SUO: Re: Link Grammar and Parser - RRGs
Rich,
That is not an empirical question, but a preference that many
people choose in order to make their theories more convenient:
> Could languages be organized into a lattice, instead of
> a directed acyclic graph? If we believe ontologies are
> organized in lattice form, perhaps there is something in
> the human mind that makes lattices, rather than DAGs,
> the most convenient way to compartmentalize mental life.
Given any DAG, it is possible to derive a lattice by inserting
extra nodes to ensure that every pair of nodes has a unique
infimum (maximal common lower bound) and supremum (minimal
common upper bound).
The reason why a lattice is convenient is that those extra
nodes ensure that many useful operations are well defined.
But since you can always derive a lattice from a DAG, there
is no empirical evidence that can "prove" that one or the
other is more "natural" for the way that people think or use
language or concepts.
There are, however, empirical issues connected with the
question: given any DAG derived from a lexicon of terms
or concepts that people have been observed to use, how many
additional "unlabeled" nodes must be added to convert the
DAG into a lattice? If the number of unlabeled nodes is
very large, one could claim that the lattice is not "natural".
But that claim could be countered by asking (1) Was the new
lattice the minimal one that could be found for that DAG?
and (2) Does the absence of names for those extra nodes prove
that people don't use unlabeled nodes in their mental processes?
John Sowa