Re: Proposed definition of "possible world"
Martin,
There were several motivations for my proposed definition.
One was theoretical elegance, and another was support for
practical database and knowledge base design and use.
I am glad that you approve of the general approach.
Following a few comments on your comments:
>Thus, I am not quite sure why what John proposes is seen as necessarily
>modal, nor "meta-level reasoning". To me (with the additions I proposed in
>an earlier note) it is just a refinement of the black box view of an
>information system, which recognizes that we can specify a system, clone it
>to create a second system, and have each live a life of its own. Each
>system will accept different axioms over time consistent with the common
>ones they started with. Similarly, a published general ontology can be
>viewed as a set of axioms, to which further consistent axioms can be added
>to produce a more specialised ontology.
The modal aspect comes from the parallels between the
philosophical talk about accessibility between possible worlds
and the database talk about updates from one database to
another. The two have the same formal structure: a collection
of databases that can be derived from one another by updates
that are consistent with certain policies constitute what the
logicians call a Kripke model. Most logicians aren't familiar
with DB theory, and most database practitioners don't know
the work in models for modality. But there are many people,
such Chris Menzel and I, who work with both and adapt logical
theory as a way of giving a formal basis for DB practice.
The reason for calling it a metalevel approach is that any
language that talks about the axioms and their truth value
is at the metalevel of Tarski's hierarchy of languages.
A conventional RDB with the SQL query subset is a first-order
object language. The parts of SQL that enable a DB adminstrator
to assert and modify constraints is a metalevel language with
respect to the SQL query language.
Any talk about what policies DB administrators must observe
in working with constraints is at the metalevel with respect
to the constraints and at the metametalevel with respect to
the query language.
Similar theoretical issues arise in consideration of AI
knowledge bases as well.
John