  This paper compares a qualitative reasoning model of translation with a
quantitative statistical model. We consider these models within the context of
two hypothetical speech translation systems, starting with a logic-based design
and pointing out which of its characteristics are best preserved or eliminated
in moving to the second, quantitative design. The quantitative language and
translation models are based on relations between lexical heads of phrases.
Statistical parameters for structural dependency, lexical transfer, and linear
order are used to select a set of implicit relations between words in a source
utterance, a corresponding set of relations between target language words, and
the most likely translation of the original utterance.
