There is a need to develop a suitable computational grammar formalism for free word order languages for two reasons : First , a suitably designed formalism is likely to be more efficient . Second , such a formalism is also likely to be linguistically more elegant and satisfying . In this paper , we describe such a formalism , called the Paninian framework , that has been successfully applied to Indian languages . This paper shows that the Paninian framework applied to modern Indian languages gives an elegant account of the relation between surface form ( vibhakti ) and semantic ( karaka ) roles . The mapping is elegant and compact . The same basic account also explains active-passives and complex sentences . This suggests that the solution is not just adhoc but has a deeper underlying unity . A constraint based parser is described for the framework . The constraints problem reduces to bipartite graph matching problem because of the nature of constraints . Efficient solutions are known for these problems . It is interesting to observe that such a parser ( designed for free word order languages ) compares well in asymptotic time complexity with the parser for context free grammars ( CFGs ) which are basically designed for positional languages . A majority of human languages including Indian and other languages have relatively free word order . tn free word order languages , order of words contains only secondary information such as emphasis etc . Primary information relating to ' gross ' meaning ( e.g. , one that includes semantic relationships ) is contained elsewhere . Most existing computational grammars are based on context free grammars which are basically positional grammars . It is important to develop a suitable computational grammar formalism for free word order languages for two reasons : 1 . A suitably designed formalism will be more efficient because it will be able to make use of primary sources of information directly . 2 . Such a formalism is also likely to be linguistically more elegant and satisfying . Since it will be able to relate to primary sources of information , the grammar is likely to be more economical and easier to write . In this paper , we describe such a formalism , called the Paninian framework , that has been successfully applied to Indian languages . 1 It uses the notion of karaka relations between verbs and nouns in a sentence . The notion of karaka relations is central to the Paninian model . The karaka relations are syntactico-semantic ( or semantico-syntactic ) relations between the verbals and other related constituents in a sentence . They by themselves do not give the semantics . Instead they specify relations which mediate between vibhakti of nominals and verb forms on one hand and semantic relations on the other ( Kiparsky , 1982 ) ( Cardona ( 1976 ( Cardona ( ) , ( 1988 ) ) ) . See Fig . 1 . Two of the important karakas are karta karaka and karma karaka . Frequently , the karta karaka maps to agent theta role , and the karma to theme or goal theta role . Here we will not argue for the linguistic significance of karaka relations and differences with theta relations , as that has been done elsewhere ( Bharati et al . ( 1990 ) and ( 1992 ) ) . In summary , karta karaka is that participant in the action that is most independent . At times , it turns out to be the agent . But that need not be so . Thus , ' boy ' and ' key ' are respectively the karta karakas in the following sentences 1The Paninian framework was originally designed more than two millennia ago for writing a grammar of Sanskrit ; it has been adapted by us to deal with modern Indian languages . The boy opened the lock . The key opened the lock . Note that in the first sentence , the karta ( boy ) maps to agent theta role , while in the second , karta ( key ) maps to instrument theta role . As part of this framework , a mapping is specified between karaka relations and vibhakti ( which covers A. 2 collectively case endings , post-positional markers , etc . ) . This mapping between karakas and vibhakti depends on the verb and its tense aspect modality ( TAM ) label . The mapping is represented by two structures : default karaka charts and karaka chart transformations . The default karaka chart for a verb or a class of verbs gives the mapping for the TAM label tA_hE called basic . It specifies the vibhakti permitted for the applicable karaka relations for a verb when the verb has the basic TAM label . This basic TAM label roughly corresponds to present indefinite tense and is purely syntactic in nature . For other B. 1 TAM labels there are karaka chart transformation rules . Thus , for a given verb with some TAM label , appropriate karaka chart can be obtained using its basic karaka chart and the transformation rule B.2 depending on its TAM label . 2 In Hindi for instance , the basic TAM label is tA_hE ( which roughly stands for the present indefinite ) . The default karaka chart for three of the B.3 karakas is given in Fig . 2 . This explains the vibhaktis in sentences A.1 to A.2 . In A.1 and A.2 , ' Ram ' is karta and ' Mohan ' is karma , because of their vibhakti markers ¢ and ko , respectively . 3 ( Note that B.4 ' rAma ' is followed by ¢ or empty postposition , and ' mohana ' by ' ko ' postposition . ) A.I rAma mohana ko pltatA hE. 2The transformation rules are a device to represent the karaka charts more compactly . However , as is obvious , they affect the karaka charts and not the parse structure . Therefore , they are different from transformational granmlars . Formally , these rules can be eliminated by having separate karaka charts for each TAM label . But one would miss the liguistic generalization of relating the karaka charts based on TAM labels in a systematic manner . 3In the present examples karta and karma tm'n out to be agent and theme , respectively . Fig . 3 gives some transformation rules for the default mapping for Hindi . It explains the vibhakti in sentences B.1 to B.4 , where Ram is the karta but has different vibhaktis , ¢ , he , ko , se , respectively . In each of the sentences , if we transform the karaka chart of Fig . 2 by the transformation rules of Fig . 3 , we get the desired vibhakti for the karta Ram . In general , the transformations affect not only the vibhakti of karta but also that of other karakas . They also ' delete ' karaka roles at times , that is , the ' deleted ' karaka roles must not occur in the sentence . The Paninian framework is similar to the broad class of case based grammars . What distinguishes the Paninian framework is the use of karaka relations rather than theta roles , and the neat dependence of the karaka vibhakti mapping on TAMs and the transformation rules , in case of Indian languages . The same principle also solves the problem of karaka assignment for complex sentences ( Discussed later in Sec . 3 . ) In summary , this paper makes several contributions : • It shows that the Paninian framework applied to modern Indian languages gives an elegant account of the relation between vibhakti and karaka roles . The mapping is elegant and compact . 8The modified verb in the present sentences is the main verb . • The same basic account also explains activepassives and complex sentences in these languages . This suggest that the solution is not just adhoc but has a deeper underlying unity . • It shows how a constraint based parser can be built using the framework . The constraints problem reduces to bipartite graph matching problem because of the nature of constraints . Efficient solutions are known for these problems . It is interesting to observe that such a parser ( designed for free word order languages ) compares well in asymptotic time complexity with the parser for context free grammars ( CFGs ) which are basically designed for positional languages . A parser for Indian languages based on the Paninian theory is operational as part of a machine translation system . As part of our future work , we plan to apply this framework to other free word order languages ( i.e. , other than the Indian languages ) . This theory can also be attempted on positional languages such as English . What is needed is the concept of generalized vibhakti in which position of a word gets incoporated in vibhakti . Thus , for a pure free word order language , the generalized vibhakti contains preor post-positional markers , whereas for a pure positional language it contains position information of a word ( group ) . Clearly , for most natural languages , generalized vibhakti would contain information pertaining to both markers and position .

Challenge: Although most human languages are order-free, most existing parsers use positional information.
Approach: They propose to apply the Paninian framework originally designed for Sanskrit to parse Indian languages.
Outcome: They show that the Paninian framework can be successfully applied to Indian languages such as Hindi.