Exploring a genotype based formalisation for tree adjoining grammar derivations

Abstract

Tree Adjoining Grammars (TAGs) are very useful psycholinguistic formalisms for syntax and dependency analysis of phrase structures. Since natural languages are finitely ambiguous, TAGs are ideal to model them being mildly context sensitive. But these grammars are very hard to parse as they have a worst case complexity of $$O(n^6)$$ . In reality most conventional TAG parsing algorithms run in $$O(n^3)$$ and give the most probable parse, but trying to extract multiple ambiguous parses for a given phrase degrades the performance of the traditional TAG parsing algorithms toward worst case runtime, especially for longer sentences. Ambiguity in TAGs are not as well understood as in CFGs due to their complex derivation process; hence one of the ways to understand it is to find a finite set of ambiguous derivations for the given phrase structure. In this article we extend the definition of the containing formalism introduced as GATAGs on which a genetic algorithm can be deployed in order to find ambiguous derivation structures for longer sentences. We shall formalise the genotypes, phenotypes and the fitness functions for the entailing genetic algorithm, exploring various avenues for their efficient computations. Our main objective here is to explore the possibility of random derivations evolving to good derivations though a natural selection.