Polarized Unification Grammars

Proceedings of the 21st International Conference on Computational Linguistics and 44th Annual Meeting of the ACL, pages 137–144, Sydney, July 2006. c⃝2006 Association for Computational Linguistics Polarized Unification Grammars Sylvain Kahane Modyco, Université Paris 10 sk@ccr.jussieu.fr Abstract This paper proposes a generic mathemati- cal formalism for the combination of various structures: strings, trees, dags, graphs and products of them. The polari- zation of the objects of the elementary structures controls the saturation of the final structure. This formalism is both elementary and powerful enough to strongly simulate many grammar formal- isms, such as rewriting systems, depend- ency grammars, TAG, HPSG and LFG. 1 Introduction Our aim is to propose a generic formalism as simple as possible but powerful enough to write real grammars for natural language and to handle complex linguistic structures. The formalism we propose can strongly simulate most rule-based formalisms used in linguistics.1 Language utterances are both strongly struc- tured and compositional and the structure of a complex utterance can be obtained by combining elementary structures associated to the elemen- tary units of language.2 The most simple way to 1 A formalism A strongly simulates a formalism B if A has a better strong generative capacity than B, that is, if A can generate the languages generated by B with the same struc- tures associated to the utterances of these languages. 2 Whether a natural language utterance contains one or several structures depends on our point of view. On the one hand it is clear that a sentence can receive various structures according to the semantic, syntactic, morphological or phonological point of view. On the other hand these differ- ent structures are not independent from each other and even if they are not structures on the same objects (for instance the semantic units do not correspond one to one to the syn- tactic units, that is the words) there are links between the different objects of these structures. In other words, consid- ering separately the different simple structures of the sen- tence does not take into account the whole structure of the sentence, because we lost the interrelation between struc- tures of different levels. combine two structures A and B is unification, that is, to build a new structure C by partially superimposing A and B and identifying a part of the objects of A with those of B. This idea recalls an old idea, used by Jespersen (1924), Tesnière (1934) or Ajduckiewicz (1935): the sentence is like a molecule whose words are atoms, each word bearing a valence (a linguistic term explic- itly borrowed from chemistry) that forces or al- lows it to meet some other words. Nevertheless, unification grammars cannot directly take into account the fact that some linguistic units are unsaturated in a sense that they must absolutely combine with other structures to form a stable unit. Saturation is ensured by additional mecha- nisms, such as the distinction of terminal and non-terminal symbols in rewriting systems or by requiring some features to have an empty …

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