[Top] [All Lists]

Re: [ontolog-forum] what is a proposition?

To: lisadawncolvin@xxxxxxxxx
Cc: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
Date: Sun, 03 Jun 2007 17:10:51 -0400
Message-id: <46632E5B.6060206@xxxxxxxxxxx>
Lisa,    (01)

I wanted to comment on the relationship between possible worlds
and databases (or knowledge bases):    (02)

 > It looks like the OMG model is using the possible world model view.
 > In that view, some believe that propositions are assertions
 > (concept and predicate) which have a truth value with respect to
 > a possible world - which is basically a model with various attributes.
 > The existence of possible worlds is a big area of debate with
 > philosophers because of what can be entailed from this model    (03)

The main debate is about claims that possible worlds are ontologically
similar to the world we live in.  I find that claim hard to swallow,
but I'm happy with using the term 'possible world' as a metaphor that
refers to a model, i.e., a collection of data in tables (for an RDB),
in networks (for an OODB), or the kinds of models used for CL or IKL.    (04)

 > It appears that OMG is taking this model theoretic approach in order
 > to address change over time.  By using a possible worlds model, one
 > can explicitly state that an assertion is true with respect to many
 > variables, one being time.    (05)

To make the discussion more concrete, I'll use RDB terminology, but
exactly the same points can be stated about an OODB:    (06)

  1. Each "possible world" or "model" can be represented by the data
     stored in the tables of an RDB.  The DB constraints represent
     laws that must be true of the data.    (07)

  2. Given a particular state of the RDB, anything provable from the
     constraints is assumed to be necessarily true, anything consistent
     with the constraints is possible, and anything stored in the tables
     or derived from the tables by means of an SQL query is contingently
     true.    (08)

  3. Kripke's accessibility relation between possible worlds defines
     permissible DB updates:  If an update to a DB state w1 leads
     to a new state w2 that is consistent the constraints (or laws),
     then that update is permissible.  The new state w2 is said to be
     "accessible" from the old state w1.    (09)

  4. Various axioms for modal logics (called by names such as S5, S4,
     etc.) determine how and whether the DB constraints are allowed
     to change from one state of the DB to another.    (010)

  5. The S5 axioms impose very strong limitations:  the database
     constraints are fixed and frozen, although the data can change.
     The accessibility relation is an equivalence relation that
     allows any series of updates to be retracted to return to the
     original state.    (011)

  6. The S4 axioms are more flexible because they allow constraints
     to be added, but the old constraints must remain.  That makes
     the accessibility relation transitive, but not an equivalence.    (012)

With this interpretation, the term 'possible world' is just a metaphor
for 'the current state of the data in the DB plus the DB constraints'.
It can be applied to an RDB, an OODB, or many kinds of knowledge bases.    (013)

This interpretation can answer your questions:    (014)

 > Since data can change rapidly, does this mean that there is a separate
 > model for each point in time?    (015)

It implies that there must exist a way of accessing (or reconstructing)
a version of the DB for each point in time (but constant data need not
be duplicated for each point in time).  Each such version represents
a model of a "possible world" at that point in time.    (016)

 > Is this supposed to be used in real applications?    (017)

This interpretation is consistent with many DB applications that have
been implemented and used for the past 30 years or so.    (018)

The explanation I gave above is consistent with the semantics for modal
logic stated by the logician Saul Kripke.  However, the terminology is
closer to the equivalent formulation by Michael Dunn.  For a summary of
Dunn's version with a discussion of how it is related to Kripke's, see
Sections 1 and 2 of the following paper:    (019)

    Laws, Facts, and Contexts    (020)

John Sowa    (021)

Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/  
Subscribe/Config: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/  
Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx
Shared Files: http://ontolog.cim3.net/file/
Community Wiki: http://ontolog.cim3.net/wiki/ 
To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx    (022)

<Prev in Thread] Current Thread [Next in Thread>