in siddha block or the asiddha block finds condition in A. • A is passed to C without any transformation. Final result is [śādhi] Third International Symposium on Sanskrit Computational Linguistics, HCU, Hyderabad. 15-17 Jan 2009

  8. Input Input Siddha Siddha Block Block A B A A Asiddhavat Asiddhavat Block Block Legend Legend Legend Asiddha Asiddha Block Block Sutra group A, B A, B A, B – – – Environment Environment Environment C C C – – – Final state/result Final state/result Final state/result C C Illustration – Asiddha Block • Let A = [dvau atra]. • The sutra ‘ecoyavāyāvaḥ’ in the siddha block finds its condition and gets applied. A is changed to [dvāv atra]. • No sutra in the siddha block or the asiddhavat block finds condition in A. • The sutra ‘lopaḥ śākalyasya’ in the asiddha block finds the condition and gets applied. A is changed to [dvā atra]. • Since this state is invisible to the sutras either in the siddha block or in the asiddhavat block, even though there is condition for the ‘akaḥsavarṇe dīrghaḥ’ in the siddha block, this sutra does not find condition for application. • The sutras subsequent to ‘lopaḥ śākalyasya’ do not find any application due to non availability of their condition, though the current state is visible. • C has the final form [dvā atra]. Third International Symposium on Sanskrit Computational Linguistics, HCU, Hyderabad. 15-17 Jan 2009

  9. Representation of Sutras • Sutras are objects in Object oriented programming terms. • The sutras are grouped in the form of a tree for each of the topics (ekavākyaṃ). • The most general sutra is placed on the top of tree (root node) and exception (apavāda) sutras will be child nodes. Third International Symposium on Sanskrit Computational Linguistics, HCU, Hyderabad. 15-17 Jan 2009

  10. Example 2 1 5 1. iko yaṇaci 6.1.77 2. ecoyavāyāvaḥ 6.1.78 3. vānto yi pratyaye 6.1.79 4. dhātostannimittasaiva 6.1.80 5. ādguṇaḥ 6.1.87 6. vṛddhireci 6.1.88 3 11 6 8 11 4 10 9 7 10 12 12 7. etyedhatyūṭhsu 6.1.89 8. eṅi pararūpaṃ 6.1.94 9. omāṅgośca 6.1.95 10. ato guṇe 6.1.97 11. akaḥ savarṇe dīrghaḥ 6.1.101 12. prathamayoḥ pūrvasavarṇaḥ 6.1.102. Third International Symposium on Sanskrit Computational Linguistics, HCU, Hyderabad. 15-17 Jan 2009

  11. Conflict Resolution Techniques • What is Conflict ? • When two or more sutras find their condition in a particular context then all these sutras are said to be in conflict (vipratiṣedha), as only one sutra need to be applied at a time. • Ways of Conflict Resolution are found in • Aṣtādhyāyī • Vartikas • Aṣtādhyāyī • Vipratiṣedhe paraṃ kāryaṃ • Siddha-Asiddha Principle • etc • Vartikas. • Para-nitya-antaraṅga-apavādānāṃ uttarottaraṃ balīyaḥ • Varṇādāṅgaṃ balīyo bhavati • Lakṣye lakṣaṇaṃ sakṛdeva pravartate • etc Third International Symposium on Sanskrit Computational Linguistics, HCU, Hyderabad. 15-17 Jan 2009

  12. Sutras are Siddha (visible) unless explicitly mentioned as Asiddha(invisible) Asiddhatva is explicitly mentioned in the sutras- Ṣatvatukorasiddhaḥ 6.1.86 Asiddhavadatrābhāt 6.4.22 Pūrvatrāsiddhaṃ 8.2.1 Siddha Rule precede over Asiddha rule. 1. Śivachāyā 2. Śivatchāyā 6.1.73 (che ca) 3. Śivadchāyā 8.2.39 4. Śivajchāyā 8.4.40 5. Śivacchāyā 8.4.55 Here ‘jhalāṃ jaśonte’ 8.2.39 and ‘stoḥ ścunā ścuḥ’ 8.4.40 both have the condition, since 8.4.40 is asiddha for 8.2.39, siddha rule is given priority in application. Similarly the case is repeated in 8.4.40 and ‘khari ca’ 8.4.55. Siddha-Asiddha Principle Third International Symposium on Sanskrit Computational Linguistics, HCU, Hyderabad. 15-17 Jan 2009

  13. Let A(X,) returns result of application of sutra X in the state  and returns zero if sutra X is not applicable. If (A(X, A(Y, )) != 0, then X is Nitya else X is Anitya. =[tud tip] X = ‘tudādibhyaḥ śaḥ 3.1.77’, Y = ‘Pugantalaghūpadasya ca 7.3.86’. A(Y, )= [tod tip] A(X,A(Y, )) = [tod śa tip] != 0. Hence X is Nitya. Similarly, A(X, )= [tud śa tip] A(Y,A(X, )) = 0. Hence Y is Anitya. Mathematical Definition of Nitya and Anitya Third International Symposium on Sanskrit Computational Linguistics, HCU, Hyderabad. 15-17 Jan 2009

  14. Let F(X, ) returns the number of Conditions for sutra X in the state . if F(X, ) < F(Y, ) then X is Antaraṅga and Y is Bahiraṅga else Y is Antaraṅga and X is Bahiraṅga X = ‘Sarvādīni sarvanāmāni 1.1.27’ Y= ‘Prathamacaramatayālpakatipayanemāśca 1.1.33’  = [ubhaya jas] F(X, )= 1, F(Y, )=2. F(X, ) < F(Y, ), therefore X is Antaraṅga and Y is Bahiraṅga Determination Formula for Antaraṅga and Bahiraṅga. Third International Symposium on Sanskrit Computational Linguistics, HCU, Hyderabad. 15-17 Jan 2009

  15. Input Input Siddha Siddha Block Block A B A A Asiddhavat Asiddhavat Block Block Legend Legend Legend Asiddha Asiddha Block Block Sutra group A, B A, B A, B – – – Environment Environment Environment C C C – – – Final state/result Final state/result Final state/result C C Limitations of this Structure • There are some exceptions in SA that are found applied after the application of TP. Eg. Sivorcyah, where ru prescribed in tripadi, gets a substitute by a rule from SA. How to handle such cases? • Cases like jahi may get transformed into undesired form by application of sutra ‘ato heh’. How to prevent ? • Cases of ekadesha where satva(TP) and tuk (SA) are asiddha are not taken care of in this model. • Conflict resolver does not find any place in the structure. Third International Symposium on Sanskrit Computational Linguistics, HCU, Hyderabad. 15-17 Jan 2009

  16. Enriched Model • Siddha and Asiddha concepts along with exceptions are handled with the use of Filters. • Conflict Resolver is introduced in this model • Each state of environment is observed by TP simultaneously with SA. Third International Symposium on Sanskrit Computational Linguistics, HCU, Hyderabad. 15-17 Jan 2009

  17. Summary • We have tried to show the feasibility of computing of Astadhyayi that was claimed to be the first and foremost computer program authored sans a machine. • Traditional conflict resolution techniques shown in mathematical formulae will exhibit the computability of Astadhyayi a complete and coherent system developed 25 centuries ago in India. • This proves that Panini is Father of Computation. Third International Symposium on Sanskrit Computational Linguistics, HCU, Hyderabad. 15-17 Jan 2009

  18. Thanks To The Chair, Organizers, Editors, Reviewers and Participants Third International Symposium on Sanskrit Computational Linguistics, HCU, Hyderabad. 15-17 Jan 2009

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