Pāṇini's fourth century BC Sanskrit grammar uses rewrite rules utilizing an explicit formal language defined through a semi-formal metalanguage. The grammar is generative, meaning that it is capable of expressing a potential infinity of well-formed Sanskrit sentences starting from a finite symbolic inventory. The grammar's operational rules involve extensive use of auxiliary markers, in the form of Sanskrit phonemes, to control grammatical derivations. Pāṇini's rules often utilize a generic context-sensitive format to identify terms used in replacement, modification or deletion operations. (...) The context-sensitive rule format is itself defined using Pāṇini's more general method of auxiliary markers, the latter used to define many dozens of linguistic categories and rules controlling derivations of Sanskrit sentences through the manipulation of ‘non-terminal’ and ‘terminal’ symbols. This technique for controlling formal derivations was rediscovered by Emil Post in the 1920s and later shown by him to be ca... (shrink)

Is Pāṇini’s grammar prescriptive or descriptive, or perhaps both at the same time? The answer determines, among many other things, how we should render vā and vibhāṣā in his optional rules. If the grammar is prescriptive, these terms can mean “preferably” and “marginally”. If it is purely descriptive, then only “frequently” and “rarely” are appropriate translations. In Pāṇini as a Variationist (henceforth PV )I suggested that both translations are equally valid, on the grounds that the Aṣṭādhyāyī is at the same (...) time a faithful record of the usage of a community of śiṣṭas, and part of a project to canonize that usage as correct, meant to be binding on all users of the language. Devasthali (1983), however, objected that the idea of “better” or “worse” usage is “foreign to the ancient Sanskrit grammatical works and grammarians”, because they do not deal with incorrect apaśabdas, only with sādhusabdas – the correct words of the divine language. (shrink)

In Pninis grammar of Sanskrit one finds the ivastras, a table which defines the natural classes of phonological segments in Sanskrit by intervals. We present a formal argument which shows that, using his representation method, Pninis way of ordering the phonological segments to represent the natural classes is optimal. The argument is based on a strictly set-theoretical point of view depending only on the set of natural classes and does not explicitly take into account the phonological features of the segments, (...) which are, however, implicitly given in the way a language clusters its phonological inventory. The key idea is to link the graph of the Hasse-diagram of the set of natural classes closed under intersection to ivastra-style representations of the classes. Moreover, the argument is so general that it allows one to decide for each set of sets whether it can be represented with Pninis method. Actually, Pnini had to modify the set of natural classes to define it by the ivastras (the segment h plays a special role). We show that this modification was necessary and, in fact, the best possible modification. We discuss how every set of classes can be modified in such a way that it can be defined in a ivastra-style representation.1. (shrink)

The following principles are seen to operate in the rules Pānini provides for Sanskrit grammar. (1) The obvious principle that the introduction of affixes and augments which condition sound replacements necessarily precede the latter. (2) Bracketing, whereby an operation whose condition is internal relative to a condition causing another operation applies prior to the latter. (3) The derivational prehistory of a form is pertinent to the operations which apply to it. (4) Blocking: a rule R2 is said to block an (...) R1 if, in a given domain, R1 tentatively applies (and would apply in the absence of R2) wherever R2 can apply, while R2 would be vacuous if R1 applied. (4a) Limited blocking, which obtains where R1 and R2 overlap but also have independent domains of application. These principles account for correct derivations in cases where post-Paninian grammarians invoked rule order: where two rules conflict, that one takes precedence which is stated later in the grammar. This principle is not generally tenable, since some derivations require that a rule stated previously in the grammar take precedence. Hence, the grammarians who invoke such rule ordering in cases of conflict must admit that only a knowledge of the correct results to be obtained by applying the rules allows one to correctly apply the rules in the first place. It is argued that Pānini avoided this weakness. (shrink)

In the preceding we have argued that brevity in the form of Generalizing Brevity is an important theoretical principle underlying Panini's grammar. It applies blindly at the metalevel, when the grammar is being chosen. Generalization is a concern at one remove: A device for the metalanguage is only chosen such that its use in accord with the maximum brevity leads to some generalization. Many potential brevity increasing devices are not chosen for this reason. But at the metalanguage level brevity (...) is paramount. To prove this we have shown that Panini maximizes brevity in many cases at the cost of other possible theoretical principles. We have also shown that many features of the grammar flow from the brevity criterion. We have concluded that logical organization, generality, and other aspects of explanation largely follow from brevity and that this can be regarded as a substantial aspect of the explanatory power of the theory behind the grammar. Generalization should follow on the heels of maximum brevity. And, considering Panini's domain of data this is a perfectly reasonable expectation. (shrink)

The ninth volume contains ahnikas, divisions, forty-two to forty-seven, and the tenth volume contains ahnikas forty-eight to fifty-six. Each Panini sutra is followed by the relevant bhashya, commentary, and the varttika, annotation, of Vararuchi. Each volume has indexes of the sutras, varttikas, nyayas, paribhashas, and important Sanskrit and English words.

카라카(kāraka)는 문장에서 동사와 연결되어 동사의 의미를 완성시키도록 돕는 것이다. 파니니(Pāṇini)는 이 개념에 대해 정의내리고 있지는 않지만, 자신의 文典(Aṣṭādhyāyī)의 P. 1.4.23에서 ‘처격으로 표시된 의미조건’으로서 제시하고 있다. 그리고 이하 P. 1.4.55에 이르기까지, 범어 구문론의 중추를 이루는 이 개념을 행위 주체를 의미하는 kartṛ, 행위의 목적(대상)을 나타내는 karma, 행위 성취의 수단을 나타내는 karaṇa, 증여를 표시하는 saṁpradāna, 분리를 나타내는 apādāna, 행위발생 장소인 adhikaraṇa라는 6개 항목으로 분류하여 다루고 있다. 그중 파니니가 가장 먼저 규정하고 있는 것은 ‘제5격 어미’를 취하여, ‘탈격’이라고도 불리는 아파다나 카라카(apādāna-kāraka)로, P. 1.4.24-31에서 취급되고 있다. (...) 여기서 ‘아파다나 카라카’로 규정되고 있는 것들은, ① 떠남(분리)와 관련된 행위에 관해 고정점, ② 두려움과 관련된 행위에 관해 그 대상, ③ 굴복하는 행위와 관련된 대상, ④ 제지 행위와 관련하여 도달하고자 원하는 대상, ⑤ 숨는 행위와 관련하여 보이지 않기를 원하는 대상, ⑥ 지식 획득과 관련된 행위에 관한 그 敎示者, ⑦ ‘태어남’을 의미하는 행위와 관련하여 그 행위 주체의 탄생 근원, ⑧ √bhū와 관련한 행위 주체의 初出 장소라는 8항목들이다. 이상에 대한 고찰은, 아파다나 카라카라는 문장 구성 요소가 어떻게 행위 주체의 ‘행위 성취’를 돕는지(kāraka)를 명확히 하기 위한 것으로, 이를 통해 제5격의 적용 근거가 분명히 드러남을 살펴보았다. (shrink)

This paper explains how mathematical computation can be constructed from weaker recursive patterns typical of natural languages. A thought experiment is used to describe the formalization of computational rules, or arithmetical axioms, using only orally-based natural language capabilities, and motivated by two accomplishments of ancient Indian mathematics and linguistics. One accomplishment is the expression of positional value using versified Sanskrit number words in addition to orthodox inscribed numerals. The second is Pāṇini’s invention, around the fifth century BCE, of a formal (...) grammar for spoken Sanskrit, expressed in oral verse extending ordinary Sanskrit, and using recursive methods rediscovered in the twentieth century. The Sanskrit positional number compounds and Pāṇini’s formal system are construed as linguistic grammaticalizations relying on tacit cognitive models of symbolic form. The thought experiment shows that universal computation can be constructed from natural language structure and skills, and shows why intentional capabilities needed for language use play a role in computation across all media. The evolution of writing and positional number systems in Mesopotamia is used to transfer the thought experiment of “oral arithmetic” to inscribed computation. The thought experiment and historical evidence combine to show how and why mathematical computation is a cognitive technology extending generic symbolic skills associated with language structure, usage, and change. (shrink)

Commentary on Aṣṭādhyāyī of Pāṇini, classical work on Sanskrit grammar.