From: mailbox@dmitry-kazakov.de   
      
   On 19 Jan 2004 18:16:02 -0800, wsiler@aol.com (William Siler) wrote:   
      
   >Dmitry A. Kazakov  wrote in message    
   ews:...   
   >> On 16 Jan 2004 08:59:54 -0800, wsiler@aol.com (William Siler) wrote:   
   >>   
   >> >Dmitry A. Kazakov  wrote in message   
   news:...   
   >> >> >So I have two questions. What does Dmitry mean by "contradictory"? And   
   >> >> >can he give an example of a contradictory proposition where Nec(X) >   
   >> >> >Pos(X)?   
   >> >>   
   >> >> Let X be "my first name is Dmitry"   
   >> >>   
   >> >> Then to answer / evaluate / estimate X as Pos(X)=0, Nec(X)=1 is   
   >> >> contradictory. It would mean neither X nor not X is possible, provided   
   >> >> that not X = "my first name is not Dmitry" includes all possible names   
   >> >> except Dmitry and no name too.   
   >> >   
   >> >In our system, it is impossible to have Nec(X) = 1 and Pos(X) = 0; the   
   >> >system will not permit it. If one attempted to read in this Nec-Pos   
   >> >pair, the system would give an error message. It can never be computed   
   >> >from valid data.   
   >>   
   >> Yes, but you never know whether data are valid when received from   
   >> human experts. Then as with grades of [un]certainty, we could work   
   >> with ones of contradiction.   
   >   
   >So far, you have defined a contradiction as Nec(X) = 1 and Pos(X) = 0,   
   >or (I suppose) more generally Nec(X) > Pos(X). As I have said, our   
   >system would give an error message, and would not permit a   
   >contradiction of thie kind.   
   >   
   >However, aside from that situation, it would be possible to input   
   >invalid data in the sense of incorrect, through typographical error or   
   >whatever. This is a common problem in inputting typed-in data, and   
   >there are many ways of checking, such as range checks on numeric data   
   >and so on. We could also input contradictory data as "X = 3" and X =   
   >4"; this could be an error, or could be valid (although contradictory)   
   >data from two different sources. I think errors of this kind would be   
   >application-dependent, and must be discovered during the reasoning   
   >process.   
   >   
   >In the real world, we encounter ambiguities and contradictions all the   
   >time; the question is, how do we handle them?   
      
   Humans handle them in the same way as uncertainty. We let them   
   propagate up to the utimate point where an unambiguous decision has to   
   be made. I believe that ambuguity and contradiction are two sides of   
   one coin. When we force amguitiy or contradiction to certainty too   
   early, we make a logical error. This is also typical for the human way   
   of reasoning.   
      
   --   
   Regards,   
   Dmitry A. Kazakov   
   www.dmitry-kazakov.de   
      
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