A Synopsis by Amrutha MK (Research Associate, NIAS) – on “Pāṇini’s Aṣṭādhyāyī from Computational Perspective”
Lecture given by Prof. Amba Kulkarni on 07 April 2021
Series Title: Sanskrit Language & its Traditions: A Journey Through its History and Contemporaneity
Organised by: NIAS Consciousness Studies Programme, National Institute of Advanced Studies, Bangalore, India
Prof. Amba Kulkarni presented the twelfth lecture on the topic “Pāṇini’s Aṣṭādhyāyī from Computational Perspective” for the series “Sanskrit Language and its Traditions: A Journey Through its History and Contemporaneity” on 7th April 2021. Ancient Indian linguistic tradition dealt with theories of verbal cognition and grammar, but to provide an account of the contemporariness of this tradition Prof. Kulkarni chose grammar as the focus of the lecture. She showed how the “knowledge base” of Pāṇini’s grammar became an aid for evaluating the feasibility of an operation, which was crucial for any computational linguistic tasks like language processing, information extraction, and machine translation. In the first part of the lecture, she demonstrated the way in which Aṣṭādhyāyī can be looked at from the “information encoding” perspective that helped “feasibility studies” in computational linguistics. The second part of the lecture was on “the organization of Aṣṭādhyāyī”. With these two parts, she presented a novel approach (“navya-vyākaraṇa”) to study Aṣṭādhyāyī from a computational perspective.
Prof. Kulkarni chose three sūtras from Aṣṭādhyāyī to address the following three aspects, namely, where the information was coded, how much information was coded, and how the information was coded. She picked the sūtra “anabhihite” (1.3.1) to examine “where the information was coded” and with the example of gacāmi, she demonstrated that the information of aham was coded within the suffix mi which enabled the user to drop aham from the expression. Knowing where the information is encoded, helps a computational linguist to extract the information whenever needed. The sūtra “samānakartṛkayoḥ pūrvakāle” (3.4.21) was selected to show “how the information was coded”, i.e., whether the information was coded implicitly or explicitly. Extracting information from an explicitly coded statement is easier compared to an implicitly coded statement. She took the sūtra “svatantraḥ kartā” (1.4.54) as an example to examine “how much information was coded”. Taking three sentences, devadattaḥ pacati (devadatta cooks), sthālī pacati (A vessel cooks) and edhāḥ pachanti (the log cooks) she pointed out that, different labels like agent, container, instrument were not assigned to these different “actors” by Pāṇini. Instead, Pāṇini called all of them kartha. Therefore, she pointed out that “the concord between a noun and a verb” is the sole relation that could be extracted from this linguistic expression, but to decide whether it is the agent or instrument, word knowledge is necessary. Thus, in her opinion, Aṣṭādhyāyī showed how much information could be extracted from a statement without any “extra-linguistic information” and decided the feasibility of an operation through grammar rules and language strings.
In part two of the lecture, Prof. Kulkarni focused on the organisation of sūtrās in Aṣṭādhyāyī and presented the following aspects of it, the concept of anuvṛtti, the data structure in Śivasūtras, the syntax of rules, and rule ordering and conflict resolution. She began the second section discussing the concept of “distributivity in language” and analysed seven (1.3.2 to 1.3.8) sūtras of Aṣṭādhyāyī. These seven sūtras had a word count of 16 in the original composition. But in Siddhānta Kaumudī when the words were “reorganised” to make a sutra meaningful by borrowing words from the previous sūtra, the word count became 35. To perform some mathematical operations on these sūtras Prof Kulkarni replaced those words using variables and did factorization. She showed that Pāṇini had “factored out the words which were common in all sūtras” and arranged them accordingly. Thereby she pointed out that Pāṇini had used “the principle of distributivity or factorisation” and achieved brevity. She explained the necessity to bring brevity and the measure of brevity achieved through anuvṛtti. She found that due to compression through anuvṛtti and with proper arrangement of sūtras, the word count got decreased from 40000 to 7000 which was 1/6th of the original. In an oral tradition, this technique had practical relevance, i.e., if this compression technique was not applied it would have taken three years to memorise Aṣṭādhyāyī instead of six months with compression technique applied. Prof. Kulkarni explained the importance of expectancy (ākāṅkṣāḥ) in deciding anuvṛtti and using verses 1.1.1, 1.1.2, 1.1.3, 3.3.65 she showed that the decision to borrow words from previous sūtras were based on the principle of expectancy. Following this, she argued that the grammar which Pāṇini developed was for humans and not for machines.
Prof. Kulkarni discussed Śivasūtras and compared it with “innovative data structures” from the computational perspective. She said that Pāṇini required 41 subsets of alphabets to describe different operations. But it was not easy to memorize each one of them. An important contribution of Pāṇini was that he “linearised the partially ordered sets by introducing markers” called anubandha. Thus, from this one set of sutra 41 subsets could be generated. From a computational point of view, this made the retrieval of information easier and faster. She said that the sutras in Aṣṭādhyāyī, had the syntax and the programme fused together. Thus, she commented that though Aṣṭādhyāyī is in Sanskrit, just by knowing Sanskrit one may not understand its sūtra style construction, which is like an artificial language. She also gave three sūtras (1.1.65, 1.1.66, 1.1.48) as examples of syntax from Aṣṭādhyāyī and explained about “Pāṇini Backus form”. In the final part, she discussed some rules and constraints for deciding priority when more than one rule was applicable. She presented a graphical representation of how various rules were applied one after another and how these rules interacted with each other. She diagrammatically represented “the visibility of data space” based on the rules applied and how conflict resolution took place using some sūtras (8.2.1, 6.4.22, 6.1.83). The fascinating lecture ended with a lively question-answer session.
Additional Reference: https://sanskrit.uohyd.ac.in/scl/
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