[Scl] Re: Logic, Topic Maps, and RDF

[John F. Sowa]

Jon,

JS> An individual is simply an entity that cannot be used to
 > relate other entities.  If you write r(x,y) where r is not
 > a relation, there is no syntax error.  You have simply made
 > a false statement.

JA> Honestly, this worries me a lot.

I'm not worried at all.  When Pat and Chris proposed it,
I admit that I was worried at first.  But I got over it.

JS> When you say "r(x, y)" is a false statement,
 > this is to say that r is false of <x, y>.

JA> Do you mean to say that "app(r, <x, y>)" is false?
 > That seems like another way of saying "syntax error".
 > And it requires a rather heavy type-checking regime.

No.  It says that there is no type checking whatever.
If you implement the CL logic, it means, in effect, that
any tests are done at "run time" instead of "compile time".

I will certainly admit that for a theorem prover,
a typeless language, such as unconstrained CL, may take
more time.  There are many examples that show how a
sorted or typed language can speed up certain kinds of
theormm proving.  That is one reason (among many) why I
recommend that people use the usual typed version of CGs
for most applications.  I would not recommend unconstrained
CGs except for statements that are imported from other
unconstrained languages.

 > Then again, as became evident the last time that you
 > said this stuff about S/CL, you still maintain the
 > distinction between connectives and predicates,
 > which is a distinction with no pragmatic difference,
 > and generates a host of further confusions among
 > the communicants of GOL.

In conceptual graphs, as in Peirce's existential graphs,
the only privileged connectives are conjunction and
the ability to enclose any collection of graphs in an
enclosure (boxes in CGs and ovals in EGs).  There are
no other distinctions between relations that apply to
entities of type Proposition and relations that apply
to entities of any other type.  And I believe that
there are very strong pragmatic reasons (especially
for mapping to and from natural languages) for making
conjunction and context enclosure privileged.

That is for CGs.  CL has a different approach, which
I can map to CG notation.

John