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