Grail Tutorial - Extensions to NL

The advantage of the non-associative Lambek calculus over other Lambek calculi is that it permits the analysis of sentences for a given grammar in polynomial time. A disadvantage is that there is no satisfactory analysis for many linguistic phenomena in NL. In part, this is due to the fact that NL grammars can generate only context-free languages, but even compared to the associative Lambek calculus L, which generates only context-free languages as well

In order to extend the generative capacity of NL and to better analyse linguistic phenomena which are problematic for NL, Grail allows grammars to use a number of extensions to NL. These extensions, taken together are called multimodal categorial grammars, or sometimes the multimodal Lambek calculus.

Modes

The basic extension is the use of different modes of composition. Grail displays modes in the central circles of the connections between nodes in the lexical graphs. The only change this will make to the base NL parser is that the contractions now have the additional requirement that the both main and the auxiliary connection need to have the same mode.

Structural Rules

A second extension is the addition of structural rules. Structural rules allow us to rewrite trees of main constructors. For example, the structural rule of associativity allows us to rebracket the binary branching tree of connections any way we like. Adding this structural rule to NL gives us the associative Lambek calculus L.

However, when we combine structural rules with modes we can get more subtle effects. Instead of structural rules applying globally, we can specify lexically when a structural rule can apply, simply by the choice of modes we use in the lexicon. The example grammar hitchhiker.pl illustrates some possibilities of the combination of an associative mode a and a non-associative mode 0.

Unary Branches

A final extension is the addition of unary branches to our lexical graphs. Unary branches can serve both for encoding linguistic features and for giving access to structural rules.

What's Next

Learn about modes first, or see them directly in combination with structural rules. You can also learn about the unary branches. Finally, when you have familiarized yourself with all of the extensions, you can learn how they work together in a multimodal grammar.
Richard.Moot@labri.fr
Last modified: Sat Feb 21 18:02:38 CET 2009