Hierarchical Translation Equivalence over Word Alignments

We present a theory of word alignments in machine translation (MT) that equips every word alignment with a hierarchical representation with exact semantics defined over the translation equivalence relations known as hierarchical phrase pairs. The hierarchical representation consists of a set of synchronous trees (called Hierarchical Alignment Trees – HATs), each specifying a bilingual compositional build up for a given word aligned, translation equivalent sentence pair. Every HAT consists of a single tree with nodes decorated with local transducers that conservatively generalize the asymmetric bilingual trees of Inversion Transduction Grammar (ITG). The HAT representation is proven semantically equivalent to the word alignment it represents, and minimal (among the semantically equivalent alternatives) because it densely represents the subsumption order between pairs of (hierarchical) phrase pairs. We present an algorithm that interprets every word alignment as a semantically equivalent set of HATs, and contribute an empirical study concerning the exact coverage of subclasses of HATs that are semantically equivalent to subclasses of manual and automatic word alignments.