Re: Proposed definition of "possible world"
Frank McCabe wrote
>Sorry to jump in with both feet here... but I cant see the
>meta-levelness in:
>> Definition: A possible world W is a pair (L,D) consisting of a set
>> of first-order propositions L and a set of ground-level assertions D.
This is not a definition of a metalanguage, but it is a
definition of an entity W, which contains two pairs of
linguistic entities inside.
If you implement this definition "under the covers", you get
something that will support a version of modal logic. That is
why Chris Menzel has been claiming that Kripke's semantics and
Dunn's semantics are indistinguishable at the object level.
At that level, Chris and I are in complete agreement. But my
primary reason for recommending that definition is to provide
the hooks for a system that also includes a metalanguage for
getting access to the laws and facts.
The SQL query language, for example, does not support any
metalevel constructs. But the overall SQL system does support
a way of asserting DB constraints. That facility is the
metalevel.
In my previous note, I did not propose a specific metalanguage,
but I mentioned several, including Tarski's hierarchy of
metalevels, which I did not spell out in detail in that note.
That hierarchy, which I do discuss in more detail in Ch 5 of
my KR book, is something that could be supported by facilities
that are currently available in the KIF and conceptual graphs
languages, provided that the appropriate predicates are defined
for the naming component, reflection component, and any other
kinds of components you might want -- for example, a security
component, an authorization component, a commenting component.
That would be a separate proposal, which I think we should
also consider. At the moment, I just proposed one definition
and gave some informal arguments in support of it.
>Sorry, if this seems impertitent or off the mark
No, it's a good comment. I admit that my informal discussion
went far beyond the definition in the opening. The two
issues, possible worlds and levels of metalanguage, are
distinct. I would like to use them together, but they can
and should be proposed as separate issues.
John Sowa