From: mailbox@dmitry-kazakov.de   
      
   On 15 Jan 2004 08:15:20 -0800, wsiler@aol.com (William Siler) wrote:   
      
   >I am having trouble with a few terms that Dmitry uses, "contradictory"   
   >and "reverse proposition".   
   >   
   >Dmitry A. Kazakov  wrote in message    
   ews:...   
   >> >> [*] Even if Nec(X)=1, that alone does not warranty that X is true. It   
   does   
   >> >> only if X is not contradictory.   
   >   
   >I assume that X is a proposition. Here is a compound proposition that   
   >I would consider to be self-contradictory:   
   >   
   >"My first name is Bill AND my first name is Dmitry."   
   >   
   >But surely that proposition is false, with both Nec(X) and Pos(X)   
   >being zero So Nec(X) <= Pos(X). It is obvious that Nec(X) = 0. The   
   >only problem is that discovering that Pos(X) = 0 requires parsing the   
   >proposition to discover that the two clauses are contradictory.   
   >   
   >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 the process of resolving contradictions we sometimes encounter the   
   >situation where a calculated posibility is less than the previous   
   >necessity. In that case, we imeediately reduce the new necessity to   
   >the lower new possibility, since "Nec(X) <= Pos(X)" requires this.   
      
   It is OK, if you a-priory know that all data are non-contradictory in   
   the sense "Nec(X) <= Pos(X)". Then if the set of rules has only &, V,   
   not, it is impossible to run into a contradiction at any stage. The   
   problem is that in some cases cannot assume the data being   
   non-contradictory. Then I would keep all contradictions until   
   defuzzification.   
      
   >> >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.   
      
   --   
   Regards,   
   Dmitry A. Kazakov   
   www.dmitry-kazakov.de   
      
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