Free Word Order in S anskrit and Well-nestedness (2020)

Abstract: The common wisdom about Sanskrit is that it is free word order language. This word order poses challenges such as handling non-projectivity in parsing. The earlier works on the word order of Sanskrit have shown that there are syntactic structures in Sanskrit which cannot be covered under even the non-planarity. In this paper, we study these structures further to investigate if they can fall under well-nestedness or not. A small manually tagged corpus of the verses of Śrīmad-Bhagavad-Gītā was considered for this study. It was noticed that there are as many well-nested trees as there are ill-nested ones. From the linguistic point of view, we could get a list of relations that are involved in the planarity violations. All these relations had one thing in common - that they have unilateral expectancy. It was this loose binding, as against the mutual expectancy with certain other relations, that allowed them to cross the phrasal boundaries.

## introduction sanskrit is inflectionally rich and it rarely uses position to encode any syntactic or semantic relation between words. this enables sanskrit to move the words freely in a sentence. within indian tradition, the word order was regarded as free, provided the proximity (sannidhi) is not violated. the indian theorists found the sentences with different arrangements of words to be equivalent in meaning, with an exception of subject-predicate @xcite . the difficulty in understanding the verses due to deviation from the 'default' word order, however, had been realised. the commentators commenting on the verses have followed this 'default' word order known as the anvaya of a verse (śloka) foot_0 . but this default word order is not followed strictly either by the commentators or by the authors while composing prose. when the sanskrit texts started being translated into fixed word order european languages, the free word order of sanskrit had been noted. the westerners tried to propose a framework for the sanskrit word order. however, these studies also lead to only a preferential, or frequent arrangement, and not 'the' arrangement. the deviations were considered to be the exceptions. even while discussing the syntax, much emphasis had been laid on the concord and government rather than order. though sanskrit allows free movement of words, and there are preferential word orders, certainly not all permutations of the words are allowed. so the attention of the researchers then was drawn to the restrictions on word order rather than possible word orders. the first systematic account of the word order in sanskrit was by @xcite . he introduced a concept of 'wild tree' which allows the movement of the items within a phrase freely. in this model, any two items from different phrases cannot interleave or the words in one phrase cannot leave their place and move to the domain of other phrases. this model was formalised and empirically tested by gillon on a corpus of approximately thousand classical sanskrit prose sentences. half of the sentences of this corpus was from a single text, 2 and the other half was selected at random from the sentences found in @xcite . his empirical observations confirm the model suggested by staal viśes . an . am puraskr . tya viśes . yam tadanantaram | kartr . karmakriyāyuktam etad anvayalaks . an . am || (samāsacakra karikās 4, 10) (english: starting with kartr . , followed by other words, placing the non-finite verb forms such as ktvā, tumun, lyap in between, place the main verb at the end. starting with adjectives, targeting the headword, in the order of kartr . -karmakriya gives an anvaya (natural order of words).) with an exception of movement of genitives and adjectives across the clause boundaries. @xcite studies the modern sanskrit texts and conversations from the point of view of the flexibility in word order. he found that the modern writings and the conversations follow the default word order. @xcite presents the preliminary observations with regards to the comparison of the word order in prose and verse which confirm more flexibility in verses than in prose. in order to develop a computational parser for sanskrit, these theoretical insights are very much useful. @xcite studied and carried out an empirical study of the verses in srimad-bhagavad-gītā(bhg). the aim of this study was to gain insights regarding the flexibility in the word order to build a computational model of grammatical sentences in sanskrit. they could fit a weakly non-projective (or planar) model for the sanskrit sentences, barring a few cases. one important observation was that the number of cases of violation of planarity condition in verse was higher than the number of exceptions studied by gillon in prose. another observation was with respect to the relations involved in the planarity violation. it was observed that in addition to the two relations viz. the adjective (viśes . an . a) and the genitive, pointed out by gillon, a few other relations such as vocative, negation etc. also violated the planarity of the graph. but these relations were not as frequent as the genitive and adjective. at the same time, the behaviour of these relations was the same irrespective of whether the text is a prose or a verse. these relations which do not conform to the planar graphs had a special status. a peep into the indian theories of verbal cognition revealed that these exceptions correspond to the cases where the words have unilateral expectancy (utthāpya ākāṅks . ā). such grammatically accepted sentences were studied further in order to build a proper computational model for parsing them. in this paper, we test whether the exceptions to the planar graphs fall under the category of well-nested graphs or not. the organisation of the rest of the paper is as follows. in the next section, we describe various parameters to classify the syntactic structures mathematically. in the third section we discuss two major concepts-the concept of expectancy (ākāṅks . ā) and the concept of proximity (sannidhi)-from indian theories of verbal cognition (śābdabodha) that are useful from the point of view of dependency. in the fourth section, we describe the empirical experiments we carried out to classify the cases of proximity violation. we show that the violations do occur both in the well-nested as well as ill-nested graphs and that the non-planarity is mainly due to the adjectival and genitive relations with a few cases of other non-kāraka relations such as negation, vocative, conjunction, etc. finally we conclude that the utthita and utthāpya ākāṅks . ā provide a better classification for the non-planar graphs rather than well-nested and ill-nested classification. ## dependency structures in this section we present the formal definition of various mathematical structures associated with the dependency. the dependency parse of a sentence is expressed in the form of a tree structure. this tree is a directed acyclic graph with one root node, and all other nodes connected to at least one other node in the tree by a direct edge. ## indian theories according to the exegesists (mīmām . sakas) a sentence is defined as arthaikatvāt ekam vākyam sākā ṁks . am cet vibhāge syāt | ms 2.1.46 (a sentence is an integral unit conveying a single purpose, and when it is split into two parts, some words in one part would have an expectancy for some other words in the other part.) this implies that each word in a sentence either satisfies an expectancy of or has an expectancy for some other word in a sentence. that is every word in a sentence should be connected with at least one other word in it. let us represent the words in a sentence by the nodes, and the expectancies between words by edges joining the nodes. two nodes connected by an edge do not have the same status. one of them has an expectancy and the other one satisfies the expectancy. hence we use directed edges to mark this asymmetry. ## dependency graphs and planarity sanskrit is inflectionally rich. so the common wisdom is that we can move around the words in any order. for example, the following sentence with three words, (1) śvetah . white aśvah . horse dhāvati runs can have 3! (=6) permutations. but among these the following permutation, for example, this is the hero who has become the topic of your speech. in this sentence, the demonstrative adjective 'sah . ' modifying a predicate noun 'vīrah . ', intervenes between its predicate 'bhūtah . ' and the agent (kartā) of the 'speech' (vāk) viz. 'te', as shown in figure 9 . below is a part of a verse from śrīmad-bhagavad-gītā (bhg) that exhibites similar phenomenon. cañcalam hi manah . kr . s . n . a pramāthi balavat dr . d . ham | tasya aham nigraham manye vāyoh . iva sudus . karam || bhg 6.34 (english: for, o krishna, the mind is unsteady, turbulent, strong and obstinate, i consider its control to be as difficult as of the wind.) tasya aham nigraham manye its i control consider karma karma kartā figure 10: analysis of bhg 6.34 in the second line of this verse the main verb is 'manye' (consider) whose kartā is 'aham' (i). the karma of the verbal noun 'nigraham' (control) is the pronominal 'tasya' (its), which refers to 'manah . ' (mind) in the first part of the verse. thus the word sequence 'tasya aham nigraham manye' produces two crossing edges involving the relations of kartā and karma. let us see one more example. this is 18 th śloka of 10 th chapter. in this verse, again we look at the second part of the second line in the verse. the kartā of the main verb 'asti' (is) is 'tr . ptih . ' (satisfaction), the karma of 'śr . n . vatah . ' (while listening) is 'amr . tam' (immortal), and there is a genitive relation between 'me' (my) and 'tr . ptih . ' (satisfaction). we see two crossings, one between the kartā and karma, and the other between genitive and karma. there is an important difference between the crossing in figures 9 , 10 and 11 though all of them are grammatically sound. in figure 9 the relations involved in crossings are genitive and adjective. in figure 10 the relations are kartā and karma, which are the arguments of the verb, called kāraka relations in sanskrit grammar. so in one sentence, there is a crossing between two kāraka relations. in another, the crossing is between non-kāraka relations. as we have seen earlier, the kāraka relations have mutual expectancies, while the non-kāraka relations such as genitive and adjective have unilateral expectancy. and in figure 11 , we see both types of crossings. further we notice that while the graphs of figure 9 and figure 10 are well-nested, the graph of figure 11 is ill-nested. now we describe the empirical observations of the dependency trees of bhg with special reference to the crossings involved and the well-nestedness. ## discussions the majority of the sentences (around 83%) have dependency graphs that are weakly non-projective. the remaining 17% graphs did not have planar graphs as they involved crossings of the dependency relations. several of the sentences had more than one crossing. some of these crossings show well-nestedness while the others show illnestedness. we notice that trees with only wellnested crossings are considerably less than trees with only ill-nested crossings. further, there are almost double the number of sentences that have both ill-nested as well as well-nested crossings. any graph, that involves both ill-nested as well as well-nested crossings, essentially is an ill-nested graph. thus we notice that almost 14% of the sentences have ill-nested graphs. thus every sixth sentence of the corpus has a non-planar graph, involving crossings between the disjoint graphs, with the majority of them being ill-nested. in order to understand more about these crossings, we looked at the relations involved in them. we noted down the relations involved in crossings, and counted the number of instances of crossings that show well-nestedness or ill-nestedness. as expected, we noticed that, barring a few cases, at least one relation among the two relations involved in crossing has unilateral expectancy. kulkarni et al. (2015 in this dependency graph, we notice that there is a crossing between karma and an adjective, and neither of the heads governs the other, giving rise to an ill-nested graph. this graph also shows another crossing between a kartā and a karma relation, which corresponds to the well-nested graph. now we present two examples, where both the relations have unilateral expectancy. the first one is a well-nested graph which corresponds to the 4 th śloka of 18 th chapter. in this graph, there is a crossing of two unilateral relations viz. genitive and vocative. the graph is well-nested, as the head of the genitive is governed by the head of the vocative relation. the example of an ill-nested graph involving two unilateral relations is the first śloka of the 9 th chapter. we show the partial graph with crossing relations. in this graph, we see three crossings. the first one between the recipient and the adjective, the second one between the karma and the adjective, and the third one between the two adjectives. the first two crossings correspond to the well-nested graph. but the third one corresponds to the ill-nested one. finally, among the unilateral relations that contribute to either well-nested or ill-nested graphs, adjective, vocative, genitive and negation are prominent, followed by conjunction. among the relations having mutual expectancy, kartā, karma and adhikaran . a ṁ are more prominent. ## conclusion sanskrit, as the common wisdom goes, is a free word order language. the calder mobile model of staal which conjunctures the free movement of the words within a phrase was found to be partially correct. gillon through empirical study pointed out that there are certain cases of violation of this model. later kulkarni et al, again through the empirical study showed that the cases of violations of planarity correspond to the relations exhibiting unilateral expectancy. in this paper, we showed that there are as many cases of well-nested crossings as ill-nested ones. thus not all syntactic structures of sanskrit can be covered under the wellnested trees. a majority of non-planar graphs are ill-nested. in most of the cases, unilateral relations are involved in the violation of planarity as well as well-nestedness.