From: mailbox@dmitry-kazakov.de   
      
   On 16 Jan 2004 08:59:54 -0800, wsiler@aol.com (William Siler) wrote:   
      
   >Dmitry A. Kazakov  wrote in message    
   ews:...   
   >> >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.   
      
   >> >> >Necessity is the extent to which the evidence supports a proposition;   
   >> >> >Possibility is the extent to which the evidence fails to refute a   
   >> >> >proposition.   
   >> >>   
   >> >> Right. If we consider a reverse proposition, then necessity and   
   >> >> possibility will swap each other.   
   >> >   
   >> >What is a reverse proposition? Does Dmitry mean that if A is a   
   >> >proposition, NOT A is a reverse proposition?   
   >>   
   >> Yes.   
   >   
   >In this case, Nec and Pos do not swap. Instead, we have   
   >   
   >Nec(NOT A) = NOT(Pos(A))   
   >Pos(NOT A) = NOT(Nec(A))   
      
   Yes, this is what I meant. The possibility of A becomes the [inversed]   
   necessity of not A.   
      
   --   
   Regards,   
   Dmitry A. Kazakov   
   www.dmitry-kazakov.de   
      
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