Kathy, (01)
The term "possible world", as used by Kripke, means nothing
more nor less than an element of an undefined set W. The
real semantics lies in the accessibility relation R, which
links pairs of elements in W. (02)
For some people who read Leibniz, the term "possible world"
is a colorful metaphor, but for anybody else (including many
philosophers), that term is more confusing than helpful. (03)
> For example, in a recent discussion on whether we could agree
> on a common semantics for various formalisms for combining
> probability and logic, there were some well known and
> highly respected researchers in the room who vociferously
> argued against a possible worlds semantics on the grounds that,
> for example, in a system for doing diagnostic reasoning, the
> statements are not about possible worlds -- they are about
> symptoms and failures and states of systems. We couldn't get
> past that blockage, and so we ended up not coming to agreement
> on common semantics. (04)
That is why I recommend Dunn's semantics, which replaces each
of Kripke's undefined "worlds" with a pair (M,L), where M is a
set of "facts" and L is a subset of M called "laws". Depending
on the audience, you can either emphasize the connection to
Kripke or avoid mentioning him and his "worlds". (05)
> the statements are not about possible worlds -- they are
> about symptoms and failures and states of systems. (06)
That's fine. Just talk about statements that are either "facts"
about observations or "constraints" (i.e., laws or axioms) on
the expected facts. No need to mention worlds. (07)
For a summary of Dunn's semantics and its formal equivalence
with Kripke's version, see (08)
http://www.jfsowa.com/pubs/laws.htm
Laws, Facts, and Contexts (09)
and/or (010)
http://www.jfsowa.com/pubs/worlds.pdf
Worlds, Models, and Descriptions (011)
John (012)
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