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    ELECTRONIC NEWSLETTER ON  REASONING ABOUT ACTIONS AND CHANGE        
Issue 98031             Editor: Erik Sandewall             29.3.1998
Back issues available at http://www.ida.liu.se/ext/etai/actions/njl/
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                    *********  TODAY  *********

Today: Ray Reiter and John McCarthy join the debate about the ontology 
of time.


                   *********  DEBATES  *********

            ---  ONTOLOGIES FOR ACTIONS AND CHANGE  ---

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|  FROM: Ray Reiter
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During all the years that the debate has raged about time points vs intervals,
we devotees of the sitcalc have never seen it as an issue. Here's why I think
this is so.

In the sitcalc, a fluent (LightOn) has a truth value only with respect to
a situation (= sequence of action occurrences). So, we might have

   LightOn(do(switchOn,do(switchOff,S0))), 
and 
   ~LightOn(do(switchOff,do(switchOn,S0))). 

In the sitcalc with explicit time,
the first might become 

   LightOn(do(switchOn(3.14),do(switchOff(1.41),S0))), 

meaning that as a result of the action history consisting of first
switching off the light at time 1.41, then switching on the light at time 3.14,
the light will be on. Notice that there is no way of expressing the claim that
the light is, or is not on at time 3.14 (or 3.5), independently of the 
situation leading up to this time. On
the other hand, time based formalisms do allow one to write LightOn(3.14), 
without expicitly referencing, in their notation, the history leading up
to the time 3.14 at which the fluent's truth value is to be determined.
This seems to be the source of all the problems about open vs closed vs 
semi-open intervals and predicate truth values over these, and also why these
seem to be non-issues for the sitcalc. 

Now, one could rightly object to the above account because it provides only for
fluent truth values at discrete time points, namely at the action occurrence
times. So we are tempted to understand 

   LightOn(do(switchOn(3.14),do(switchOff(1.41),S0))) 

to mean that the light is on at time 3.14, but it tells us nothing about time 
3.5 say. This is particularly bad for (functional) fluents that vary 

continuously with time, for example, the location of a falling object. To 
handle this, introduce a time argument for fluents, in addition to their 
situation argument. For the light, one can write:

   LightOnT(t,s) <=> LightOn(s) & t >= start(s).

Here, start is defined by
   start(do(a,s)) = time(a),
where time(a) is the time at which the action a occurs in the history do(a,s).

An instance of this would be

   LightOnT(t,do(switchOn(3.14),do(switchOff(1.41),S0))) <=> t >= 3.14

Here we have committed to the light being on at exactly the time
of the switchOn action, and forever thereafter, relative to the history  
do(switchOn(3.14),do(switchOff(1.41),S0)). In other words, provided
switchOff(1.41) and switchOn(3.14) are the ONLY actions to have
occurred, then the light will come on at time 3.14, and remain on forever.
Notice especially that we would have BOTH

   LightOnT(3.14,do(switchOn(3.14),do(switchOff(1.41),S0))) 
and
   ~LightOnT(3.14,do(switchOff(1.41),S0))

without contradiction. This seems to be precisely the point at which purely
time-based formalisms run into difficulties, and the sitcalc version
of this problem illustrates the role that explicit situation arguments 
play in resolving these difficulties.

Now, we can axiomatize falling objects:

   positionT(t,s) = position(s) + velocity(s) * (t - start(s)) 
                 + .5 * g * (t - start(s))^2 

--------------------------------------------------------
|  FROM: John McCarthy
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When my car accelerates, there is a time point at which it passes 65
miles per hour.  It is awkward to describe this point in a language
not providing for time points.


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