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Re: [ontolog-forum] intangibles (was RE: Why most classifications are fu

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: sowa@xxxxxxxxxxx
Date: Tue, 26 Jul 2011 09:34:12 -0400 (EDT)
Message-id: <84857d0612ebdd0c781c6c3d99eb09ea.squirrel@xxxxxxxxxxxxxxxxxxxx>

Dear Matthew,

> I'm still left with the same question: how do you distinguish between
> worlds
> where the only difference is the facts and not the laws.

In any semantics for modal logic (Kripke's or Dunn's), there is no requirement for worlds to be the same, similar, or different.  In fact, there are different choices of axioms for the worlds.  In axiom system S5, for example, all worlds have the same laws.  The only difference between them is in the facts.

One useful application of modal logic is to describe possible updates in database systems.  To be specific, let's assume that we have a collection of relational databases:

 1. Each DB is considered a possible world w.

 2. The laws of w are the constraints on permissible updates.

 3. The facts of w consist of all the tuples stored in the tables of the DB plus any inferences derivable from the data and the DB constraints.

 4. DB w2 is accessible from DB w1 iff there exists some permissible sequence of updates to w1 that makes it identical to w2.

Note that if all databases have exactly the same laws (constraints), every DB is accessible from any other DB -- because it would be possible to delete every tuple from w1 and assert all the tuples in w2 while observing the same constraints that are used by both.


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