Semantics of Spatio-Directional Geometric Terms of I ndian Languages (2021)

Abstract: This paper examines widely prevalent yet little-studied expressions in Indian languages which are known as geometrical terms be-cause “they engage locations along the axes of the reference object”. These terms are andara (inside), b ̄ahara (outside), ̄age (in front of), s ̄amane (in front of), p ̄ıche (back), ̄upara (above/over), n ̄ıce (under/below), d ̄ayem. (right), b ̄ayem. (left), p ̄asa (near), d ̄ura (away/far) in Hindi. The way these terms have been interpreted by the scholars of the Hindi language and handled in the Hindi Dependency treebank is misleading. This paper proposes an alternative analysis of these terms focusing on their triple – nominal, modifier and relational - functions and presents abstract semantic representations of these terms following the proposed analysis. The semantic representation will be explicit, unambiguous abstract and therefore universal in nature. The correspondence of these terms in Bangla and Kannada are also identified. Disambiguation of geometric terms will facilitate parsing and machine translation especially from Indian Language to English because these geometric terms of Indian languages are variedly translated in English de-pending on context.

## introduction geometric terms that "engage locations along the axes of the reference object" @xcite play multiple roles -relational, nominal, modifier -in indian languages and their equivalents in english can vary based on their functional role. for example, the geometric term nīce in (1-a) and (1-b) is translated differently into english depending on the function of the word in the given two contexts: ## geometric terms in hindi, bangla and kannada geometric terms under considerations are andara (inside), bāhara (outside), āge (in front of), sāmane (in front of), pīche (back), ūpara (above/over), nīce (under/below), dāyem . (right), bāyem . (left), pāsa (near), dūra (away/far) in hindi. there are some more geometric terms which are used in hindi such as āra-pāra (across), ora (towards) which are purely relational markers and hence we keep them out of scope of this paper. table-1 presents equivalent lexical terms in hindi, bangla, kannada and english for the relational variant of these terms and their morpholexical properties. most of the english terms apart from 'right', 'left', 'inside' and 'outside' are spatial prepositions which are indeclinable. table-2 gives a quick comparative study of these lexical items in hindi, bangla and kannada. the gloss for each example given in table-2 is given in appendix-1. fortis and fagard following levinson et al. have shown that relational nouns (spatial nominals) in japanese and korean follow a structure [ground-gen spatial nominal-postp] which, we see, is quite similar to indian languages. ## semantic interpretation of geometric terms @xcite has introduced figure-ground geometric sense 6 "to refer to the located vs locating entity". figure is "the object which is considered as moving or located with respect to another object" and ground is "the object with respect to which a first is considered as moving or located" @xcite in the context of spatial configuration. ground is alternatively referred to as a reference object. in indian grammatical tradition, the relation is described between ādhāra (ground) and ādheya @xcite . two kinds of relations between ādhāra and ādheya have been identified in the literature which is very much relevant for our interpretation of geometric terms. this analysis also explains data recorded by talmy in a different light that fits to our multirole analysis of these terms. the two relations are sam . yoga-sambandha (contact by touch) and sāmīpya-sambandha (contact by proximity) @xcite . when there is a temporary physical contact (sam . yoga) between the ādhāra and the ādheya then the spatial relationship is said to have a sam . yoga-sambandha. ## abstract semantic representation of expressions with geometric terms keeping in tune with our analysis given in section 3, we will present here an abstract semantic representation of the geometric terms. before we present our representation, we will examine how these terms have been represented in the hindi dependency treebank. in hindi grammar, these geometric terms have been considered as part of complex post-positions @xcite @xcite . in hindi dependency treebank, however, they are lexically marked as noun-space-time (nst) thus distinguishing them from other post-positions which are tagged as psp foot_6 @xcite . the tag nst indicates that these lexical items are nouns denoting space and time, but their role in the context is not that of a noun. the semantic relation that has been annotated for the sentence "lad . akā ghara ke bāhara khad . ā hai." where 'bāhara' is an nst as shown in figure in dependency tree structures the content words are represented as nodes, the verb is the head of the tree (in case of simple sentences) and relational markers are all semantic labels on the edges connecting the nodes as shown in figure -1. the convention of hindi dependency treebank is that the syntactico-semantic relations are marked among the chunks. each chunk has a head and the relation is to be understood between the heads of the chunk. the meaning of this structure is that 'ke bāhara' (which is annotated as psp nst at the pos level) is a relational marker and conveys 'deśādhikaran . a' (locative) information. this analysis implies 'ghara' (house) the location where the boy stands. this is a misleading analysis because the boy does not stand at the house rather he stands in a place which is outside the house. 'bāhara' conveys that information but the analysis in the treebank does not explicitly capture that. according to our interpretation of geometric terms, the representation of relational and nominal/modificational variants are postulated differently. the semantic label spatial on indicates that ped . a is a reference object for the action 'sitting' whose kartā is paks . ī (bird). the labels for geometric terms are given in table-3. semantic classes in terms of positive and negative values for features are also specified. the nominal/modificational variant of geometric terms are represented in the form of constructions. constructions in construction grammar @xcite are linguistic patterns in which some aspect of its form or its meaning cannot be predicted from its component parts. in indian grammatical tradition, it is called vr . tti. vr . tti is defined as 'parārthābhidhānam vr . ttih . ' -an aggregated wordform that gives a sense which is different from the literal sense of its constituents @xcite . in our construction, geometric terms entail a space which is not lexically expressed but whose geometric relation to the reference object is conveyed by the geometric terms. the linguistic patterns can be represented as a template and the template is assigned a meaning. for example, the following template defines the form-meaning pair for the nominal/modificational usage of the geometric terms: the subscripts define the meaning and x, ke term and y are variables for physical expressions in 1. for the sentence (5), the template-1 can be instantiated as follows: in the above sentences, 'big trees' are the figure / ādheya and the space denoted by the geometric terms sāmane / pāsa / pīche is the ground / ādhāra. in sentences ( 20 ) ghara is a reference point with respect to which 'ādhā' has to be interpreted. in (19), the reference point is not explicitly mentioned, and it is from the context the reference point has to be determined. for the above sentences the final part of the template [ke/vālā] [y]loc is null, and therefore they represent nominal variants. for ( 21 ) and ( 22 ) below, the construction is used as a modifier and the full template is instantiated as shown below: (21) ghara ref-obj ke sāmane spatial/directional-ground / cārom . ora spatial/directional-ground / pīche spatial/directional-ground ke bagīce loc mem . bad . e bad . e ped . a fig haim . (22) ghara ref-obj ke sāmane spatial/directional-ground / cārom . ora spatial/directional-ground / pīche spatial/directional-ground vāle bagīce loc mem . bad . e bad . e ped . a fig haim . ## developing a corpus search cum annotation interface for geometric terms from the above discussion, it has become clear that the semantics of geometric terms are quite chequered. we have done a corpus study to understand how these terms are translated into english. we present here example sentences for 4 geometric terms in table -4 . from table-4, we find that nīce has been translated into as many as 5 different words while sāmane into 4 different words. there is also one case of idiom and one phrasal verb attested in the data. we get the adjectival form of bāhara as bāharī. in order to be able to disambiguate the geometric terms so that we get appropriate translations into hindi bangla kannada semantic class semantic label andara bhitare ol . age (r foot_8 ) loc: interior; con +, (n/m foot_9 ) loc: interior; con -spatial inside bāhara bāhira, bāire horage (r) loc: exterior; con -(n/m) loc: exterior; con -spatial outside āge āge mu ṁde (r) loc: anterior; dir + directional ahead sāmane sāmane eduru (r) loc: anterior; dir + directional front facing pīche pichane hi ṁde (r) loc: posterior; dir + directional behind ūpara opara, opore, upare mēle (r) loc: superior; dir +; con + (n/m) loc: superior; dir +; con -directional on nīce nīce kel . age (r) loc: interior; dir +; con + (n/m) loc: interior; dir +; con -directional under dāyem . dāine balakke (r) loc: right side; dir +; con + (n/m) loc: right side; dir +; con -directional left bāyem . bāmye edakke (r) loc: left side; dir +; con + (n/m) loc: left side; dir +; con -directional right cārom . ora cāradik, cāridike suttalu (r) loc: circumferential; con + (n/m) loc: circumferential; con -directional around bīca mājhakhāne madhya (r) loc: medial; con + (n/m) loc: medial; con -spatial between pāsa pāśe, kāche hattira (r) approx spatial proximity: +; con + (n/m) approx spatial proximity: +; con -spatial near dūra dūre dūra (r) approx spatial proximity: -; con + (n/m) approx spatial proximity: -; con -spatial far english, we need to understand the context of occurrence of these terms more thoroughly. one way of doing this is to study their usage in corpora, both monolingual and indian language-english bilingual corpora. to facilitate this study we propose to design an interface for intelligent search of these terms in different contexts. for that purpose, we create a database of existing annotated monolingual corpora as well as a database of parallel corpora. for monolingual corpora, we use pos tags, actual lexical items and syntactic relations as ques for searching the database. when we set out to do that, we find that the geometric terms irrespective of their functional status are annotated as nst in the existing corpora @xcite . in order to make the search more meaningful, we have integrated an annotation facility to the search interface for annotating the geometric term for relation markers, nouns and modifiers. this will help in future to search these terms for their different functions. ## conclusion the paper has examined the spatio-directional geometric terms and their semantics in a great detail mainly for hindi and also for bangla and kannada. we have observed that even though these geometric terms have some morpho-syntactic differences in these three languages they are very much in alignment in terms of interpretations. this paper is the beginning of an in-depth study of geometric terms of indian languages. there remains much work to be done in laying out systematically the subtler differences among apparently close terms such as āge, sāmane; bāhara, sāmane and so on. for example, we can almost interchangeably say the following two sentences: it appears that the semantics of reference objects are playing a role in licensing the geometric terms. this paper draws the conclusion that in indian languages (at least for those under consideration), spatio-directional geometric terms play three roles: relational, nominal and modificational. we have proposed to design an interface for annotating geometric terms for their different interpretations. the information can be useful for natural language understanding, natural language generation and knowledge rich machine translation.