A study of tree adjoining grammars
Constrained grammatical system have been the object of study in computational linguistics over the last few years, both with respect to their linguistic adequacy and their computational properties. A Tree Adjoining Grammar (TAG) is a tree rewriting system whose linguistic relevance has been extensively studied. A key property of these systems is that a TAG factors recursion from the co-occurrence restrictions.^ In this thesis, we study some mathematical properties of TAG's. We show that TAG's have several interesting properties and are a natural generalization of Context Free Grammars. We show the equivalence of the classes of languages generated by TAG's with those generated by Head Grammars and a linear version of Indexed Grammars, which have been studied for their linguistic applicability. We define the embedded pushdown automaton, an extention of the pushdown automaton, and prove that they are equivalent to TAG's. We show that the class of Tree Adjoining Languages form a substitution closed abstract family of languages, and that each Tree Adjoining Language is a semilinear language. We show that a TAG can be parsed in polynomial time by adapting the Cocke-Kasami-Younger algorithm for CFL's.^ Feature structures, essentially a set of attribute value pairs, have been used in computational linguistics to make statements of equality to capture some linguistic phenomena such as subcategorization and agreement. We embed TAG's in a feature structure based framework. We show that the resulting system has several advantages over TAG's. We give a mathematical model of this system based on the logical calculus developed by Rounds, Kasper, and Manaster-Ramer. Finally, we propose a restriction of this system and show how parsing of such a system can be done efficiently. ^
Vijayashanker, K, "A study of tree adjoining grammars" (1987). Dissertations available from ProQuest. AAI8804974.