Re: Interoperability and Vagueness
On the contrary, the lattice of theories is the simplest
formalization that meets the minimal requirements.
RF> Fair enough, and as I say I am sympathetic to the
> approach as one which recognizes that variable senses
> are central. But as stated such a model for meaning
> appears very complex. Can we not find a system which
> has these properties, without having this complexity?
I am not claiming that the lattice of theories is how
people think, and any model of how they really do what
they do is likely to be vastly more complex.
I also realize that typical programmers who take hold
of such ideas and implement them will probably create
an incredibly complex kludge.
I would cite Ted Codd's original ideas on relational
databases. The simplest way of implementing them is
Datalog (a very simple subset of Prolog), and the
first version of Prolog I used (on an IBM mainframe,
no less) was implemented in a module of 64K bytes
(note K, not M or G). When Codd discovered Prolog,
his comment was "I wish I had invented it."
The reason it sounds complex is that most programmers
who have never learned math (note the word "learned",
not "studied" or "exposed to") tend to panic when they
see anything mathematical. Instead of reading a one
page specification in math, they read a 50-page informal
summary, which they implement in a program whose manual
is the size of the Manhattan telephone book. See the
latest versions of SQL, for example.
For a summary of the math and logic that is needed,
see my 36-page summary on the web:
Section 7 is on lattices, 8 on propositional logic,
9 on predicate logic, and 10 on axioms and proofs.
Each section is about 3 pages long. After you get
your axioms, you bundle them in theories, put the
theories in the lattice, and voila! That's it.
An awful lot more can be and has been said about these
things because their implications are enormous. But
the ideas are about as simple as you can get -- and
much, much simpler than you would get if you turned
a typical mathematically innocent programmer loose
on the subject -- e.g. SQL, RDF, OWL, etc., etc.
I realize that a lot of mathematically sophisticated
people have worked on SQL and the SemWeb, but they
were not leading the parade, they were at the back
with the shovels behind the horses.