Order-independence and Underspecification

In standard Montague Semantics we find a very close correspondence between syntactic and semantic rules (the ‘Rule-to-Rule Hypothesis’). This is attractive from a processing point of view, as we like to think of syntactic and semantic processing as being done in tandem, with information flowing in both directions, from parsing to interpretation and vice versa. The parsing procedure erects the necessary scaffolding for interpretation, while semantics (and via semantics context and world knowledge) ideally rules out wrong parses at an early stage. Montague Semantics, however, also favours a strictly bottom up semantic processing architecture. The principle of Compositionality, which says that the meaning of a mother node is to be computed from the meanings of her daughters, seems to enforce such a bottom up procedure. Since we know that parsing algorithms that make use of top down predictions are often much more efficient than those that do not, and since we do not therefore expect human syntactic processing to be strictly bottom up, there is a dilemma. On the one hand, we want interpretation to be order-independent: it should not be decided a priori whether we assign meanings in a top-down, a bottomup, or any other fashion. On the other hand, the building block picture of meaning that the principle of Compositionality has to offer is attractive too, if it were only because it explains why language users seem to be able to construct unlimited numbers of meanings from the finite set they find in the lexicon.