TAILIEUCHUNG - Báo cáo khoa học: "Mathematical Aspects of Command Relations"

In GB, the importance of phrase-structure rules has dwindled in favour of nearness conditions. Today, nearness conditions play a major role in defining the correct linguistic representations. They are expressed in terms of special binary relations on trees called command relations. Yet, while the formal theory of phrase-structure grammars is quite advanced, no formal investigation into the properties of command relations has been done. We will try to close this gap. In particular, we will study the intrinsic properties of command relations as relations on trees as well as the possibility to reduce nearness conditions expressed by command. | Mathematical Aspects of Command Relations Marcus Kracht II. Mathematisches Institut Arnimallee 3 D - 1000 Berlin 33 GERMANY email Abstract In GB the importance of phrase-structure rules has dwindled in favour of nearness conditions. Today nearness conditions play a major role in defining the correct linguistic representations. They are expressed in terms of special binary relations on trees called command relations. Yet while the formal theory of phrase-structure grammars is quite advanced no formal investigation into the properties of command relations has been done. We will try to close this gap. In particular we will study the intrinsic properties of command relations as relations on trees as well as the possibility to reduce nearness conditions expressed by command relations to phrase-structure rules. 1 Introduction Historic Origin Early transformational grammar consisted of a rather complex generative component and an equally complex and equally imperspicuous transformational component. But since the aim always has been to understand languages rather than describing them there has been a need for a reduction of these rule systems into preferably few and simple principles. The analysis of transformations as series of movements - an analysis made possible by the introduction of empty categories - was one step. This indeed drastically simplified the transformational component. A second step consisted in simplifying the generative component by reducing the rules in favour of well-formedness conditions so-called filters. While this turned transformational grammar into a real theory now known as GB the relationship of GB with other syntactic formalisms such as GPSG LFG categorial grammar etc. became less and less clear. This in addition to Noam Chomsky s often repeated scepticism with respect to formalizations has led to the common attitude that GB is simply gibberish unformalizable or hopelessly untractable at best. However since it is

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