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Re: [ontolog-forum] Conjunction and Disjunction

To: Rich Cooper <rich@xxxxxxxxxxxxxxxxxxxxxx>
Cc: "'[ontolog-forum] '" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Ed Barkmeyer <edbark@xxxxxxxx>
Date: Fri, 10 Jul 2009 14:53:01 -0400
Message-id: <4A578E0D.7010503@xxxxxxxx>
Rich,    (01)

I see that I wasn't clear in my attempt to communicate.    (02)

I wrote:
>  Consider a 
> security system with two sensors, one of which notices whether there is 
> a person in a restricted area, and the other notices whether there is an 
> authorized personnel badge in the same restricted area.
> I want the security rule to read:
>    IF person detected AND NOT badge detected, THEN Sound Alarm.
> By comparison:
>    IF person detected OR NOT badge detected, THEN Sound Alarm
> will probably produce continuous cacophony. ;-)
> So, yes, there is absolutely a very strong reason to choose AND over OR 
> in interpreting the sensor input.    (03)

That is:
If the sensory system interprets the entry of a person with no badge 
into the restricted area as  "person-detected OR no-badge-detected",
the first security rule above will not fire, the alarm will not sound!
The alarm will only sound if the sensory system interprets the two 
inputs as AND.  So it is very important that the system interpret the 
pair of sensed states as an AND.    (04)

AND is a stronger condition than OR. x AND y implies x OR y, but not 
vice versa.  So, while the OR is not an erroneous interpretation of the 
two sensor inputs, it is a *weaker* interpretation -- it loses 
information!  That is the reason for choosing AND over OR when x AND y 
holds.    (05)

In the example, if you modify the rule so that the weaker condition -- 
the system interprets that situation as an OR -- sounds the alarm, the 
weaker condition will also produce false alarms.    (06)

> P.S. With apologies to Rich, this strikes me as an excellent candidate 
> for Hatlo's Inferno. (for those of you old enough to remember) ;-)    (07)

Rich wrote:
> I don't recall Hatlo's Inferno Ed; that was before my time.  I'm only 64.
> You must be one of the "greatest generation"!    (08)

Although I am your senior by perhaps two years, I think the real 
difference is the side of the pond on which one spent one's childhood. 
Hatlo's Inferno was a feature of newspaper comics of the late 1950s, but 
surely only in the U.S.    (09)

> But do you think the alarm should only ring if the burglar comes in both the
> living room and the kitchen window (AND) at the same time?  Think again lad!    (010)

Of course not, but that is two different sensors from the ones in the 
example, and the simulataneous condition is not what I am trying to 
detect.  In that case,
   IF kitchen-entry-detected OR living-room-entry-detected, THEN sound 
alarm.    (011)

is the rule that is desired.  The weaker condition is sufficient to 
sound the alarm.  And if the sensory system actually interprets the 
simultaneous entry condition as "kitchen-entry-detected AND 
living-room-entry-detected", no harm done, because that condition (with 
appropriate circuitry) IMPLIES "kitchen-entry-detected OR 
living-room-entry-detected" and sounds the alarm!    (012)

And that, my lad, is what results from thinking again. ;-)
(It is also what results from being old enough to have built/repaired 
systems like that with wires and relays instead of chips.)    (013)

-Ed    (014)

Edward J. Barkmeyer                        Email: edbark@xxxxxxxx
National Institute of Standards & Technology
Manufacturing Systems Integration Division
100 Bureau Drive, Stop 8263                Tel: +1 301-975-3528
Gaithersburg, MD 20899-8263                FAX: +1 301-975-4694    (015)

"The opinions expressed above do not reflect consensus of NIST,
  and have not been reviewed by any Government authority."    (016)

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