Belief Revision Conditionals: Basic Iterated Systems - Research ...

Report 10 Downloads 324 Views
Carnegie Mellon University

Research Showcase @ CMU Department of Philosophy

Dietrich College of Humanities and Social Sciences

1998

Belief Revision Conditionals: Basic Iterated Systems Horacio Arlo-Costa Carnegie Mellon University, [email protected]

Follow this and additional works at: http://repository.cmu.edu/philosophy Part of the Philosophy Commons

This Article is brought to you for free and open access by the Dietrich College of Humanities and Social Sciences at Research Showcase @ CMU. It has been accepted for inclusion in Department of Philosophy by an authorized administrator of Research Showcase @ CMU. For more information, please contact [email protected].

      



  

     ½       

      

 ! 

                                         

        ! "#   

 $%     &  '   ()              (       ' *       (     +                 

 &  

  ,)      -       .           /                     0                                1       

 

     

                 .        2 0                    3                   4 '       .     3     4                                



            3   '"5     4

                

6                          

7     +  !            

     

   

  

                                         

           !       "  #

  "$      %           & '      ' %       '     (  #        %% "      %     "%           "      )         *           "%        

     

,-      



) +

.           

              "                      "     "       %             "" %       /          "   "%  %   0  .  +                 

0*1 2       "     "% 

          0*1  "%     

 

              

3 "      "           "          "        

  "    

            #   

.       2     "   

 "    "%        



2       

         1  +  /   +   .  3+4 1              

 7 $%     '"5                 7 .   2              7 )        8    !   $9         :  +  ;

 7                     

  5   "        " % 

                 "  2 



 "   



 

.   .3



  "       

          

                     

  ?    -     %  ?

    %   2

            2-      =       %          



       

-      "        %    %% ,-      +              +             %     

  %      D              1                      0          "    #

    '  



6 !  '  

 " '   

"                   # "   1   '    " /             B               

A

          '     



      

         "           "         "    



2      %              #

   "               

 %  -                #    "                 #    %  %     "  "                        

   " .    %            "%  ?      '     



    ?   

%    "   % "          #  % I         + I "   %          %    "       #   #    *          "   %             %

      

!    

 "              

    #                       =    

              ?                     ?     "   F

"    

 =  



 %           

  %     %     ?  

 6    =)   C   ?$   3D4      :   $E  (   E (            .                        

 7 ?  1   F  :    F

G3G3F44   F

 :

:   G3F4

G3:4



F

G3F4 G3F4 H



 1 I G3I)4@ I)     I 

G3I4 H G3 4  G3 4           

  



J

    





  

  @    "    ?     ?  

             "     "% "      %          &       "     #  % 4      F



¼

?



   =       & 9 

   

 

 

 

   :  



"    "       " +   



  "           



   







  ? 



 

 

¼







3   "    "   "       2        "     

2  "         

2  "          "   

F





"       & 9







 

:







4   





        

   F

? "              



2   



       

?     "  "      %  

         =     %     % *

 ?    ?          "    ?    ?   

 ?

        "  



   & 9    #  % 4  

   

  :  

 



   



?





 

.

  



@ 

   =   

           .





 

 







     

# $   %  



 

  

 %&         @      &  ¼ @       &   @   5      5&               >          +            2  -  2-  /

 

5 " %               3&

          2   2      2

 2   

2

 25   2   

9K

 







)  %     2



 2  

   %

 .    

> 



  

    

  

            ) %  

        "%  

 2 

 25     2   

    2        2           .    %  

 %   2





> 

  

  % 2 

 

 2

3          "     =           ?  =    

:  2 > ?  2

&

' 

)     =          



         ? ?

 ( 

?        %     



? (



# 

F



 "  ( 

 ?

       #

        ?-   -    

          +  ?? )           "           



                ?     ?   ?   -                            

% 



         "% 2- (



   (    ) (  

.  +   

99

 



            + )      %  "            )   "          

 "   

"     I % 

  $  "            .     "  $     %        "    #

               %              "         



     %   % 

       %   %     #

                                  )     "     #           

&

?2- 











 

  +   "     %      #   "%  %  %     %     %     /          %   

25

  "%    .        %   "  %          )   %  D             5    "          " #

    + )  %  %   2-   "  

    

      *       3  

                 2-  

%        "      ,     #          %     .                     + ?           8A;        "   #     & '                       " 0              

           %    "  

        %                         # %                 "      "$     7                  

 0  

                  

      /       

2

25 >

25

1  "            %    

      84 2         '

 

25 >

25

 3(  G4  2        

     2     6                2  33'

(4  G4 5    B  

   2                   3  B     2  '         2  33'

 3(  G4    

(4  G44L    

Æ               5"   6             5"  ,

   

             2    -   &  '    (   G)   33'

       2    

(4  G4 (           5") 

  5"                 '





 G4                33'  G4 0     2        B           $    5"      

3( (4

   

9A

? $      

25L   

 

25L >

25

     "    (   1                  &    

?9    

?4   

?:  

?

 

255 >

25 



25

25 25 

255



255

.     +      89K; ) +       "    /    



            

            %   

            +       "%  /         "            = &



>

 



            

  & 



 > K

       

(   1     89K;   

          %    &

      >      >    L 9              +  

    

                    $   

     9 I 9  '   #      

     9       4   :

 7 C              

9J



1" 

K

9

9

4 :

4

   

  +               "%   * >

9 : =



1" 

K



   "%



1" 

9

K

:

9

:

9

4 9

4

4

4

   

0  "%      %   





 9 >  4 :



 

 9 % &

1" 

K

: 4

9

9

4

   

.                 0         %                                            *





9



:  /     *  

 %               



       "   

     "      %   % ) +  "%         2                            "   

  *     /  

  '            %  *       "     % %      "    

 7            

  $     

  =  %      0                      

4K

  ,-   

.  " +                  #     " %  D             "      "           "  #        E F -  + "                  %     

       -   %           "    "% ?     ?  F  .%     

O    %       "                                  " %      % 0  %        (   1   "               %      "      6                    #

         +   %     %   "%                    ) + F 

     "     89J;    #   + %   %         

    " "   *        (   1  "  1      ?   "     "       " ""%   "           %   "      ) +     $ =      "    %        "     /%  %       "      84:;     " %    "     89A;     %    %   %                   /  "%    % 0     "  /%      "         "     %         #   *  "          . "    "B      )                       "     

0           0  1    01 F     =                 #

       01             1 #       0 $   %  "                        M           '"5           

       C ; N  %9

49

 $       1        "            1   

   %            "          01      "   .         "    01 "%                 $      

        D    0  1     

     &

01 

  







   

!    +    "% F   84

2  

2    %   &

2    "% 5-

255



25

25

¾

                 " #                 "      " %

5- , +   89C;   8A;      

    /       F            #       %  /      .      ,     %        

  

5- 

 %                  &

?-1 









    



 "              %      

        '"        %   %    

  "     "    



      "     

                    -      &          "%  

4C

  ?-1   %   "     -,  @ 

%   "   "%   /   

                    -      

  %     I        8A;                  -    " "      /  %     #     %           2-     " %     /         -   # %          3          % 

        +      =          /             -

(                          #                  "   

 "                  0  =      "    %         %               -  - "     "          #                 0                            



 "               0  1  #             ,-         +#  B     *  ,- +      /   +   % . %   =    %            "  "  /%  -           

) $*+          "% "%  %     F             - %         %  "  +   %           #            " " %                     : & )                      F   5 >

4A

       -

 ! E !    E  !    %                 ) %       "    "%    %   

)

%





& 

          



%&&' ' &       %  %   ??      

           %   %  )  "   "%      + %   



   &             







             "%      2          .         + %            + "  2

     







   "     2

.   %  %&               F % 



   $   

F      F    

       %          



     



  



> K  

       F    $  

  %    F# "  

)        0   





  

#    



  &  



        

   3              =   /    &

 







  



 

  

        

 &



>

    



  

   

 

4J



   

. &  %



> ?

 



 

        =  %

                  "     0        ,       >



  ?



>

 





&

> ?



    

> 

              &      &   &              &     

0         =

     

  >     )  2 2 >   )  2  2 >       5  >   & 

  

0    %  



 

)        2         

      

   





&



2         

     2      



3        



 

  2-

   2

    

      

      

   5



 2 %        

   





 2

   %

        

      

0        2  



>





 2 >





&





& 

                                   

 

)   %  "%     2       2

  ?  ?  "    . 2       .  "%   



            

   





? 

?



%  !    

 #    

+ )       % 





?

 

.  %       2           %  

  2   #  %  



"  "%

"     2 

 2   



  

 2

?





"% ?-

 





 

 2 ) %  ?

% ??   ! 



  !    

:K

?



   ?





 

 %        2  





 ?  

        



?

 2



?



?



     

 







 ?









 



?



?





  

 2 3 

           #  .         2

      %       2 









 % +    

   

 

      

) %        





. 



2   "    "%   

      +  ??         ?-    %       %    " %   



 





 



 2







2



 2 

  %  /   25 

  















25 "%  =   



25

 2      2   

 2     















 2

25 ) %  



 2   "%     2      

   

 2       %      

> 

0          9   =      "  "%   



          = 

    % &

9 "%    

    9   =  "%  

 0 2  

* =   " +    2P1 >

       

  "% !  9   =  "%  

  &

 

    ?         ?   .      ?    "%        ?    ?   >   "% !          ?         

 

 

0        

 3     2   2   ?       2 I "        

.  %          ? 



   



 ?



"%      ?      

   

4  %   "%       



    

0    +     % 2 >

% !



       /  ?&

  >  2

¾

 

  

 "%     %    %#

2 > ?

:9



  > ?     ? 

  $ - ' 

&  "    3+ 8  $;?4

 : ' O .G   =       $?*E

   3$;;E4

% : ' O .G -        @ = 1 P    G " G ' :> 

   " ! 

  ! 

302 Q ! 02 $;;4 $;%*%; C :  ' O .G  +  !  R0         G 3  4S  5  $;;  : ' O .G (    @       + G5Q.!: =.NC

  " '  (  "  ) '  3 AG' $;;%4

E G (  &+       ) @

? ( G   (    * $%

(  " 

 *  3$;?4 $%%

N A G  (  +   ! 3$;;$4

+ " ,    ! "#  34 G       G 7

; G( G +    &G    .    )  ; $9 ' 8    A !  &0         )

' N; 3$;;?4 $.;

&    " ! 

$$ 5 8

)

38  = $;;4

$ / 1   A T : @ $;;E &(  @   )   $% ! "# 

-    . $

35  ! G  5  $;NN4

$C ! "#  7 =#  5 5  6 + >@ $;N; &    +  @ '     ) 

& *  " &  

34

1   ' 5  5 7.K   $;.$%C $ ' "         @ 6 :  + 7   " !  

'"

3+ 8  $;N94

$E 70 :       +   *C9

(  " 

 3$;;4

$? : F   ' 5 > 0    

! 

   " ! 

 

302 Q ! 02 $;;4 $C?*$;%

$  = $;?? &7B    )

     %C 

C%.C   = $;NN &         +  )

    

?E C;*N$ %  = $;;$

& )$  "  "     G  Q !

G 

.   % "  !0 ,!        '  '"  1 !      3G  Q ! G 

C  = $;;E $;;E4

 8 = $;?E &!          )



 ,     N  ;?.%$

E K 5" ' 2      CE*C?$

(  " 

 3$;N4

+ (   C $99$ * $9$ N 1! +  

 

: ' 5   3G  Q

? G 5  G "  $;;C &G   )

! G  $;;94

& *  " &   34 1   ' 5  5 7.K   $%.$N$ %9 ( 7  $;N? &Q    5'I-/ ) &   2   ; : + $;N; &'       ) 

 * CE

::