Towards Meaningful Information Processing

8/13/2019 Towards Meaningful Information Processing

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!"#$% !' (")*$ + !,-%./ 0' 1")2"%3

4$5")6% 7."#8#9/:; 0#/$).irces three classifications of sign, consisti#9 $/ 3KI LMI "#6 NN

.;.


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.'&/011 &'#0$*07 )..'&)/, ()5 @0 #$*0'01*#$2 %'&( ) 10(#&*#/ .0'1.0/*#B0 )1

?044C 8$7007+ @5 &%%0'#$2 )$ #$%&'()*#&$)4 )$)451#1 *& &-' (&704 ?0 )'0 )@40 *&

1,&? #*1 .&*0$*#)4 %&' ) '0.'010$*)*#&$ &% *,'00 *5.01 &% '04)*#&$+ /&$1#1*#$2 &% OP

(meaningful), 28 (syntactic), and 66 (semantic) classes, which are analogous

to Peirces three classifications of sign.

M,0 .&11#@#4#*5 &% ) .'&/011 (&704 &% ,-()$ #$*0'.'0*)*#&$ ()5 0$)@40 )

.)')7#2()*#/ /,)$20 #$ ,-()$computer interfacing. As Peirces sign theory is

100$ @5 ()$5 )1 ) *,0&'5 &% *,0 E$&?)@40 ;*,0 *5.01 &% 7#1*#$/*#&$1 *,)* /)$ @0

1#2$#%#07 @5 1#2$1>+ &-' (&704 ()5 %)/#4#*)*0 *,0 #$*'&7-/*#&$ &% ) $&B04 )..'&)/,

#$ E$&?40720 '0.'010$*)*#&$+ $)*-')4 4)$2-)20 (&704#$2+ )$7 .'&@40(

specification. The possibility of a common representation for Peirces different

/4)11#%#/)*#&$1 ()5 &.0$ $0? .0'1.0/*#B01 #$ 1#2$ *,0&'0*#/)4 '010)'/, )1 ?044

;D0#11 Q H-'E1+ ORST>+ ;G)'#)1 Q U-0#'&V+ WPPX>+ ;H-'/,+ WPOO>+ ;3)$70'1+ ORYP>C

M,0 (&704 1-2201*07 #$ *,#1 .).0'+ )$7 *,0 '04)*#&$ @0*?00$ *,0 -107

representation and Peirces sign aspects has been introduced earlier in (3)'@&+

G)'E)1+ Q B)$ H'00(0$+ WPOO>+ )(&$21* &*,0'1C M,0 2&)4 &% *,#1 .).0' #1 *& 1,&?

*,)* &-' (&704 #1 )@40 *& '0.'010$* *,0 (&'0 /&(.40: /&$/0.*1 &% 60#'/0)$ 1#2$

*,0&'5 )1 ?044C

8$ .)1* '010)'/,+ ?0 0:.0'#(0$*)445 *01*07 *,)* &-' *,0&'5 #1 #$ 4#$0 ?#*,

,-()$ #$*0'.'0*)*#&$C M& *,#1 0$7 ?0 70B04&.07 (&7041 &% #$%&'()*#&$

.'&/011#$2 #$ 7#%%0'0$* E$&?40720 7&()#$1+ 1-/, )1 *,0 7&()#$ &% $)*-')4

language, naive logic, and naive reasoning. The test results showed that

/&$/0.*1 20$0')*07 @5 *,010 (&7041 ()5 @0 (0)$#$2%-4 %'&( ) ,-()$

.0'1.0/*#B0+ )1 ?044C

I-' *,0&'5 #1 '0(&*045 '04)*07 *& 3#*-)*#&$ 9)4/-4-1 ;Z/9)'*,5 Q [)501+

OR\R>C 8$ &-' (&704+ 1#*-)*#&$1 )'0 '0.'010$*07 @5 .0'/0.*1 ;/%C 10*1 &% .0'/0#B07

A-)4#*#01>+ %4-0$*1 @5 040(0$*1 &% ) .0'/0.*+ )/*#&$1 @5 '04)*#&$1 @0*?00$

A-)4#*#01 ;/%C @#$7#$21>C G&'(-4)0 -107 #$ )/*#&$ .'0/&$7#*#&$1 )'0 '01*'#/*07 *&

H&&40)$ 0:.'011#&$1C


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Note that meaningful information (]#*)$5#+ WPP\) and meaningful

information processing are not the same. The first is related to Shannon

#$%&'()*#&$W )$7 ) 7#1*#$/*#&$ @0*?00$ -10%-4 '02-4)'#*5 )$7 '07-$7)$/5

;=7'#))$1+ WPPR>+ *,0 10/&$7 *& #$%&'()*#&$ )1 1*#(-4-1 )$7 #$*0'.'0*)*#&$ @5 *,0

(#$7C Z)5@0 *,0 $024#20$/0 &% *,#1 7#%%0'0$/0 0:.4)#$1 *& 1&(0 0:*0$* *,0 @4#$7

1.&* ?,#/, #$%&'()*#&$ 1/#0$*#1*1 ,)B0 ,)7 #$ *,0#' )..'&)/, *& *,0 #(.&'*)$/0

&% 0(@077#$2 #$%&'()*#&$ .'&/011#$2 #$ ) *,0&'5 &% 1#2$1C 9-'#&-145+ #$

#$%&'()*#&$ *,0&'5 *,0 *0'( (0)$#$2%-4 ()5 '0%0' *& ) %&'()4 .'&.0'*5+ @-* )41&

*& ) .'&.0'*5 &% ;,-()$> .'&/011#$2C =$ 0:)(.40 &% *,0 10/&$7 #1 *,0 M-'#$2

M01*+ ?,#/, )11-(01 *,0 0:#1*0$/0 &% )$ &@10'B0'+ /).)@40 &% ;'0>/&2$#V#$2

#$*044#20$* ,0$/0 (0)$#$2%-4 /&((-$#/)*#&$C K&*)@45 *,0 1)(0 /&$/0.* #1

involved in Shannons concept of information as event probability, as well.

D,0'0)1 *,0 /&$/0.* &% .'&@)@#4#*5 #1 -1-)445 %&'()445 70%#$07+ $&* 1& *,0

/&$/0.* &% )$ 0B0$* ?,#/, #1 '04)*07 *& /&$/0.*-)4#V)*#&$ ;,&? /)$ ?0 E$&? *,)*

an event has occurred) hence to meaningfulness from an interpreters

.0'1.0/*#B0C =1 E$&?40720 ()5 )'#10 %'&( ;(0)$#$2%-4> #$*0'.'0*)*#&$ *,'&-2,

20$0')4#V)*#&$+ 4#(#*)*#&$1 /)-107 @5 ) 4)/E &% 10(#&*#/ 0(@077#$2 ()5

/,)')/*0'#V0 *')7#*#&$)4+ %&'()4 E$&?40720 '0.'010$*)*#&$ *&&C

M,0 1*'-/*-'0 &% *,#1 .).0' #1 *,0 %&44&?#$2C 8$ 30/*C W+ ?0 #$*'&7-/0 )

(&704 &% #$%&'()*#&$ .'&/011#$2 &$ *,0 @)1#1 &% )$ )$)451#1 &% )/*#&$'0)/*#&$

phenomena. This is followed by an analysis of our model, from a syntactic, and

a semantic point of view, in Sect.XTC 8$ 30/*C \ ?0 04)@&')*0 &$ *,0 '04)*#&$

between our model and Peirces different classifications of sign. We close th 0

.).0' ?#*, ) 1-(()'5C

2Following (Adriaans et al., 2010), Shannon information can be used to find an optimal

compression for a sequence of messages. The related concept, Kolmogorov complexity can be

used to define an optimal probability distribution for a binary string: the universal distribution.

Kolmogorov complexity and Shannon information seem to be dual notions: the shortest code for a

binary string in the sense of Kolmogorov complexity is its optimal code in the sense of Shannon

information using the universal distribution.


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L A?=8$#)."?=8$# CD.#$C

3The theory of this section is based on (Sarbo et al., 2011).


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189:). 3@ = (&$)7#/ ;)>+ 75)7#/ ;@>+ )$7 *'#)7#/ ;/> /&$/0.* &% )/*#&$'0)/*#&$

.,0$&(0$)C = 7)1,07 4#$0 #1 -107 *& 0:.'011 ) 70.0$70$/5 @0*?00$ 0B0$*1C =

.)#' &% $&701 *,)* /)$ @0 (0'207 #$*& ) 1#$240 $&70 #1 #$7#/)*07 @5 ) 7&**07

/#'/40C

8% ?0 )'0 #$*0'01*07 #$ *,0 ?)5 #$ ?,#/, '0)/*#&$1 )'#10 %'&( )/*#&$1+ ?0

()5 #$*'&7-/0 *,0 ,5.&*,01#1 *,)*+ #$ 0B0'57)5 .,0$&(0$)+ )/*#&$ )$7 '0)/*#&$

)'0 '04)*07 *& 0)/, &*,0' )//&'7#$2 *& ) '04)*#&$ &% 70.0$70$/5C =11-(#$2+ %&'

*,0 (&(0$*+ /)-1)4 70.0$70$/5+ *,0 '01-4* #1 ) )+()#* /&$/0.* &% )/*#&$

'0)/*#&$ .,0$&(0$)C 300 G#2C O;@>C

D0 ()5 %-'*,0' '0%#$0 &-' (&704 @5 )11-(#$2 *,)* '0)/*#&$1 )'#10 %'&(

)/*#&$1 *,'&-2, )$ )/* &% #$*0'.'0*)*#&$C 8$7007+ 0B0$ )* *,0 .,51#/)4 40B04+ *,0

)@#4#*5 &% &@L0/*1 *& 1,&? 7#%%0'0$* '0)/*#&$1 *& 7#%%0'0$* )/*#&$1 ()5 @0 100$ )1

*,0#' .&*0$*#)4 %&' #'!,-.-,!#'/actions by (re)cognizing them and generating a

'0)/*#&$C `-1* )1+ #$ .'#$/#.40+ .,51#/)4 &@L0/*1 #$B&4B07 #$ )/*#&$'0)/*#&$

.,0$&(0$) (-1* @0 #$70.0$70$* ;&*,0'?#10 *,0#' /&a&//-''0$/0 /)$$&* )..0)'

)1 ) .,0$&(0$&$>+ #$*0'.'0*)*#&$ )11-(01 *,0 0:#1*0$/0 &% E$&?40720 )@&-*

*,&10 &@L0/*1 )$7 *,0 .&11#@40 /&$10A-0$/0 &% *,0#' /&a&//-''0$/0C G&' 0:)(.40+

#$ &-' '-$$#$2 0:)(.40+ *,0 $)#4 ()5 @0 1)#7 *& #$*0'.'0* *,0 )..0)'#$2 %&'/0+ @5

(re)cognizing its measure and generating a counter force, as well as a

7#)(0*')4 .#0'/#$2 (&B0(0$*C 8$ 1-(+ *,'&-2, *,0 #$*'&7-/*#&$ &% *,0 /&$/0.* &%

#$*0'.'0*)*#&$ #$ &-' !-#()#*(&704+ *,0 '04)*#&$ @0*?00$ )/*#&$ )$7 '0)/*#&$ /)$

@0 1.4#* #$*& *?& '04)*#&$1" &$0 @0*?00$ )/*#&$ )$7 /&''01.&$7#$2 E$&?40720

;'0/&2$#*#&$> )$7 )$&*,0' @0*?00$ *,)* E$&?40720 )$7 ) /&''01.&$7#$2 '0)/*#&$

;20$0')*#&$>+ 100 G#2C O;/>C

D#*, *,0 )11-(.*#&$ &% )$ #$B&4B07 70.0$70$/5 @0*?00$ )/*#&$ )$7

'0)/*#&$+ *,0 /&$/0.* &% 70B04&.(0$* /&(01 #$*& 1#2,*C


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L'3 O#$5;.69. =D)$:9D 8#=.)#"; C)$?.%%8#9

In Newtons world, action and reaction are unambiguously related to each other.

I@L0/*1 &//-''#$2 #$ *,0 K0?*&$#)$ ?&'47 1#(.45 7& $&* ,)B0 *,0 .&*0$*#)4 &%

changing their reaction strategy. The knowledge in the node interpretation in

G#2C O;/> '0()#$1 *,0 1)(0C D,)* ,)..0$1 #% ?0 0:*0$7 &-' %&/-1 )$7 #$/4-70 #$

&-' (&704 &@L0/*1 *,)* 7& ,)B0 *,0 .&*0$*#)4 *& )/A-#'0 E$&?40720F

Obviously, Newtons 3rd law holds for such entitie1 )1 ?044C [&?0B0'+ *,0

.&*0$*#)4 *& 20$0')*0 (&'0 /&(.40: '0)/*#&$1 0$)@401 *,0 #$*'&7-/*#&$ &% (&'0

'0%#$07 (&7041 &% )/*#&$'0)/*#&$ .,0$&(0$)C M,'&-2, (0(&'#V)*#&$+ *,0

#$*0'.'0*#$2 151*0( &@*)#$1 #$%&'()*#&$ )@&-* &//-''#$2 )/*#&$'0)/*#&$ 0B0$*1

*,)* ()5 .'&B0 -10%-4 #$ 4)*0' #$*0')/*#&$1C 8% *,0 #$*0'.'0*#$2 151*0( ,)1 *,0

.&*0$*#)4 *& &@10'B0 #*104% )$7 *& (0(&'#V0 #*1 &@10'B)*#&$1+S #* ?#44 @0 )@40 *&

7#1*#$2-#1, #$%&'()*#&$ )@&-* 0:*0'$)4 )/*#&$1 %'&( *,0 .&11#@40 /&$10A-0$/01

*,&10 )/*#&$1 /)$ @'#$2 )@&-* *& *,0 #$*0'.'0*#$2 151*0(C M,0 4)**0' E#$7 &%

information may be called the systems knowledge about itself. Through

)@1*')/*#&$ )$7 20$0')4#V)*#&$+ *,0 #$*0'.'0*#$2 151*0( ()5 #$*'&7-/0 /&$/0.*1

*,)* /)$ %)B&')@45 @0 -107 *& .'07#/* *,0 /&$10A-0$/01 *,)* )..0)'#$2 0:*0'$)4

A-)4#*#01 ()5 ,)B0C M,#1 .&*0$*#)4 &% *,0 #$*0'.'0*#$2 151*0( *& .'07#/* %-*-'0

0B0$*1 )11-(01 )$ )@#4#*5 *& /&.0 ?#*, (&7)4#*#01 &*,0' *,)$ *,0 (0/,)$#/)4

&$0+ 1-/, )1 ?)B0a*5.0 A-)4#*#01+ %&' #$1*)$/0+ *,0 &@10'B)*#&$ &% 4#2,* ')51 #$

B#1-)4 )/*#&$'0)/*#&$ .,0$&(0$)" #% ?0 100 *,0 A-)4#*#01 &% ) ,)((0' (&B#$2 #$

&-' 7#'0/*#&$+ ?0 ()5 1*0. )?)5+ &' 1,&-*+ #$ &'70' *& .'0B0$* /0'*)#$

-$%&'*-$)*0 (0/,)$#/)4 0%%0/*1C

L'L 45$


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20$0')*#&$ &% '0)/*#&$1+ ?0 (-1* 1?#*/, .0'1.0/*#B0 )$7 )$)45V0 )/*#&$'0)/*#&$

.,0$&(0$) %'&( *,0 1*)$/0 &% *,0 #$*0'.'0*#$2 151*0( #*104% ; #'!,-'(123#,4>C

G&44&?#$2 *,#1 1*)$/0+ ?0 1-2201* *,)* *,0 #$*0'.'0*#$2 151*0( &//-''#$2 #$ 1&(0

$!(!, #1 #$ #$*0')/*#&$ ?#*, *,0 0:*0'$)4 %&'/0 ;A-)4#*5>CT M,#1 0:*0'$)4 %&'/0

)..0)'1 )1 )$ ,55,*! #$ *,0 #$*0'.'0*#$2 151*0(C M,0 A-)4#*#01 &% *,#1 1*)*0 )$7

0%%0/* ?#44 @0 /)4407 *,0 #$.-* 1*)*0 )$7 0%%0/* A-)4#*#01 &'+ @'#0%45+ #$.-* A-)4#*#01C

M,0 '04)*#&$ @0*?00$ !"#$ 1*)*0 )$7 0%%0/* #1 *,0 2'&-$7 %&' *,0 '0)/*#&$

20$0')*07 @5 *,0 &@10'B0'C

189:). L@ 8$%&'()*#&$)4 '04)*#&$ -$70'45#$2 #$*0'.'0*)*#&$ ;)>+ ()*/,#$2 (&70

&.0')*#&$ ;@>+ )$7 )$)451#1 (&70 &.0')*#&$ ;/>C = /&$*#$-&-1 4#$0 #1 -107 *&

represent a flow of emerging information, not just a dependency. K stands %&'

the observers knowledge

M,0 )%&'0(0$*#&$07 #$*0')/*#&$ #1 1*&'07 @5 *,0 #$*0'.'0*#$2 151*0( #$ )

/&440/*#&$ &% ;-$)$)45V07> #$.-*+ 1*)*0+ 0%%0/*)$7 ;#$*0''04)*07> 1*)*00%%0/*

qualities. These storing events, which come down to est)@4#1,#$2 '04)*#&$1+ )'0

)44 *'#220'07 @5 *,0 0:*0'$)4 %&'/0 ;)/*#&$>C 8$*0'.'0*)*#&$ /)$ @0 1-//011%-4 &$45

#% *,010 0B0$*1 /&$1#1*0$*45 %(!*" (0(&'#V07 #$%&'()*#&$C M,#1 #$%&'()*#&$)4

'04)*#&$ -$70'45#$2 *,0 20$0')*#&$ &% '0)/*#&$1 #1 70.#/*07 #$ G#2C W;)>C =

schematic model of the corresponding %(!*"#'/ mode operation of

5External-view representation is possible also in this case. By considering the external force to bea representation of a phenomenon, the observer may be able to derive hypotheses about the

qualities of that phenomenon.


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#$%&'()*#&$ .'&/011#$2 #1 70.#/*07 #$ G#2C W;@>C For example, the state can be

defined by the mass and the velocity of the nail and the hammer, the effect by

*,0 /,)$20 #$ *,0#' B04&/#*#01C

Note that all storing events included in Fig. W;@> )'0 #$*0'$)4C M,05 )'0

'04)*07 *& *,0 &//-''#$2 )/*#&$ )$7 '0)/*#&$+ ?,#/, )'0 0:*0'$)4C M,0 4)**0'

'04)*#&$1 )'0 0:.'01107 @5 (0)$1 &% 7)1,07 4#$01+ /&$$0/*#$2 *,0 $&701 )/*#&$

)$7 '0)/*#&$ B#) *,0 $&701 #$.-*+ 1*)*0+ 0%%0/* )$7 1*)*0a0%%0/* '04)*#&$+

'0%#$#$2 &-' (&704 #$ *,0 $&70 #$*0'.'0*)*#&$+ #$ G#2C O;/>C

D0 )11-(0 *,)*+ *,'&-2, 20$0')4#V)*#&$+ .0'/0#B07 7)*) &@*)#$07 #$ .)1*

0:.0'#0$/01 ()5 @0 *')$1%&'(07 #$*& E$&?40720C 8$ *,0 /)10 &% #$70*0'(#$)*0

#$.-* A-)4#*#01 *,0 20$0')*#&$ &% ) 1*)*00%%0/* '04)*#&$ ()5 '0A-#'0 )$ ('(1+$#$

&% )44 .&11#@40 ()*/,01+ 0C2C+ #$ ) /5/4#/ %)1,#&$+\ )1 ?044 )1 *,0 1040/*#&$ &% )

1&4-*#&$+ &$ *,0 @)1#1 &% 1&(0 1*')*025C =1 .)'* &% *,#1 )$)451#1+ 7#%%0'0$*

#$*0'.'0*)*#&$1 &% *,0 #$.-* 1*)*0 ;/%C 1*)*0> )$7 0%%0/* ;/%C 0%%0/*> )1 ?044 )1

*,0#' '04)*#&$ ;/%C 1*)*0a0%%0/*> /)$ @0 20$0')*07 #$*0'$)445 @5 (0)$1 &% *,0

systems knowledge about corresponding state and effect qualities.

G&44&?#$2 *,0 )@&B0 /&$1#70')*#&$1+ ) (&704 &% )/*#&$'0)/*#&$

.,0$&(0$) /)$ @0 70'#B07 )1 %&44&?1C H5 /&$1#70'#$2 *,0 #$.-* 1*)*0 )$7 0%%0/*

qualities to be external (cf. effect), in relation to the systems knowledge which is

#$*0'$)4 ;/%C 1*)*0>+ *,0 #$*0')/*#&$ @0*?00$ *,0 1*)*0 )$7 0%%0/* A-)4#*#01 &$ *,0

one hand, and the systems knowledge on the other can be modeled by two

instances of a matching mode process. As the observers knowledge is shared

@5 *,&10 .'&/011 #$1*)$/01+ #* /)$ @0 '0.'010$*07 @5 ) 1#$240 $&70 ; b>C 8$

G#2C W;/> *,0 *?& 1-@a.'&/01101 ;'0.'010$*07 @5 ) .)#' &% 1*'-/*-'01 /&$1#1*#$2 &%

%&-' $&701> )'0 ()'E07 @5 *,0 4)@041 $!(!, )$7 ,55,*!C K&*0 *,)* *,0 )@&B0

internal refinement of our model (in the nodes state and effect, #$ G#2C W;@>>

7&01 $&* )%%0/* *,0 70.0$70$/5 @0*?00$ )/*#&$ )$7 '0)/*#&$ ;/%C 7)1,07

6We return to this point in Sect. 5.4.


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4#$01>CY8$ G#2C W;/>+ *,0 $&701 @0*?00$ )/*#&$)$7 '0)/*#&$'0.'010$* *,0 $#$0

*5.01 &% '04)*#&$ #$B&4B07 #$ )/*#&$'0)/*#&$ .,0$&(0$)C

H5 *,0 #$*'&7-/*#&$ &% )$)451#1 )$7 1040/*#&$ #$ *,0 #$*0'.'0*)*#&$ .'&/011+

*,0 .&11#@#4#*5 &% )$*#/#.)*&'5 '01.&$101 )$7 ,)@#* %&'()*#&$ )'0 )7707 *& *,0

(0/,)$#1*#/ K0?*&$#)$ (&704C

P 0#/$)

WC=/*-)4 '04)*#&$)4 .'&.0'*#01 &% A-)4#*#01 #$B&4B07 #$ )$ &@10'B07 /,)$20 ;#$

&'70' *& @0 )@40 *& #$*0'.'0* /&a&//-''#$2 1*)*0 )$7 0%%0/* A-)4#*#01 )1

constituents of) '04)*#&$>

XC 6'&.0'*#01 &% '04)*#&$1 #$B&4B07 #$ )$ &@10'B07 .,0$&(0$&$ ;#$ &'70' *& @0

)@40 *& #$*0'.'0* *,0 #$.-* )1 ) '04)*#&$ @0*?00$ ) .0'/0#B07 1*)*0 )$7

0%%0/*>C

G&' #$1*)$/0+ *,)* ) $)#4 )$7 ) ,)((0' ,)B0 E#$0*#/ .'&.0'*#01+ ?,#/, )'0 )

.&*0$*#)4 %&' ) '04)*#&$ ;O>+ *,)* ) $)#4 /)$ @0 #$ '04)*#&$ ?#*, ) ,)((0' @5

'01#1*#$2 #*1 0%%0/*+ )$7 ) ,)((0' /)$ @0 #$ '04)*#&$ ?#*, ) $)#4 @5 )%%0/*#$2 #*1

1*)*0 ;W>+ )$7 *,)* ) $)#4 )$7 ) ,)((0' ,)B#$2 /0'*)#$ E#$0*#/ .'&.0'*#01+ ()5

01*)@4#1, ) '04)*#&$ @0*?00$ ) 7#)(0*')4 %&'/0 )$7 /&-$*0' %&'/0 ;X>C

7In Fig. 2(c), dashed lines connect the nodes actionand reactionwith the nodes stateand

effectcomprised by the two sub-processes, respectively. The labels of the latter two nodes are

omitted in the diagram.


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[&? /)$ ?0 E$&? )@&-* *,0 *,'00 *5.01 &% #$%&'()*#&$F M,0 K0?*&$#)$

?&'47 /)$ @0 70%#$07 @5 ) 10* &% )/*#&$'0)/*#&$ .,0$&(0$)+ ?,#/, #(.4#01 *,)*

&'1+)/*#&$a'0)/*#&$ .,0$&(0$) /)$ @0 &@10'B07 ,0$/0+ %'&( )$ #$%&'()*#&$)4

1*)$/0+ &$45 '04)*#&$1 ;X> /)$ @0 0:.0'#0$/07C =/*-)4 '04)*#&$)4 .'&.0'*#01 ;W>

(-1* @0 70'#B07 %'&( .0'/0#B07 '04)*#&$1 ;X>+ )$7 .&*0$*#)4 .'&.0'*#01 ;O> %'&(

*,&10 )/*-)4 '04)*#&$)4 .'&.0'*#01 ;W>C M,0 &*,0' ?)5 '&-$7+ .&*0$*#)4 .'&.0'*#01

;O> (-1* -$70'45 )/*-)4 '04)*#&$)4 .'&.0'*#01 ;W>+ )$7 *,&10 *,0 .'&.0'*#01 &%

.0'/0#B07 '04)*#&$1 ;X>C G&' #$1*)$/0+ %'&( *,0 0:.0'#0$/0 &% ) '0)/*#&$ ;X>+ ?0

()5 70'#B0 *,0 0:#1*0$/0 &% ) '04)*#&$ @0*?00$ ) 1*)*0 )$7 0%%0/* ;W>+ )$7 %'&(

*,)* '04)*#&$+ ) /&a&//-''0$/0 &% /0'*)#$ E#$0*#/ A-)4#*#01 ;O>C

8$%&'()*#&$ )@&-* A-)4#*#01 ()5 0$)@40 )$ #$*0'.'0*)*#&$ &% /&a&//-''#$2

A-)4#*#01 )1 ) '04)*#&$+ #$B&4B07 #$ *,0 &@10'B07 .,0$&(0$&$C =$ 0:)(.40 #1 )

/&aoccurrence of a nail and a hammer, interpreted as nailadriving. Note that

#$*0'.'0*)*#&$ '0A-#'01 E$&?40720 )@&-* .&11#@40 /&a&//-''0$/01 &% A-)4#*#01

*,)* /)$ @0 0:.0'#0$/07 )1 ) .,0$&(0$&$+ ,0$/0 )'0 (0)$#$2%-4C

M,0 2')$-4)'#*5 &% #$%&'()*#&$ ()5 70.0$7 &$ *,0 '01&4-*#&$ @5 *,0

#$*0'.'0*#$2 151*0(C 8$ *,#1 .).0' ?0 )11-(0 %#$#*0 '01&4-*#&$ )$7 *,0 0:#1*0$/0

&% ) ()..#$2 &% A-)4#*#01+ ?,#/, )'0 ) /&$*#$--(+ *& 7#1/'0*0 B)4-01 /)4407

67(1#(C_H04&?+ ?0 -10 *,0 *0'(1 A-)4#*5 )$7 A-)4#) #$*0'/,)$20)@45C

6&1*-4)*#$2 *,0 0:#1*0$/0 &% *,'00 *5.01 &% #$%&'()*#&$ 0$)@401 )/*#&$

'0)/*#&$ .,0$&(0$) *& @0 #$*0'.'0*07 )1 ) .'&/011+ /&(@#$#$2 A-)4#*#01 #$B&4B07

#$ )$ #$*0')/*#&$ #$*& ) '04)*#&$C

P'3 Q"=.9$)8.% "#6 =BC.% $/ 8#/$)


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11

M,0 %#'1* #1 *,)* ?,&10 @0#$2 #1 1#(.45 #$ #*104%+ $&* '0%0''#$2 *& )$5*,#$2 $&'

45#$2 @0,#$7 )$5*,#$2C M,0 10/&$7 #1 *,)* ?,#/, #1 ?,)* #* #1 @5 %&'/0 &%

1&(0*,#$2 *& ?,#/, #* #1 10/&$7C M,0 *,#'7 #1 *,)* ?,#/, #1 ?,)* #* #1 &?#$2 *&

*,#$21 @0*?00$ ?,#/, #* (07#)*01 )$7 ?,#/, #* @'#$21 #$*& '04)*#&$ *& 0)/,

&*,0' ;96" WCXT\>

=$ 0:)(.40 &% %#'1*$011 )'0 A-)4#*#01 #$ *,0(104B01+ 0C2C+ $)#4+ ,)((0'C =$

0:)(.40 &% 10/&$7$011 )'0 ;)7a,&/> '04)*#&$1 @0*?00$ A-)4#*#01+ 0C2C+ ) /&a

&//-''0$/0 &% ) $)#4 )$7 ) ,)((0'C =$ 0:)(.40 &% *,#'7$011 )'0 ,)@#*-)4

;(0)$#$2%-4> '04)*#&$1 &% A-)4#*#01+ 0C2C+ ) /&a&//-''0$/0 &% ) $)#4 )$7 ) ,)((0'

(known) as nailadriving. Another example, this time in the context of the CRA, is

*,0 .0'/0.*#&$ &% )$ #$.-* 1*'#$2 )1 ) A-)4#*5 ;/%C %#'1*$011>+ )1 ) 10A-0$/0 &%

?&'71 #$ 1&(0 4)$2-)20 ;/%C 10/&$7$011>+ )$7 ) 10$*0$/0 #$ ) %)(#4#)' 4)$2-)20

;/%C *,#'7$011>C 8$ *,0 %#'1* /)10+ *,0 '0)/*#&$ /)$ @0 ) /&.5#$2 &% *,0 #$.-* ;/%C

#(.'011#&$>+ #$ *,0 10/&$7 /)10+ *,0 20$0')*#&$ &% ) 15$*)/*#/ .)'1#$2+ #$ *,0 *,#'7

/)10+ *,0 01*)@4#1,#$2 &% ) (0)$#$2%-4 #$*0'.'0*)*#&$C

M,0 *,'00 /)*02&'#01 )'0 '04)*07 *& 0)/, &*,0' )//&'7#$2 *& ) '04)*#&$ &%

70.0$70$/5" /)*02&'#01 &% ) ,#2,0' &'7#$)4 $-(@0' #'3&13, ) 4&?0' &'70'

/)*02&'5C = 7#1*#$2-#1,#$2 .'&.0'*5 &% *,0 60#'/0)$ /)*02&'#/)4 1/,0() #1 *,)*

*,#'7$011 /)$ &$45 @0 0:.0'#0$/07+ %#'1*$011 ()5 &$45 )..0)' *,'&-2,

10/&$7$011+ )$7 10/&$7$011 &$45 *,'&-2, *,#'7$011CRM,#1 $78$,-3#,'*,'04)*#&$

&% *,0 *,'00 /)*02&'#01 #(.4#01 *,)* /)*02&'#01 &% ) 4&?0' &'7#$)4 $-(@0' ,3&13,

*& ,0$/0 ',,)) ,#2,0' &'70' /)*02&'5C M,0 *?& '04)*#&$1 1,)'0 *,0 .'&.0'*5 *,)*

*,05 )'0 -,51,0#3,)$7 !-('$#!#3,C H04&? ?0 '0%0' *& *,0 *?& *5.01 &% 70.0$70$/5

between categories by the relations involve () and evolve ().

9Note the difference with Aristotles categories, that are the possible kind of things that can be thesubject or the predicate of a proposition.


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12

D0 1-2201* *,)* *,0 *,'00 *5.01 &% #$%&'()*#&$ &% A-)4#*#01+ #$*'&7-/07 #$

*,0 .'0B#&-1 10/*#&$+ )'0 )$)4&2&-1 *& *,0 *,'00 /4)1101 &% ) /)*02&'#/)4

70%#$#*#&$ &% #$%&'()*#&$ #$B&4B07 #$ .,0$&(0$)+ )1 (0$*#&$07 )@&B0"

3' 6"="" #$%&'()*#&$ #$B&4B07 #$ ) A-)4#*5 #$ #*104%+ 1-/, )1 #*1 .&*0$*#)4 %&'

)'04)*#&$ ;/%C %#'1*$011>

L' ?$##.?=8$#" #$%&'()*#&$ #$B&4B07 #$ ) '04)*#&$ &% ) A-)4#*5 ?#*, )$&*,0'

A-)4#*5+ 1-/, )1 #*1 )/*-)4 '04)*#&$)4 .'&.0'*#01 ;/%C 10/&$7$011>

P' ).;"=8$#" #$%&'()*#&$ #$B&4B07 #$ ) A-)4#*5+ 01*)@4#1,#$2 ) '04)*#&$+ 1-/, )1 #*1

,)@#*-)4 .'&.0'*#01 ;/%C *,#'7$011>C

H5 /&$1#70'#$2 *,0 70.0$70$/5 @0*?00$ *,0 60#'/0)$ /)*02&'#01 *& @0 )$

0:.'011#&$ &% ) ),3,1&.%,'!+ *,0 *,'00 /4)1101 &% #$%&'()*#&$ /)$ @0 #$*0'.'0*07

)1 $!(/,$ &% )$ #$%&'()*#&$)4 .'&/011+ 20$0')*#$2 ) '04)*#&$ ;/%C '0)/*#&$>

#$B&4B07 #$ *,0 #$.-* )/*#&$C D0 )11-(0 *,)* #$%&'()*#&$ &% ) ,#2,0' /4)11

#'3&13,$#$%&'()*#&$ &% ) 4&?0' /4)11+ )$7 *,0 &*,0' ?)5 )'&-$7+ #$%&'()*#&$ &% )

4&?0' /4)11 ',,)$information of a higher class it is evolving to. For instance, 1W"

) .&*0$*#)4 '04)*#&$)4 .'&.0'*5 ()5 @0/&(0 &.0')*#&$)4 &$45 *,'&-2, )$ )/*-)4

relation; and 32: an arising relation involves an actual relation between qualia.

=$ 0:)(.40+ #$ *,0 /&$*0:* &% *,0 9+ )$7 #$ ) (0)$#$2%-4 %)1,#&$ ;X>C

H5 01*)@4#1,#$2 ) 4#$E @0*?00$ /)*02&'#01 )$7 *5.01 &% #$%&'()*#&$+ ?,#/,

)'0 '04)*#&$1+ ?0 &.0$ *,0 ?)5 %&' ) '04)*#&$)4 #$*0'.'0*)*#&$ &% )/*#&$'0)/*#&$

.,0$&(0$)C

R S.;"=8$#"; 8#=.)C).="=8$#

G'&( ) /)*02&'#/)4 .0'1.0/*#B0+ A-)4#*#01 #$B&4B07 #$ )$ #$*0')/*#&$ (-1* @0

#$70.0$70$* ;/%C %#'1*$011>C M,0 '0)/*#&$+ ?,#/, )'#101 *,'&-2, #$*0'.'0*)*#&$+

(-1* #$B&4B0 ) A-)4#*)*#B0 /,)$20 ;/%C *,#'7$011>C G'&( *,#1 ?0 ()5 /&$/4-70 *,)*

0)/, &$0 &% *,0 #$*0')/*#$2 A-)4#*#01+ )$7 '0)/*#&$+ ?,#/, *&& #1 ) A-)4#*5+ (-1* @0

#$70.0$70$*C


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=$ 0:)(.40 &% A-)4#*#01 #$B&4B07 #$ )$ #$*0')/*#&$ )'0 ) $)#4 )$7 ,)((0'c

)$ 0:)(.40 &% ) A-)4#*)*#B0 /,)$20 #1 *,0 )'#1#$2 %&'/0 )$7 /&-$*0' %&'/0C

=$&*,0' 0:)(.40+ *,#1 *#(0 #$ *,0 7&()#$ &% ?)B0a*5.0 .,0$&(0$)+ )'0

#$*0')/*#$2 ?)B0 1#2$)41 ;/%C A-)4#*#01>+ )$7 )$ )'#1#$2 1*)$7#$2 ?)B0 ;/%C )

A-)4#*)*#B0 /,)$20>C

G'&( )$ #$%&'()*#&$)4 1*)$/0+ )$ #$*0')/*#&$ /)$ @0 /,)')/*0'#V07 @5 ) .)#'

&% A-)4#*#01 ;AO+ AW>+ *,0 '0)/*#&$ @5 *,0 A-)4#*5 &% *,0 )'#1#$2 %&'/0 )$7 /&-$*0'

%&'/0 ;AX>C =1 #$%&'()*#&$ #$B&4B07 #$ 0)/, &$0 &% *,0 X A-)4#*#01 /)$ @0

7#1*#$2-#1,07 #$ X /4)1101 ;/%C 1*)201>+ ?0 1-2201* *,)* #$%&'()*#&$ #$B&4B07 #$

)/*#&$'0)/*#&$ .,0$&(0$) /)$ @0 '0.'010$*07 @5 XdXdXeWY .&11#@40 '04)*#&$1

&' /&(@#$)*#&$1 &% #$%&'()*#&$ 1*)201c *,0 )'#1#$2 .,0$&(0$&$ #*104% @5 *,0

combination corresponding to the arising relation (which can be any one of

*,&10 .&11#@40 '04)*#&$1>C =1 )$ &@10'B)*#&$ #1 )4?)51 '04)*07 *& 1&(0

.0'1.0/*#Be by the observer, the arising relation must involve information about

a selection from the 27 combinations. By virtue of this information, the arising

'04)*#&$ (-1* @0 7#%%0'0$* %'&( *,&10 .&11#@40 '04)*#&$1C

8$ 1-(+ ?0 1-2201* *,)* )/*#&$'0)/*#&$ .,0$&(0$) /)$ @0 /,)')/*0'#V07

@5 WYfOeW_ *5.01 &% '04)*#&$C =//&'7#$2 *& &-' (&704+ *,&10 '04)*#&$1 (-1* @0

#$B&4B07 #$ *,0 #$*0')/*#&$ @0*?00$ AO )$7 AWC 8$%&'()*#&$ )@&-* *,0 '0)/*#&$+

#$B&4B07 #$ AX+ ()5 0$)@40 ) $&B04 #$*0'.'0*)*#&$ &% *,0 0:#1*#$2 '04)*#&$1+ @-* $&

#$*'&7-/*#&$ &% '04)*#&$1 #$70.0$70$* %'&( AO )$7 AW ;*,0 0:#1*0$/0 &% 1-/,

'04)*#&$1 ?&-47 #(.45 *,)* '0.'010$*)*#&$ @5 *,0 &@10'B0' ()5 $&* @0 *'-*,%-4>C

R'3 0#=.)#";TF8.5 ).C).%.#="=8$#

=4*,&-2, %'&( *,0 .$* &% B#0? &% #$*0')/*#&$+ *,0 &@10'B0' /)$ @0 #70$*#/)4 *&

&$0 &% *,0 #$*0')/*#$2 A-)4#*#01+ %'&( *,0 1*)$/0 &% #$*0'.'0*)*#&$+ *,0 &@10'B0'

()5 '0.'010$* *,0 #$.-* #$*0')/*#&$ %'&( *,0 .0'1.0/*#B0 &% )$5 &$0 &% *,0 *?&

#$.-* A-)4#*#01C M,0 *?& .0'1.0/*#B01 &% #$*0'.'0*)*#&$ )'0" AO #1 )%%0/*#$2 AW+ )$7


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AW #1 )%%0/*#$2 AO+ *,)* ?0 ?#44 /)44 0%%0/*a+ )$7 1*)*0aB#0?+ '01.0/*#B045COP

H5

B#'*-0 &% *,0 #1&(&'.,#1( @0*?00$ *,0 *?& .0'1.0/*#B01+ *,0#' '04)*#&$1 /)$ @0

(0'207 #$*& ) 1#$240 '0.'010$*)*#&$C D0 ?#44 '0*-'$ *& *,#1 .$* #$ 30/*C T+ #$

?,#/, ?0 #$/&'.&')*0 #$ &-' (&704 ) '0.'010$*)*#&$ &% AX+ )1 ?044C

H04&?+ ?0 04)@&')*0 &$ )$ 0%%0/*aB#0? #$*0'.'0*)*#&$ ;AO #1 )%%0/*#$2 AW>C

9&$%&'( *,#1 .0'1.0/*#B0+ *,0 *?& A-)4#) )'0 #$*0'.'0*07 7#%%0'0$*45" AO )1 )$

0:.'011#&$ &% *,0 #$.-* 0%%0/*+ AW )1 )$ 0:.'011#&$ &% ) '04)*#&$ &% *,0 #$.-* 1*)*0

?#*, *,0 #$.-* 0%%0/*C M,0 *,'00 /4)1101 &% '04)*#&$)4 #$%&'()*#&$ #$B&4B07 #$ AW

/)$ @0 70%#$07 )1 %&44&?1 ;100 G#2C X>"

G3H 8#6.C.#6.#=" )$ 0:.'011#&$ &% *,0 '04)*#&$ &% AW ?#*, AO+ )1 ) /&a&//-''0$/0

&% #$70.0$70$* A-)4#) ;/%C %#'1*$011>

GLH ?$T.E8%=8#9" )$ 0:.'011#&$ &% *,0 '04)*#&$ &% AW ?#*, AO + )1 ) /&a0:#1*0$/0 &%

#$*0''04)*07 A-)4#) ;/%C 10/&$7$011>

GPH ?$)).%C$#68#9" )$ 0:.'011#&$ &% *,0 '04)*#&$ &% AW ?#*, AO+ )1 )

/&''01.&$70$/0 &% A-)4#) ;/%C *,#'7$011>C

G&44&?#$2 *,0 70.0$70$/5 @0*?00$ *,0 /)*02&'#01 ;100 30/*C XCO>+ *,0

above classes are related to one another: (1)(2)(3) and (3)(2)(1) where

and are used as polymorphic operators.

=1 AW )$7 AO )'0 /&((&$45 #$*0'.'0*07 %'&( *,0 .0'1.0/*#B0 &% AO+ *,0#'

#$%&'()*#&$ /)$ @0 (0'207 #$*& ) 1#$240 '0.'010$*)*#&$C M,0 *,'00 -.a'#2,*

7#)2&$)41 70.#/*07 #$ *,#1 7#)2')( '0.'010$* AO %'&( *,0 .0'1.0/*#B0 &% %#'1*$011+

10/&$7$011+ )$7 *,#'7$011+ )//&'7#$2 *& AW+ *,)* ?0 /)44 *,0 *,'00

'0.'010$*)*#&$1 &% AOC M,0 *0'(#$&4&25 -107 #$ G#2C X+ )1 ?044 )1 @04&?+ /&(.4#01

?#*, *,0 *0'(#$&4&25 -107 #$ ;3)'@& 0* )4C+ WPOO>C

;O> G#'1* '0.'010$*)*#&$ &% AO )//&'7#$2 *& AW

',7!-(1e#$70.0$70$*7)*)" )$ 0:.'011#&$ &% *,0 #$.-* A-)4#) )1 $0-*')4

'04)*#&$)4 .'&.0'*#01 &' ) .&*0$*#)4 %&' ) '04)*#&$

10In syntactic language phenomena, related notions are active and passive voice.


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15

.($$#3,e#$70.0$70$*/&$$0/*#&$" )$ 0:.'011#&$ &% *,0 #$.-* A-)4#) )1

.)11#B0 '04)*#&$)4 .'&.0'*#01 0$)@4#$2 )$ )/*-)4 '04)*#&$

(*!#3,e#$70.0$70$*'04)*#&$" )$ 0:.'011#&$ &% *,0 #$.-* A-)4#) )1 )/*#B0

'04)*#&$)4 .'&.0'*#01 #$B&4B07 #$ ) ,)@#*-)4 '04)*#&$

=$ 0:)(.40 )'0 #$70.0$70$* A-)4#) &% )$ #$*0')/*#&$ )..0)'#$2 )1 7)*) ;/%C

$0-*')4>c *,0 .&*0$*#)4 &% AO %&' ) '04)*#&$ ?#*, )$ #$70.0$70$* &*,0' A-)4#*5+

'0.'010$*07 @5 AW ;/%C .)11#B0>c )$7 *,0 ,)@#*-)4 .'&.0'*#01 &% ) '04)*#&$ #$B&4B07

#$ AO+ #$ /&(@#$)*#&$ ?#*, ) *5.0 &% A-)4#) '0.'010$*07 @5 AW ;/%C )/*#B0>C

;W> 30/&$7 '0.'010$*)*#&$ &% AO )//&'7#$2 *& AW

*&'$!#!7,'!e/&a0:#1*#$2

7)*)" )$ 0:.'011#&$ &% *,0 #$.-* A-)4#) )1

/&$1*#*-0$*1 &% ) .&*0$*#)4 '04)*#&$

%&)#5#,'e/&a0:#1*#$2/&$$0/*#&$" )$ 0:.'011#&$ &% *,0 #$.-* A-)4#) )1

.)11#B0 /&$1*#*-0$*1 0$)@4#$2 )$ )/*-)4 '04)*#&$

.-,)#*(!,e/&a0:#1*#$2'04)*#&$" )$ 0:.'011#&$ &% *,0 #$.-* A-)4#) )1

#$*0''04)*07 )/*#B0 /&$1*#*-0$*1 #$B&4B07 #$ ) ,)@#*-)4 '04)*#&$

=$ 0:)(.40+ #$ 15$*)/*#/ 4)$2-)20 .,0$&(0$)+ )'0 /&a0:#1*0$* ?&'71 &% )$ #$.-*

1*'#$2+ )..0)'#$2 )1 7)*) ;/%C /&$1*#*-0$*>c 15$*)/*#/ (&7#%#0'1+ /&$$0/*#$2 *& *,0#'

)'2-(0$*1 ;/%C (&7#%#0'>c )$7 B0'@ .,')101+ .'07#/)*#$2 *,0 1-@L0/* &% *,0

10$*0$/0 ;/%C .'07#/)*0>C

;X> M,#'7 '0.'010$*)*#&$ &% AO )//&'7#$2 *& AW

(8$!-(*!e/&''01.&$7#$27)*)" )$ 0:.'011#&$ &% *,0 #$.-* A-)4#) )1 )@1*')/*

.'&.0'*#01 #$B&4B07 #$ ) .&*0$*#)4 '04)*#&$

$!-7*!7-,e/&''01.&$7#$2/&$$0/*#&$" )$ 0:.'011#&$ &% *,0 #$.-* A-)4#) )1

#$*0''04)*07 .'&.0'*#01 #$B&4B07 #$ )$ )/*-)4 '04)*#&$

8#')#'/e/&''01.&$7#$2'04)*#&$" )$ 0:.'011#&$ &% *,0 #$.-* A-)4#) )1 )$

)()42)()*#&$ &% .'&.0'*#01 #$B&4B07 #$ ) ,)@#*-)4 '04)*#&$C

=$ 0:)(.40+ *,#1 *#(0 #$ ?)B0a*5.0 .,0$&(0$)+ )'0 /&''01.&$7#$2 1#2$)41 &% )

?)B0 .,0$&(0$&$+ )@1*')/*07 )1 4&$2#*-7#$)4 &' *')$1B0'1)4 ?)B0a%&'(1 ;/%C

)@1*')/*>c ) /&(@#$)*#&$ &% ?)B0 1#2$)41 #$*& )$ #$*0'%0'0$/0 &' 1-.0'.&1#*#&$ ;/%C


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16

1*'-/*-'0>c )$7 ) '04)*#&$ &% ?)B0 1#2$)41+ )..0)'#$2 )1 ) 1*)$7#$2 ?)B0+

/,)')/*0'#V07 @5 )$ )'#1#$2 $0? ?)B0 .)**0'$ ;/%C @#$7#$2>C

H5 /&(@#$#$2 #$%&'()*#&$ %'&( AW )$7 AO #$*& ) 1#$240 '0.'010$*)*#&$+ ?0

4)5 *,0 2'&-$7 %&' )$ #$%&'()*#&$)4 )$)451#1 &% &-' (&704 &% )/*#&$'0)/*#&$

.,0$&(0$)C

189:). P@ 9&(@#$07 1*)*0 )$7 0%%0/* #$%&'()*#&$ #$ 0%%0/*aB#0? #$*0'.'0*)*#&$C

M,0 *,'00 -.a'#2,* 7#)2&$)41 #44-1*')*0 *,0 *,'00 '0.'010$*)*#&$1 &% AO ;)//&'7#$2

*& AW>

U 0#/$)


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17

A-)4#*5+ ?0 )11-(0 *,)* AX /)$ @0 '0.'010$*07 @5 (0'2#$2 #$%&'()*#&$ #$B&4B07

#$ AW )$7 AOC

D0 1-2201* *,)* -$)'5+ @#$)'5+ )$7 *0'$)'5 '04)*#&$1 @0*?00$ A-)4#*#01 /)$

@0 '0.'010$*07 @5 '04)*#&$1 @0*?00$ 1*)201 %'&( ) 1#$240+ ) .)#' &%+ )$7 )44 *,'00

'0.'010$*)*#&$1 &% AO+ '01.0/*#B045C H5 B#'*-0 &% *,0#' /)*02&'#/)4 %&-$7)*#&$+

'04)*#&$1 @0*?00$ #$%&'()*#&$ 1*)201 (-1* '01.0/* *,0 70.0$70$/5 @0*?00$

/)*02&'#01C D0 /)44 *,#1 *,0 /&$7#*#&$ &% *(!,/&-#*(1 ),.,'),'*+C G&' 0:)(.40+ )

10/&$7$011 /)*02&'5 #$%&'()*#&$ 1*)20 /)$ @e in an involve relation () with

%#'1*$011 )$7 10/&$7$011 /)*02&'5 #$%&'()*#&$ 1*)20;1> &$45C H04&? ?0 @02#$

?#*, )$ )$)451#1 &% -$)'5 )$7 @#$)'5 '04)*#&$1C D0 '0*-'$ *& *0'$)'5 '04)*#&$1 #$

30/*C TCOCXC

U'3 (B#="?=8? %=):?=:).%

8$ &'70' *& #$*'&7-/0 )$ #$%&'()*#&$)4 )$)451#1 &% &-' '0.'010$*)*#&$+ ?0 0(@07

*,0 10* &% 1*)201 &% ) A-)4#*5 #$*& *,0 &'70'07 10* &% #$*020'1 :egO+W+XhC G&'

#gO+Wh+ ?0 70%#$0" A# e:,C D0 '0.'010$* *,0 10* &% '04)*#&$1 0$)@407 @5 AW )$7

AO @5 *,0 &.0')*#&$ 4)**#/0 (-4*#.4#/)*#&$ ;i)B05 Q 6'#01*405+ORRP>C 8$ *,#1

10/*#&$+ ?0 '01*'#/* &-'104B01 *& )$ )$)451#1 &% *,0 '04)*#&$1 '0.'010$*07 @5 *,0

[)110a7#)2')( &% *,0 )'#1#$2 &'70'#$2+OO

that we refer to by the symbol AWdAO.

We allow to designate the relations involve and evolve, ambiguously. We

/)44 )$ 040(0$* &% *,0 10* -$70'45#$2 AWdAO ) 1*)20COW

= 1*)20 &% AWdAO /)$ @0

referred to by its coordinates (i)j, designating stage j of AO, from the i*,

.0'1.0/*#B0+ )//&'7#$2 *& AWC G&' #$1*)$/0+ ;X>O 701#2$)*01 1*)20 O &% AO+ %'&(

*,0 .0'1.0/*#B0 &% X'7$011+ )//&'7#$2 *& AWC 300 )41& G#2C SC j40(0$*1 &% AWdAO+

*,)* )'0 '04)*#&$1+ /)$ @0 '0%0''07 *& @5 ) .)#' &% /&&'7#$)*01+ 10.)')*07 @5 )

,5.,0$ 15(@&4+ %&' #$1*)$/0+ ;X>Oa;X>WC Oa;X>Wa;W>W #1 1,&'* %&' g;X>Oa;X>W+ ;X>Wa;W>WhC

OOM,0 [)110 7#)2')( &% ) 4)**#/0 ;#1 ) '0.'010$*)*#&$ &% ) (#$#()4 '04)*#&$ 20$0')*#$2 ;@5 (0)$1

&% ) /4&1-'0 &.0')*#&$COW

K&*0 *,0 )(@#2-&-1 -10 &% *,#1 *0'(C


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189:). R@ = '0.'010$*)*#&$ &% AWdAOC 3*)201 &% AWdAO )'0 4)@04407 @5 ) .)#' &%

#$*020'1+ '0.'010$*#$2 *,0 /)*02&'5 &% ) 1*)20 &% AW ;#$ .)'0$*,0101> )$7 ) 1*)20

&% AOC 3*)201 &% AW )'0 -107 )1 ;'04)*#&$)4> '0.'010$*)*#&$1 &% ) 1*)20 &% AOC G&'

0:)(.40+ ;X>O 701#2$)*01 1*)20 O &% AO+ %'&( ) X'7$011 .0'1.0/*#B0 )//&'7#$2 *&

AWC M,#1 /&$B0$*#&$ #1 -107 #$ 4)*0' 7#)2')(1 )1 ?044C

8$ &'70' *& )/,#0B0 &-' 2&)4 10* #$ *,0 @02#$$#$2 &% 30/*C T+ ?0 70'#B0 70/&(a

.&1#*#&$1 &% AWdAOC 8$ *,0 /)10 &% -$)'5 '04)*#&$1 ;/%C %#'1*$011> *,#1 @) 7&?$ *&

70/&(.&1#*#&$1 &% AO ;H#'E,&%% Q H)'*00+ ORYP>C 8$ &-' /)*02&'#/)445 #$1.#'07

)$)451#1 ?0 '01*'#/* &-'104B01 *& 70/&(.&1#*#&$1 *,)* )'0 ,&(&20$0&-1 ,0$/0

/)$ @0 /,)')/*0'#V07 @5 ) 1#$240 *5.0 &' /)*02&'5C D0 70%#$0 ) ,&(&20$0&-1

70/&(.&1#*#&$ &% ) '04)*#&$ #70$*#*5+ ;W>

/&(.&1#*#&$+ ;X> '0/-'1#&$C 870$*#*5 ;O> 0$)@401 ) 70%#$#*#&$ &% #$1*)$/01 &% -#$ #1 ) %-$/*#&$ &$ #$1*)$/01 &% -C H5 B#'*-0 &% *,0 0:#1*0$/0 &% *,0

13We specify our functions by means of examples (a formal definition is omitted).


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*?& &'70' '04)*#&$1+ *,#1 &.0')*#&$ ,)1 *?& B0'1#&$1+ /&(@#$)*#&$ )$7

/&(.40(0$*)*#&$+ 0$)@4#$2 ) /&(.&1#*#&$ &% #$1*)$/01 &% -+ ,)B#$2 #70$*#/)4 )$7

7#%%0'0$* &'70'#$21+ '01.0/*#B045C G#$)445+ '0/-'1#&$ ;X> 0$)@401 )$ #$*'&7-/*#&$ &%

) $0? #$*0'.'0*)*#&$ &% ) '04)*#&$C M,#1 %-$/*#&$ ,)1 *,'00 B0'1#&$1" *')$1#*#B0

/4&1-'0+ 0$/).1-4)*#&$+ )$7 (0'2#$2C j$/).1-4)*#&$ 0$)@401 ) 1-@10* &% + '0/-'1#&$ &$ 1-@10*1 -$70'45#$2 ) $0? /&$/0.* ;/%C

*,#'7$011>C =41& $&*0 *,0 )$)4&25 @0*?00$ *,010 %-$/*#&$1+ )$7 *,0 %-$/*#&$1

-107 @5 ) ()*,0()*#/)4 *,0&'5 &% /)*02&'#01 ;H)'' Q D0441+ ORRP>C

D0 /)44 ) ,&(&20$0&-1 70/&(.&1#*#&$ &% +

*,0 A-)7')$240 /)$ @0 '0/-'1#B045 /&$/0.*-)4#V07 ;/%C 0$/).1-4)*#&$> )1 ) '04)*#&$

@0*?00$ %&-' )$2401 ;/%C (0'2#$2>C H5 /&(@#$#$2 *,0 '04)*#&$1 '0.'010$*#$2 ) .)#'

&% /&(.40(0$*)'5 )$2401 #$*& ) 1#$240 '04)*#&$ ;/%C /&(.40(0$*)*#&$>+ *,0

A-)7')$240 /)$ @0 /&$/0.*-)4#V07 )1 ) /&-.40 &% .)#'1 &% )$2401 ;3)'@&+ ORR\>C

U'3'3 V#")B %=):?=:).%

M,0 1()4401* -$)'5 -$#* '04)*#&$ #1 70%#$07 @5 *,0 '04)*#&$ &% )$ #$%&'()*#&$ 1*)20

&% AOC 300 G#2C T;)>C M,0 /&''01.&$7#$2 -$)'5 70/&(.&1#*#&$ &% AO #1 ) *'#B#)4 &$0C

= (&'0 #$*0'01*#$2 -$#* '04)*#&$ /)$ @0 %&-$7 *,'&-2, /&(.&1#*#&$ )$7 *')$1#*#B0

/4&1-'0C 300 G#2C T;@>C = ,&(&20$0&-1 70/&(.&1#*#&$ &% *,0 *,'00

'0.'010$*)*#&$1 &% AO #$*& *,'00 -$)'5 #$%&'()*#&$ 1*'-/*-'01 #1 70.#/*07 #$


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G#2C T;/>C =$ )..4#/)*#&$ &% @&*, B0'1#&$1 &% *,0 )@&B0 -$#* '04)*#&$ 7& $&* 0$)@40

$0? /&$/0.*-)4#V)*#&$1+ 7#%%0'0$* %'&( *,0 0:#1*#$2 &$01C J$)'5 #$%&'()*#&$1

1*'-/*-'01 1)*#1%5 *,0 /&$7#*#&$ &% /)*02&'#/)4 70.0$70$/5+ *'#B#)445C

M,0 $-(@0' &% -$)'5 #$%&'()*#&$ 1*'-/*-'01 #1" PC

189:). U@ J$#* '04)*#&$1 0$)@4#$2 ) *'#B#)4 ;)>+ )$7 ) $&$a*'#B#)4 -$)'5

70/&(.&1#*#&$ &% AO ;@>C M,0 *,'00 -$)'5 #$%&'()*#&$ 1*'-/*-'01 ;/> 20$0')*07 @5

-$#* '04)*#&$ ;@>C H-440*1 &% ) 4#2,*0' 2'05 1,)70 1*)$7 %&' 1*)201 &% AO *,)* )'0

/4&107C i&**07 4#$01 )'0 -107 %&' )$ 0:.'011#&$ &% *,0 *,'00 '0.'010$*)*#&$1 &%

AO+ )1 %#'1*$011 /)*02&'5 '04)*#&$1 #$B&4B07 #$ AWdAOC

U'3'L W8#")B %=):?=:).%

M,0 1()4401* @#$)'5 -$#* '04)*#&$ #1 70%#$07 @5 *,0 .)#' &% '04)*#&$1 &% )$

#$%&'()*#&$ 1*)20 &% AWdAOC M,0 *?& B0'1#&$1 &% *,#1 '04)*#&$ )'0 7#1.4)507 #$

G#2C \;)> )$7 G#2C \;@>C =$ #$1*)$/0 &% *,0 %#'1* B0'1#&$ #1 ;W>Oa;O>Oa;O>WC =

,&(&20$0&-1 70/&(.&1#*#&$ &% AWdAO #$*& @#$)'5 #$%&'()*#&$ 1*'-/*-'01 #1

70.#/*07 #$ G#2C Y(a), by small triangles.14 8$1*)$/01 &% *,0 *?& B0'1#&$1 &% *,0

unit relation, ordered by evolve () and involve (), are represented by

triangles pointing downward and upwar7+ '01.0/*#B045C M,'&-2, /&(.&1#*#&$

;/%C /&(@#$)*#&$> )$7 *')$1#*#B0 /4&1-'0+ AWdAO /)$ @0 /&$/0.*-)4#V07 )1 ) 10* &%

large triangles. See Fig.Y;@>C

14For reasons, explained later in Sect. 5.1.3, binary information structures are represented bytriangles.


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189:). N@The two versions of the used binary unit relation, ordered by evolve

(a) and involve (@>C = 1)(.40 @#$)'5 #$%&'()*#&$ 1*'-/*-'0 ;/>+ )$7 *,0 /4&1-'0 &%

) /&(.&1#*#&$ &% @#$)'5 #$%&'()*#&$ 1*'-/*-'01 ;7>C = %#44#$2 .)**0'$ #1 -107 %&' )$

illustration of binary structures as triangles

H5 /&(@#ning a pair of small triangles into a single relation (cf.

/&(.40(0$*)*#&$>+ ?0 ()5 /&$/0.*-)4#V0 AWdAO as a set of small quadrangles.

300 G#2C _;)>C =$ 0:)(.40 #1 *,0 /&(.40(0$*)*#&$ &% ;W>Oa;O>Oa;O>W @5 ;W>Oa;W>Wa

;O>W+ &@*)#$#$2 ;W>Oa;W>Wa;O>Wa;O>OC Considering small quadrangles to be a single

040(0$* ;/%C 0$/).1-4)*#&$>+ 0$)@401 AWdAO *& @0 '0/-'1#B045 /&$/0.*-)4#V07 )1 )

large quadrangle ;/%C (0'2#$2>C 300 G#2C _;@>C H#$)'5 #$%&'()*#&$ 1*'-/*-'01

1)*#1%5 *,0 /&$7#*#&$ &% /)*02&'#/)4 70.0$70$/5+ *'#B#)445C G&' 0:)(.40+ #$ G#2C \;/>+

(1)1(2)1 and (1)1(1)2, as (1)(2) and 11, and (1)(1) and 12, respectively.

M,0 $-(@0' &% @#$)'5 #$%&'()*#&$ 1*'-/*-'01 #1" ;_fW>f;SfO>e 3UC

189:). X@ = /&$/0.*-)4#V)*#&$ &% AWdAO as small (a) and large triangles (b)


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189:). M@= /&$/0.*-)4#V)*#&$ &% AWdAO as small (a) and large quadrangles (b).

j7201 '0.'010$*#$2 '04)*#&$1 )'#1#$2 *,'&-2, /4&1-'0+ )'0 &(#**07 ;0C2C+ #$ ;)>+

;O>Oa;W>W+ )$7 #$ ;@>+ ;O>Oa;X>X>

U'3'P 4.)#")B %=):?=:).%

M0'$)'5 '04)*#&$1 )'0 '04)*#&$1 @0*?00$ AX+ AW+ )$7 AOC G'&( )$ )$)45*#/)4

.0'1.0/*#B0+ AX ;/%C '0)/*#&$> (-1* #$B&4B0 #$%&'()*#&$ )@&-* AW )$7 AO+ )1 ?044

)1 )@&-* #*104%C [&?0B0'+ @#$)'5 '04)*#&$1 0$)@407 @5 AWdAO ()5 '0.'010$*

#$%&'()*#&$ #$B&4B07 #$ AW )$7 AO &$45C D0 ()5 /).*-'0 *,0 )@&B0 /&(.40*0$011

&% AX+ @5 70%#$#$2 *0'$)'5 '04)*#&$1 *& #$/4-70 #$%&'()*#&$ %'&( )44 *,'00

'0.'010$*)*#&$1 &% AO ;)//&'7#$2 *& AW>C =1 ) '01-4*+ ?0 ()5 70%#$0 *,0 1()4401*

*0'$)'5 -$#* '04)*#&$ *& @0 ) '04)*#&$ @0*?00$ ) 1#$240 #$%&'()*#&$ 1*)20 %'&(

0)/, &$0 &% *,0 *,'00 '0.'010$*)*#&$1 &% AOC =$ #$1*)$/0 &% *,#1 -$#* '04)*#&$ #1

70%#$07 @5 *,0 #$%&'()*#&$ 1*)201 ;X>O+ ;W>O+ ;O>WC

D0 '0.'010$* *0'$)'5 #$%&'()*#&$ 1*'-/*-'01 @5 *'#.401C M& *,#1 0$7+ ?0

)11-(0 *,0 0:#1*0$/0 &% )$ &'70' .'010'B#$2 ()..#$2 @0*?00$ *,0 *,'00

/)*02&'#01 )$7 *,0 *,'00 .&1#*#&$1 &% ) *'#.40C M,#1 ?)5 ?0 0$1-'0 *,)*+ #$ ) *'#.40+

*,0 /&$7#*#&$ &% /)*02&'#/)4 70.0$70$/5 %&' 1*)201 %'&( AW #1 '01.0/*07C 8$

)77#*#&$ ?0 '0A-#'0 *,)* *,0 )@&B0 /&$7#*#&$ #1 '01.0/*07 @5 *,0 1*)201 &% AO+

&//-''#$2 #$ *,0 *,'00 .&1#*#&$1 &% ) *'#.40C D0 -10 *,0 /&$B0$*#&$ *,)* ) *'#.40

(i,j,k) stands for the ternary relation (3)ia;W>La(1)k, for 1#+L+E3. For example,;O+W+W> #1 '0.'010$*#$2 ;X>Oa;W>Wa;O>WC M,#1 '04)*#&$ 1)*#1%#01 *,0 /&$7#*#&$ &%


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categorical dependency, as 122. An example of a triple which does not satisfy

*,)* /&$7#*#&$ #1 ;W+O+O>C

= ,&(&20$0&-1 70/&(.&1#*#&$ &% AWdAO #$*& *0'$)'5 #$%&'()*#&$

1*'-/*-'01 #1 70%#$07 @5 *,0 10*" g;O+O+O>+ ;O+O+W>+ ;O+W+W>+ ;W+W+W>+ ;O+O+X>+ ;O+W+X>+

;W+W+X>+ ;O+X+X>+ ;W+X+X>+ ;X+X+X>h+ ?,#/, #1 ) 1*'#/* 40:#/&2').,#/ &'70'#$2C 300 G#2C RC

8$ *,#1 7#)2')(+ 1*)201 &//-''#$2 #$ ) *0'$)'5 '04)*#&$ )'0 /&$$0/*07 @5 07201 ;/%C

'04)*#&$1 @0*?00$ #$%&'()*#&$ 1*)201>C =$ )..4#/)*#&$ &% @&*, B0'1#&$1 &% *,0

)@&B0 -$#* '04)*#&$+ )1 ?044 )1 *,0 -10 &% *,0 &.0')*#&$1+ /&(.&1#*#&$ )$7

'0/-'1#&$+OT

0$)@40 $& $0? 70/&(.&1#*#&$1C K&*0+ #$ G#2C R+ *,0 0:#1*0$/0 &%

horizontal edges, e.g., (2)1a;O>W+ ?,#/, 0:.4)#$1 &-' 0)'4#0' '0.'010$*)*#&$ &%

@#$)'5 #$%&'()*#&$ 1*'-/*-'01 @5 (0)$1 &% *'#)$2401+ #$ G#2C YC

M,0 $-(@0' &% *0'$)'5 #$%&'()*#&$ 1*'-/*-'01 #1" 3KC

189:). Y@ M0'$)'5 #$%&'()*#&$ 1*'-/*-'01 70.#/*07 @5 07201 @0*?00$ 1*)201

&//-''#$2 #$ *,0 *,'00 .&1#*#&$1 &% ) *'#.40 ;)>C M,0 #$B&4B07 10* &% '04)*#&$1 ;@>

and horizontal dependencies (c)

G&44&?#$2 *,0 )$)451#1 &% *,#1 10/*#&$ ?0 /&$/4-70 *,)* *,0 $-(@0' &% -$)'5+

@#$)'5+ )$7 *0'$)'5 #$%&'()*#&$ 1*'-/*-'01 #$B&4B07 #$ AWdAO #1" ;XfOTfOP>e LMC

K&*0 *,0 /)*02&'#/)4 $)*-'0 &% *,0 *,'00 *5.01 &% 1*'-/*-'01C J$)'5 #$%&'()*#&$

1*'-/*-'01 )'0 #$70.0$70$* ;/%C %#'1*$011>+ @#$)'5 #$%&'()*#&$ 1*'-/*-'01 )'0

OTK&*0 *,)* *,0 $-(@0' &% B)4-01 *,)* /)$ @0 )11#2$07 *& ) .&1#*#&$ &% ) *'#.40 #1 X+ ?,#/, #1 )

.'#(0 $-(@0' ,0$/0 $&* 70/&(.&1)@40C


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'04)*07 *& &$0 )$&*,0'+ @-* *,0#' '04)*#&$ #1 $&* )$ &'70'#$2 ;/%C 10/&$7$011>+

*0'$)'5 #$%&'()*#&$ 1*'-/*-'01 )'0 '04)*07 )$7 *,0#' '04)*#&$ 70%#$01 )$ #$7-/07

&'70'#$2 ;/%C *,#'7$011>C =41& $&*0 *,)*+ %'&( ) %&'()4 .0'1.0/*#B0+ *,0 10* &%

70/&(.&1#*#&$1 &% AWdAO #$*'&7-/07 #$ *,#1 10/*#&$ #1 $&* /&(.40*0C

i0/&(.&1#*#&$1 *,)* )'0 $&* (0$*#&$07 )'0 $&* /)*02&'#/)445 %&-$707 ,0$/0 )'0

$&* /&$1#70'07 *& @0 '0.'010$*)*#&$1 &% )/*#&$'0)/*#&$ .,0$&(0$)C

M,0 '04)*#&$1 #$*'&7-/07 #$ *,#1 10/*#&$ )'0 )$ 0:.'011#&$ &% ) /&a0:#1*0$/0

&% #$%&'()*#&$ 1*)201C =1+ %'&( )$ )$)45*#/)4 .$* &% B#0?+ )/*#&$'0)/*#&$

.,0$&(0$) (0'20 *,0 A-)4#*#01 &% )$ #$*0')/*#&$ #$*& ) 1#$240 A-)4#*5 ;/%C

'0)/*#&$>+ ?0 )'0 #$*0'01*07 #$ '04)*#&$1 0:.'011#$2 ) /&(@#$)*#&$ &% #$%&'()*#&$

#$B&4B07 #$ A-)4#*#01 &% ) .,0$&(0$&$C =$ )$)451#1 &% 1-/, '04)*#&$1+ '0.'010$*07

@5 AWdAO+ #1 *,0 1-@L0/* &% *,0 $0:* 10/*#&$C

189:). 3K@ )$7 1*)*0aB#0? #$*0'.'0*)*#&$ ;@>+ )$7 *,0 10* &%

'04)*#&$1 &@*)#$07 *,'&-2, (0'2#$2 ;/>

U'L (.


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7#)2')(+ *,0 0:#1*0$/0 &% )$ 0720 @0*?00$ ;O>O )$7 ;X>X+ )$7 *,0 )@10$/0O\

&%

&$0 @0*?00$ ;X>O )$7 ;O>XC 300 )41& G#2C _C

M,0 .&*0$*#)4 &% *,0 &@10'B0' *& /&$1#70' .,0$&(0$) *& @0 #$*0')/*#&$1

@0*?00$ 1&(0 1*)*0 )$7 0%%0/*+ #1 #$70.0$70$* %'&( #*1 .&*0$*#)4 *& (0'20

#$%&'()*#&$ %'&( 7#%%0'0$* #$*0'.'0*)*#&$1+ *,'&-2, (0(&'#V)*#&$C D0 )11-(0

*,)*+ #$ ) 1#$240 &@10'B)*#&$+ *,0 &@10'B0' ()5 70B04&. &',&% *,0 *?& .&11#@40

B#0?1 &% #$*0'.'0*)*#&$ #$ *,0 .'010$/0 &% (0(&'5 #$%&'()*#&$ *&&C [&? /)$ ?0

/&(.45 ?#*, *,#1 /&$7#*#&$ &% &-' (&704F

H5 )$)45V#$2 *,0 '04)*#&$1+ 7#1.4)507 #$ G#2C OP;/>+ ?0 ()5 &@10'B0 *,)*

*,0'0 )'0 *?& '04)*#&$1+ ;W>Oa;X>W )$7 ;O>Wa;W>X+ ?,#/, )'0 )$ 0:.'011#&$ &% )

/&(@#$07 2'&?*, &% /)*02&'#/)4 #$%&'()*#&$ #$B&4B07 #$ AW )$7 AO ,0$/0 /)$ @0

-107 %&' 7#1*#$2-#1,#$2 @0*?00$ *?& .0'1.0/*#B01 &% #$*0'.'0*)*#&$C =1 ;W>Oa;X>W

#1 )$ 0:.'011#&$ &% )$ #$/'0)10 &% #$%&'()*#&$ &% *,0 1*)*0 ;AW>+ %'&( 10/&$7$011

*& *,#'7$011 ;*,#1 #1 &..&107 *& )$ #$/'0)10 &% #$%&'()*#&$ &% *,0 0%%0/* ;AO>+ %'&(

%#'1*$011 *& 10/&$7$011+ ?,#/, #1 4011 (0)$#$2%-4>+ *,#1 '04)*#&$ /)$ @0 )11&/#)*07

?#*, 1*)*0aB#0? #$*0'.'0*)*#&$C G&' 15((0*'5 '0)1&$1+ ;O>Wa;W>X+ 0:.'011#$2 )$

#$/'0)10 &% #$%&'()*#&$ &% *,0 0%%0/*+ /)$ @0 )11&/#)*07 ?#*, 0%%0/*aB#0?

#$*0'.'0*)*#&$COY

In sum, we assume that stateaview interpretation is

/,)')/*0'#V07 @5 *,0 .'010$/0 &% ;W>Oa;X>W )$7 *,0 )@10$/0 &% ;O>Wa;W>Xc 0%%0/*a

B#0? #$*0'.'0*)*#&$ @5 *,0 .'010$/0 ;O>Wa;W>X &% )$7 *,0 )@10$/0 &% ;W>Oa;X>WC

300 G#2C OOC

H5 '0a#$*'&7-/#$2 *,0 *?& B#0?1 &% #$*0'.'0*)*#&$+ *,0 .&11#@#4#*5 &% )$

)$)451#1 &% '04)*#&$1 '0.'010$*#$2 ) /&(@#$)*#&$ &% #$%&'()*#&$ %'&( 7#%%0'0$*

.0'1.0/*#B01 /&(01 #$*& 1#2,*C

16This is a consequence of the V-shape relations underlying small triangles (cf. Sect.5.1.2).

17(1)1-(2)2, (2)2-(3)3, and (1)1-(3)3 do not represent an increase of categorical information

specific for q2, or q1; (2)1-(1)3, (3)1-(2)3, etc., do not represent a combined growth of categorical

information of q2and q1.


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189:). 33@ )$7 0%%0/*aB#0? #$*0'.'0*)*#&$ ;@>

U'P Z?="D.6)$# ).C).%.#="=8$#

8$ &'70' *& 0:.&10 &-' '04)*#&$1 )1 )$ 0:.'011#&$ &% #$%&'()*#&$ /&(@#$)*#&$+ ?0

&%%0' ) *')$1%&'()*#&$ *& &-' '0.'010$*)*#&$+ 70.#/*07 #$ G#2C OOC D0 #44-1*')*0

*,#1 %&' 1*)*0aB#0? #$*0'.'0*)*#&$+ 1,&?$ #$ G#2C OO;)>C Wa;O>X+ ;X> )$7 ;O>+ )1 ?044 )1 W )$7 X+

)'0 /)*02&'#/)445 7#%%0'0$*C =$ 0:)(.40 &% ) '04)*#&$ *,)* 7&01 $&* 1)*#1%5 &-'

$0071 #1 ;X>Wa;W>WC

=$ 0110$*#)4 040(0$* &% &-' *')$1%&'()*#&$ #1 ) /&(@#$)*#&$ &% #$%&'()*#&$

%'&( ) .)#' &% 1*)201 &% ) '04)*#&$ #$*& ) 1#$240 1*)20C =1 ) '01-4*+ *,0 0720

/&$$0/*#$2 *,0 *?& 1*)201 /)$ @0 '0(&B07C D0 #44-1*')*0 &-' *')$1%&'()*#&$ %&'

;X>Oa;O>W )$7 ;X>Wa;O>XC M,'&-2, (0'2#$2 *,0( #$*& ;O>W )$7 ;O>X+ '01.0/*#B045+

#$%&'()*#&$ 1,)'07 @5 *,0 '04)*#&$1 ;X>Oa;W>W )$7 ;X>Wa;W>W ()5 20* 4&1* ;/%C

information coordinated by (2)2). In order to keep the represented information

18A combination of information from different interpretations is meaningful for binary and ternary

relations only.


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#$B)'#)$*+ ?0 #$*'&7-/0 )$ #70$*#/)4 /&.5 &% ;W>W+ )1 1,&?$ #$ G#2C OW;)>COR

=1 ;O>O

)$7 ;X>X )'0 #$ '04)*#&$ ?#*, ;W>W+ *,0 '04)*#&$1 ;O>Oa;W>W )$7 ;W>Wa;X>X /)$ @0

'0.4)/07 @5 ;O>Oa@ABA)$7 @ABAa;X>XC = 1*0.?#10 *')$1%&'()*#&$ &% *,0 '04)*#&$1 #$

G#2C OO;)> #1 #44-1*')*07 @5 G#2C OW;@>a;7>C = *')$1%&'()*#&$ &% *,0 '04)*#&$1 #$

G#2C OO;@> #1 70.#/*07 #$ G#2C OXC

189:). 3L@= *')$1%&'()*#&$ &% '04)*#&$1 #$ 1*)*0aB#0? #$*0'.'0*)*#&$C 8$ ;)>;/>+

1*)201 )$7 07201 #$B&4B07 #$ (0'2#$2 )'0 2#B0$ #$ #*)4#/1+ )$7 @5 7&**07 4#$01+

'01.0/*#B045C 8$ ;7>+ B0'*#/01 )'0 4)@04407 @5 )$ 0:.'011#&$ &$ 1*)201c /&(@#$)*#&$

of information is designated by k C M,0 $-(@0' &% #$1*)$/01 &% ) 1*)20 /)$ @0

2#B0$ @5 ) 1-.0'1/'#.*+ %&' 0:)(.40+ ;W>XX[;X>O 701#2$)*01 ) /&(@#$)*#&$ &%

#$%&'()*#&$ %'&( X #$1*)$/01 &% ;W>X )$7 ) 1#$240 #$1*)$/0 &% ;X>OC l'05 1,)70 )$7

7&**07 4#$01 )'0 -107 %&' B#1-)4#V)*#&$ .-'.&101"

19A copy is required as coordination may refer to all information represented by (2)2. Note that

information is idempotent for addition. Stages involved in information combination are given in

italics, e.g., (2)2.


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189:). 3P@= *')$1%&'()*#&$ &% '04)*#&$1 #$ 0%%0/*aB#0? #$*0'.'0*)*#&$ ;)> #$*& )$

&/*),07'&$ ;@>

U'R QB?;8? 8#/$)Ok;O>X" O

;W>Xk;O>W" W

;X>Wk;O>X" X

;X>Ok;O>W>k;W>X" OfWfX

;W>Wk;W>Wk;W>Wk;W>W" WWWW

8$ *,0 /)10 &% #$70*0'(#$)*0 #$.-*+ *,0 #$*0'.'0*#$2 151*0( ()5 ,)B0 *&

/&$1#70' )44 .&11#@40 #$*0'.'0*)*#&$1+ &$0 @5 &$0+ #$ ) /5/4#/ %)1,#&$C 95/4#/

&.0')*#&$ /)$ @0 (&704407 @5 ()..#$2 *,0 B0'*#/01 &% *,0 &/*),07'&$ *& *,0

$&701 &% &-' K0?*&$#)$ (&704 &% )/*#&$'0)/*#&$ .,0$&(0$)C M,0 B0'*0:

labelled by 2*2*2*2 can be mapped to the node action+ @5 B#'*-0 &% *,0

(0)$#$2 &% ) .$*0' #$B&4B07 #$ 10/&$7$011 ;/%C W> )$7 *,0 .&*0$*#)4 &% *,0 $&70

action for a presentation of qualia of a (next) input phenomenon. The vertex

labelled by 1*2*3 can be mapped to the node reaction, by virtue of the


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29

/&(.40*0$011 &% *,#'7$011WP

and the potential of the node reaction to combine

#$%&'()*#&$ %'&( )44 *,'00 A-)4#*#01C M,0 &*,0' %&-' B0'*#/01 /)$ @0 ()..07 *&

*,0 %&-' $&701 &% &-' K0?*&$#)$ (&704+ )1 ?044 )1 *& 1*)201 &% AWdAO+ )1 %&44&?1C

300 )41& G#2C OSC

O" %="=.+ ;X>Oc )@1*')/* #$.-* 1*)*0+ '0.'010$*#$2 *,0 .&*0$*#)4 %&' ) '04)*#&$ ?#*,

)$5 0%%0/* ;/%C %#'1*$011>

W" %="=..//.?=+ ;X>Xc @#$7#$2+ @0*?00$ *,0 #$.-* 1*)*0 )$7 0%%0/*+ '0.'010$*#$2 )

'04)*#&$ ;/%C 10/&$7$011>

X" .//.?=+ ;O>Xc )@1*')/* #$.-* 0%%0/*+ '0.'010$*#$2 *,0 .&*0$*#)4 %&' ) ,)@#*-)4

'04)*#&$ ?#*, ) *5.0 &% #$.-* 1*)*0 ?,#/, #1 #$B&4B07 ;/%C *,#'7$011>

OfWfX" 8#C:=+ ;O>Oc #$.-* 1*)*0 )$7 0%%0/*+ '0.'010$*#$2 ) /&440/*#&$ &% A-)4#) ;/%C

'04)*#&$)4 .&*0$*#)4> &%%0'07 %&' #$*0'.'0*)*#&$C

189:). 3R@= '0/). &% &-' K0?*&$#)$ (&704 &% #$*0'.'0*)*#&$ ;)>+ /%C G#2C W;/>+ )$7

) /5/4#/ .'&/011 #$*0'.'0*)*#&$ &% *,0 &/*),07'&$ ;@>+ /%C G#2C OX ;?,#/, #1 /4&/Ea

?#10 '&*)*07 @5 RP&>C 8$ ;@>+ ) B0'*0: /)$ @0 4)@04407 @5 ) 1*)20 )$7 ) /)*02&'#/)4

*5.0 &% #$%&'()*#&$ 10.)')*07 @5 ) /&4&$ 15(@&4

H5 *')$1%&'(#$2 &-' '04)*#&$1 #$*& )$ &/*),07'&$ )$7 *,'&-2, ()E#$2 -10 &% *,0

()..#$2 )@&B0+ *,0 /-**#$2 .4)$0 &% *,0 &/*),07'&$ /)$ @0 #$*0'.'0*07 )1 )$

20Thirdness involves secondness and firstness.


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instance of matching mode operation. If the generated relations do not enable

this mode of operation, the interpreting system may switch to analysis mode, #$

order to generate other relations, by means of the interpreting systems

E$&?40720+ 0B0$*-)445 0$)@4#$2 ) ()*/,#$2 &% *,0 ;)-2(0$*07> #$.-* A-)4#)C

U'U S.;"=8$#% ).TC).%.#=.6

I-' ()..#$2+ 7#1.4)507 #$ G#2C OS;@>+ '0B0)41 *,0 .&11#@#4#*5 &% *,0 /-**#$2 .4)$0

of the next cycle to be primed by information from the previous cycle. It also

'0B0)41 *,0 .&*0$*#)4 &% *,#1 1*'-/*-'0 *& @0 #$*0'.'0*07 )1 )$ #$1*)$/0 &% AWdAOC

G&44&?#$2 &-' )$)451#1+ #$ 30/*C T+ AWdAO 0$)@401 ) '0.'010$*)*#&$ &% W_ 15$*)/*#/

1*'-/*-'01C =//&'7#$2 *& &-' K0?*&$#)$ (&704+ *,&10 1*'-/*-'01 (-1* @0 #$

relation with the nodes, action and reaction. From these premises we

/&$/4-70 *,)*+ *,'&-2, /&$1#70'#$2 '04)*#&$1 *& @0 0:.'011#&$1 &% #$%&'()*#&$

/&(@#$)*#&$+ *,0 &/*),07'&$ 1*'-/*-'0 /)$ @0 #$*0'.'0*07 )1 ) '0.'010$*)*#&$ &%

2*28 structures. By virtue of the potential of the nodes, action and reaction,

%&' ) '0.'010$*)*#&$ &% .'&.0'*#01 &% *,0 #$*0'.'0*#$2 151*0( #*104%+ *,&10

1*'-/*-'01 /)$ @0 /)4407 $,%('!#*1*'-/*-'01C

8$ 30/*C W ?0 ,)B0 1,&?$ *,)* &-' K0?*&$#)$ (&704 /)$ @0 #$*0'.'0*07 )1

) '0.'010$*)*#&$ &% '04)*#&$1 @0*?00$ *,0 *,'00 A-)4#*#01 #$B&4B07 #$ )/*#&$

reaction phenomena. The nodes action, and reaction, are an expression of this

'04)*#&$ )1 ) %#'1*$011+ )$7 ) *,#'7$011+ '01.0/*#B045c *,0 /-**#$2 .4)$0 )1 )

'0.'010$*)*#&$ &% *,0 1)(0 '04)*#&$ )1 ) 10/&$7$011C H5 B#'*-0 &% *,0

dependency between the cutting plane, and the nodes action, and reaction,

*,0 *?& 10*1 &% W_ 10()$*#/ 1*'-/*-'01 ;/%C WdW_> /)$ @0 1)#7 *& '0.'010$* )

relation between firstness and secondness (action/-**#$2 .4)$0>+ )$7 @0*?00$

10/&$7$011 )$7 *,#'7$011 ;/-**#$2 .4)$0reaction), respectively.

j)'4#0' ?0 '0.'010$*07 *0'$)'5 '04)*#&$1 @5 15$*)/*#/ 1*'-/*-'01 ;/%C *'#.401>+

#$ ?,#/, ) .&1#*#&$ #1 %#4407 @5 #$%&'()*#&$ %'&( ) 1#$240 .0'1.0/*#B0 &% AO ;/%C

%#'1*$011>C m)*0' ?0 #$*'&7-/07 ) '0.'010$*)*#&$ &% *0'$)'5 '04)*#&$1 @5 10()$*#/

1*'-/*-'01+ #$ ?,#/, ) .&1#*#&$ #1 %#4407 @5 #$%&'()*#&$ %'&( ) .)#' &% .0'1.0/*#B01


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&% AO ;/%C 10/&$7$011>C jB0$*-)445 ?0 70%#$0 ) *,#'7 *5.0 &% ;!-#()#*> *0'$)'5

'04)*#&$+ #$ ?,#/, ) .&1#*#&$ #1 70%#$07 @5 #$%&'()*#&$ %'&( )44 *,'00 .0'1.0/*#B01

&% AO. We assume that triadic (meaningful) ternary information structures are in

relation with the nodes actionand reaction, both. As a result we may extend

*,0 10* &% 10()$*#/ 1*'-/*-'01 @5 OP *'#)7#/ 1*'-/*-'01+ &$0 &% ?,#/, '0.'010$*#$2

the arising relation generated by the interpreting system.

M,0 $-(@0' &% 10()$*#/ 1*'-/*-'01 #1" WdW_fOPe NNC

189:). 3U@=$ &B0'B#0? &% *,0 *5.01 &% '04)*#&$ -107 @5 &-' (&704

8$ 1-(()'5+ '04)*#&$)4 #$%&'()*#&$ #1 '0.'010$*07 @5 &-' (&704 #$ *,'00 ?)51

;100 G#2C OT> @5 W_ 15$*)/*#/ 1*'-/*-'01 ;#$%&'()*#&$ %'&( ) 1#$240 '0.'010$*)*#&$

&% AO>+ WdW_ 10()$*#/ 1*'-/*-'01 ;#$%&'()*#&$ %'&( ) .)#' &% '0.'010$*)*#&$1 &%

AO>+ )$7 OP *'#)7#/ 1*'-/*-'01 ;#$%&'()*#&$ %'&( )44 *,'00 '0.'010$*)*#&$1 &% AO>C

M& *,#1 0$7+ ?0 #$*'&7-/07 *,'00 *5.01 &% '04)*#&$ ;-$)'5+ @#$)'5+ *0'$)'5>+ )$7

?#*,#$ *,)* /4)11#%#/)*#&$ ?0 ()70 ) 7#1*#$/*#&$ @0*?00$ *,'00 *5.01 &%

'0.'010$*)*#&$C c '04)*#&$1 &% *,0

10/&$7 *5.0 )'0 )$ 0:.'011#&$ &% ) /&(@#$)*#&$ &% #$%&'()*#&$ %'&( ) .)#' &%

/)*02&'#01 ;/%C @#$)'5 )$7 *0'$)'5 '04)*#&$1>c '04)*#&$1 &% *,0 *,#'7 *5.0 '0.'010$*

) (0'2#$2 &% #$%&'()*#&$ %'&( )44 *,'00 /)*02&'#01 ;/%C *0'$)'5 '04)*#&$1>C K&*0

*,)* -$)'5 '04)*#&$1 ,)B0 ) 1#$240 *5.0+ @#$)'5 '04)*#&$1 *?& *5.01+ )$7 *0'$)'5

'04)*#&$1 ,)B0 *,'00 *5.01C


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=$ #$*0'01*#$2 .'&.0'*5 &% AOdAO #1 *,)* #*1 $-(@0' &% 040(0$*1 #1 OW+

0$)@4#$2 ) 70%#$#*#&$ &% \\ .)#'1 ;/%C @#$)'5 '04)*#&$1>CWO

M,#1 ()5 @0 /&$1#70'07 *&

@0 )$ 0:.'011#&$ &% *,0 .&*0$*#)4 &% AOdAW %&' )5&-%(1'0.'010$*)*#&$ &% )/*#&$

'0)/*#&$ .,0$&(0$)C

= '0.'010$*)*#&$ &% %,('#'/571#$*0'.'0*)*#&$ #1 @05&$7 &-' .&11#@#4#*#01C 8$

4#$0 ?#*, 60#'/0)$ 10(#&*#/1+ ?0 )11-(0 *,)* #$*0'.'0*)*#&$WW

#$B&4B01 )$

#''07-/#@40 *'#)7#/ '04)*#&$ @0*?00$ *,0 *,'00 A-)4#*#01 &% )/*#&$'0)/*#&$

phenomena. This may explain why triadic (meaningful) ternary relations have

@00$ #$*'&7-/07 )1 ) 1-@10* &% 10()$*#/ '04)*#&$1C

N >.8)?."# %89# ).;"=8$#%

M,0 2&)4 &% *,#1 10/*#&$ #1 *& 1,&? *,)* &-' (&704 &% )/*#&$'0)/*#&$ .,0$&(0$)

is congruent with Peirces theory of signs. To this end, we generalize the concept

&% )$ #$*0')/*#&$ #$ *,0 /&$/0.* &% ) 1#2$+ )$7 .'010$* )/*#&$'0)/*#&$

.,0$&(0$) )1 1#2$ #$*0'.'0*)*#&$ .'&/01101C

N'3 Q"=.9$)8.%I %89#%I "#6 %89# "%C.?=%

G-$7)(0$*)4 $&*#&$1 #$ 60#'/0)$ *,0&'5 )'0 ,#1 *,'00 /)*02&'#01 &% .,0$&(0$)"

%#'1*$011+ 10/&$7$011+ )$7 *,#'7$011C =$ 0:)(.40 &% *,0 *,'00 /)*02&'#01+ #$ *,0

7&()#$ &% 1#2$1+ #1 *,0 A-)4#*5 &% .)#$ ;%#'1*$011>+ *,0 '04)*#&$ &% .)#$ ?#*, #*1

&@L0/*+ 0C2C+ *&&*,)/,0 ;10/&$7$011>+ )$7 *,0 '04)*#&$ @0*?00$ .)#$ )$7 #*1

interpreting thought by some agent, e.g., call a dentist (thirdness).WX

H5 )$)45V#$2 ,#1 /&$/0.* &% ) 1#2$ )4&$2 /)*02&'#/)4 4#$01+ 60#'/0 /&$/4-707

*,)* )44 1#2$1 (-1* #$B&4B0 $#$0 1#2$ )1.0/*1C K&*0 *,)* 1#2$ )1.0/*1 )'0 7#%%0'0$*

%'&( 1#2$1C M,05 ()5 @0 /,)')/*0'#V07 )1 .&*0$*#)4 1#2$1+ *,)* )'0 @0/&(#$2 )

1#2$C M,#1 7#%%0'0$/0 @0*?00$ 1#2$1 )$7 1#2$ )1.0/*1 /)$ @0 #44-1*')*07 @5 *,0

.,0$&(0$&$ &% )..)'0$* (&*#&$ .0'/0.*#&$C 8$ *,#1 .,0$&(0$&$+ ) 10'#01 &%

21 =6622

From a semiotic perspective, interpretation is always meaningful.23

The relation of the sign with its interpretant involves the relation of the sign with its object.


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1*0)75 .#/*-'01 ;/%C 1#2$ )1.0/*> )'0 .'010$*07C =4*,&-2, 0)/, .#/*-'0 /)$ @0

(0)$#$2%-4 #$ #*104%+ /&(@#$07 *,05 /)$ @0 #$*0'.'0*07 )1 .)')(0*0'1 #$ *,0

0:.0'#0$/0 &% *,0 0$*#'0 10'#01 &% .#/*-'01 )1 (&*#&$ ;/%C 1#2$>C

M,0 $#$0 1#2$ )1.0/*1 /)$ @0 #$*'&7-/07 @5 ) *'#)7#/ ;1-@a>/4)11#%#/)*#&$ &%

the signs relations. We call the category of a suba/4)11 ) *(!,/&-#*(1 ($.,*!+ *,0

'04)*#&$ @0*?00$ 1-@a/4)1101 &% ) *'#)7 ) *(!,/&-#*(1 -,1(!#&'C H04&?+ ?0

introduce a sign aspectual characterization of the signs primary relations: the

'04)*#&$ &% *,0 1#2$ *& #*104%+ *& #*1 &@L0/*+ )$7 #*1 #$*0'.'0*)$*C =1 ) /&$10A-0$/0

&% *,0 75$)(#/)4 $)*-'0 &% 1-//011#&$1 &% 1#2$ )1.0/*1 ;/%C 1*0)75 .#/*-'01>+ ?0

#44-1*')*0 *,0( @5 (0)$1 &% 1#2$1 ;/%C (&*#&$>C D0 701#2$)*0 /)*02&'#01 @5

integers, e.g., firstness by 1, and categorical aspects by integers in parentheses,

0C2C *,0 )1.0/* &% %#'1tness by (1).

189:). 3N@ = 60#'/0)$ /4)11#%#/)*#&$ &% 1#2$ )1.0/*1 ;)> )$7 #*1 .'&/011

#$*0'.'0*)*#&$ ;@>C 8$ ;)>+ *,0 /)*02&'#/)4 )1.0/* )$7 /)*02&'5 &% ) 1#2$ )1.0/* #1

701#2$)*07 @5 ) .)#' &% #$*020'1+ 0C2C+ ;W>OC 8$ ;@>+ $0#2,@&'#$2 1#2$ )1.0/*1 )'0

/&$$0/*07 @5 ) ,&'#V&$*)4 0720C M,0 *5.01 &% #$*0'.'0*)*#&$ 0B0$*1 )'0 70.#/*07

&$ *,0 '#2,*a,)$7 1#70 &% *,#1 7#)2')(+ #$ #*)4#/1

= /4)11#%#/)*#&$ &% 1#2$ )1.0/*1 #$ *'#)71"


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O M,0 '04)*#&$ &% *,0 1#2$ *& #*104%" ;O> A-)4#1#2$+ ;W> 1#$1#2$+ ;X> 402#1#2$C jC2C+ *,0

.0'/0.*#&$ &% .)#$ )1 ;O> ) A-)4#*5+ ;W> )$ )/*-)4 0B0$* &//-''#$2 $&?+ )$7 ;X>

) ,)@#*-)4 %004#$2C

W M,0 '04)*#&$ &% *,0 1#2$ *& #*1 &@L0/*" ;O> #/&$#/)4+ ;W> #$70:#/)4+ ;X> 15(@&4#/C

jC2C+ .)#$ #$*0'.'0*07 )1 ;O> ) (0)1-'0 &% ) A-)4#*5+ ;W> ) .$*0' .$*#$2 *&

*,0 *00*,+ )$7 ;X> ) /&$B0$*#&$)4 /&$/0.* 1-/, )1 ) *&&*,)/,0C

X M,0 '04)*#&$ &% *,0 1#2$ *& #*1 #$*0'.'0*)$*" ;O> ',0()*#/+ ;W> 7#/0$*#/ &'

.'&.&1#*#&$)4+ ;X> )'2-(0$*)*#B0C jC2C+ *,0 .0'/0.*#&$ &% .)#$ )1 ;O> )$

abstract concept (cf. pain), (2) an actual existence of pain in the teeth, and

;X> ) .'0(#10 *,)* ?0 1,&-47 /)44 ) 70$*#1*C

M,0 %#'1* *'#)7 #$ *,0 )@&B0 /4)11#%#/)*#&$ '0%0'1 *& *,0 1#2$ #$ #*104% ,0$/0 *& )

/)*02&'5c *,0 10/&$7 )$7 *,#'7 *& ) '04)*#&$ #$B&4B07 #$ *,0 1#2$ ,0$/0 *& )

categorical aspect. On the basis of their category, Peirces nine sign aspects can

@0 )'')$207 #$ ) .)'*#)4 &'70' ;D)4*,0'+ ORYR>+ ;H0$10+ ORY\>C 300 G#2C O\;)>C

+ 0$)@401 *,0 70%#$#*#&$ &% )

()..#$2 %'&( &-' #$%&'()*#&$)4 /&$/0.*1 ;/%C G#2C X> *& 60#'/0)$ 1#2$ )1.0/*1C G&'

example, neutral (qualities in themselves) can be mapped to the sign aspect

qualisign, constituent (coa0:#1*0$* A-)4#*#01> *& *,0 1#2$ )1.0/* #/&$+WT

abstraction (abstract qualia) to the sign aspect rheme.

N'L >)$?.%%


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$0#2,@&'#$2 1#2$ )1.0/*1C M,#1 #1 70.#/*07 #$ G#2C O\;@>+ #$ ?,#/, $0#2,@&'#$2 1#2$

)1.0/*1 )'0 /&$$0/*07 @5 ) ,&'#V&$*)4 0720C

M,0 #$.-* &% *,#1 .'&/011 #1 70%#$07 @5 *,0 #$.-* A-)4#)+ #$*0'.'0*07 )1 )$

0:.'011#&$ &% *,0 A-)4#1#2$ 1#2$ )1.0/*CW\

M,'&-2, $&-!#'/ *,0 #$.-* #$*& )

/&440/*#&$ &% 1*)*0+ )$7 0%%0/* A-)4#)+ *,0 #$.-* A-)4#) )'0 #$*0'.'0*07 )1 )$

0:.'011#&$ &% *,0 #/&$ )$7 1#$1#2$ 1#2$ )1.0/*1+ '01.0/*#B045C H5 10.)')*#$2 *,0

*?& *5.01 &% A-)4#) %'&( &$0 )$&*,0'+ #$ (8$!-(*!#&'+ *,0 #$.-* A-)4#) )'0

#$*0'.'0*07 )1 )$ 0:.'011#&$ &% *,0 ',0(0 )$7 402#1#2$ 1#2$ )1.0/*1C 8$

*&%.1,%,'!(!#&'+ *,0 )@1*')/* 1*)*0 )$7 0%%0/* #1 )-2(0$*07 ?#*, #$70:#/)4

#$%&'()*#&$ @5 *,0 #$*0'.'0*#$2 151*0(+ 0$)@4#$2 )$ #$*0'.'0*)*#&$ &% *,0 #$.-*

A-)4#) )1 )$ 0:.'011#&$ &% *,0 7#/0$* )$7 15(@&4 1#2$ )1.0/*1C H5 (0'2#$2 *,0

4)1* *?& '0.'010$*)*#&$1+ #$ .-,)#*(!#&'+ *,0 #$.-* A-)4#) )'0 #$*0'.'0*07 )1 )$

0:.'011#&$ &% *,0 )'2-(0$* 1#2$ )1.0/*C

In the next section we delve into an analysis of Peirces theory of sign

'04)*#&$1 *,)* *,0(104B01 )'0 1#2$1+ $&* L-1* 1#2$ )1.0/*1C I-' 2&)4 #1 *& '0B0)4 *,0

.&*0$*#)4 &% &-' (&704 %&' )$ )1.0/*-)4 '0.'010$*)*#&$ &% *,010 (&'0 /&(.40:

$&*#&$1 &% *,0 1#2$ )1 ?044C

N'P 4D. %89# "% "# $*\.?=

='2-)@45 *,0 (&1* #(.&'*)$* .'&.0'*5 &% ) .'&/011 B#0? &% 1#2$ #$*0'.'0*)*#&$ #1

#*1 .&*0$*#)4 %&' /&$1#70'#$2 *,0 1#2$ *& @0 )$ &@L0/*C M,0 .&11#@#4#*5 &% *,#1

perspective complies with Peirces theory of interpretation, as it is pointed out

@5 B)$ H'00(0$ ;B)$ H'00(0$+ WPOW>C 60#'/0 ?'#*01 ;60#'/0+ ORRW+ ORR_>"WY

8* 100(1 @01* *& '02)'7 ) 1#2$ )1 ) 70*0'(#$)*#&$ &% ) A-)1#a(#$7c %&' #% ?0

'02)'7 #* )1 )$ &-*?)'7 &@L0/*+ )$7 )1 )77'011#$2 #*104% *& ) ,-()$ (#$7+

*,)* (#$7 (-1* %#'1* )..'0,0$7 #* )1 )$ &@L0/* #$ #*104%+ )$7 &$45 )%*0' *,)*

26This, and all other expressions by this process are representations of sign aspects involved in theinput interaction.27Vol. 2, p. 391, 1906.


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/&$1#70' #* #$ #*1 1#2$#%#/)$/0c )$7 *,0 4#E0 (-1* ,)..0$ #% *,0 1#2$ )77'01101

#*104% *& )$5 A-)1#a(#$7C 8* (-1* @02#$ @5 %&'(#$2 ) 70*0'(#$)*#&$ &% *,)*

A-)1#a(#$7+ )$7 $&*,#$2 ?#44 @0 4&1* @5 '02)'7#$2 *,)* 70*0'(#$)*#&$ )1 *,0

1#2$C

60#'/0 /4)11#%#07 *,0 1#2$#%#/)*#B0 0%%0/* &% ) 1#2$ #$ *,'00 *5.01+ ?,#/, ,0 /)4407

#((07#)*0+ 75$)(#/+ )$7 %#$)4 &' $&'()4 #$*0'.'0*)$*C [#1 /4)11#%#/)*#&$ #$7#/)*01

) 70B04&.(0$* #$ #$*0'.'0*)*#&$ )1 ) .'&/011 ;/%C 40B041>+ %'&( #((07#)*0+

*,'&-2, 75$)(#/+ *& %#$)4C 8$ *,#1 10/*#&$ ?0 1-2201* *,)* *,0 )@&B0 40B041 ()5

apply to the apprehension of the sign as an object (signaobject), as well. As,

%'&( )$ )$)45*#/)4 .0'1.0/*#B0+ *,0 '04)*#&$1 #$B&4B07 #$ *'#)7#/ 1#2$1 (-1* @0 )

'01-4* &% #$*0'.'0*)*#&$+ ?0 (-1* @0 )@40 *& /,)')/*0'#V0 *,&10 '04)*#&$1 %'&( *,0

.0'1.0/*#B0 &% *,0 *,'00 40B041 &% #$*0'.'0*)*#&$C

G&44&?#$2 &-' )11-(.*#&$ &% *,0 1#2$ *& @0 )$ &@L0/*+ *,0 %#'1*$011 &% *,0

relation of the sign to itself may be associated with the immediate

'0.'010$*)*#&$ ;O> &% *,0 1#2$ ;3>+ ;W> *,0 1#2$ &% *,0 #((07#)*0 &@L0/* ;8I> )$7

#((07#)*0 #$*0'.'0*)$* ;88>+ )$7 ;X> *,0 1#2$ &% *,0 75$)(#/ &@L0/* ;iI>+ 75$)(#/

#$*0'.'0*)$* ;i8>+ )$7 %#$)4 &' $&'()4 #$*0'.'0*)$* ;K8>CW_

M,0 10/&$7$011 &%

'0.'010$*)*#&$ &% *,0 '04)*#&$ &% *,0 1#2$ *& #*1 &@L0/* ()5 @0 )11&/#)*07 ?#*, *,0

more developed, dynamic representations by the interpreting system: by the

'04)*#&$ @0*?00$ *,0 1#2$ )$7 #*1 #((07#)*0 &@L0/* ;/%C 3iI>WR

)$7 @0*?00$ *,0

1#2$ )$7 #*1 #((07#)*0 ;/%C 3i8> )$7 75$)(#/ #$*0'.'0*)$* ;/%C 3K8>+ %&44&?#$2

#$%&'()*#&$ )-2(0$*)*#&$ &% *,0 8I+ 88+ )$7 i8+ '01.0/*#B045C G#$)445+ *,0 *,#'7$011

&% *,0 '04)*#&$ &% *,0 1#2$ *& #*1 &@L0/* )$7 #$*0'.'0*)$* ()5 @0 )11&/#)*07 ?#*,

the relation between the most developed, final representation of the sign,

&@L0/*+ )$7 #$*0'.'0*)$* ;/%C 3K8iI>+ %&44&?#$2 ) ;%#$)4> #$%&'()*#&$

)-2(0$*)*#&$ &% *,0 iI )$7 i8C

28The normal interpretant (NI) is the tendency of the final interpretant towards its limit. In this

paper the two types of interpretant are used interchangeably.29

Following the above process view of interpretation, SDO is a representation of the IO,

following information augmentation mediated by S.


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=$ 0:)(.40 &% %#'1*$011 1#2$ '04)*#&$1 #1 *,0 .,0$&(0$&$ *&&*,)/,0+

1#2$#%#07 @5 -$1&'*07 A-)4#) &% ) 10$1)*#&$ &% .)#$ ;3>C ]#) #$*0'.'0*)*#&$ ?0 ()5

20$0')*0 ) *hought sign, e.g., toothache (II), as a response on the perceived

#$.-* A-)4#)C H5 1&'*#$2 *,0 #$.-* #$ ) %&'( )$7 0B0$*+ ?0 ()5 /&$/4-70 *,)* *,0

.0'/0#B07 A-)4#) 1*)$7 %&' .)#$ #$ *,0 70$*)4 )'0) ;8I>C I-' %#'1* &' #((07#)*0

#$*0'.'0*)$* ()5 *'#220' (&'0 '01.&$101 1-/, )1 ) (&*&' '0)/*#&$ &' )$

#$*0'.'0*#$2 *,&-2,* ;i8>+ @5 (0)$1 &% E$&?40720 @5 *,0 #$*0'.'0*#$2 151*0(

(observer). Examples are toothache, call a dentist, make an appointment,

take an analgesic, etc., representing increasingly more 70B04&.07 '01.&$101

;i81> &$ *,0 #$.-* 1#2$C M,0 *0$70$/5 &% *,010 '01.&$101 ;K8> /)$ @0 .)').,')107

by the interpretant stay calm, do what is necessary, e.g. take medication,

consult a dentistC

D0 1-2201* *,)* *,0 )@&B0 #$*0'.'0*)*#&$ &% *,0 60#'/0)$ 1#2$ '04)*#&$1

;60#'/0+ O_\TORPR> /)$ @0 -107 %&' *,0 #$*'&7-/*#&$ &% )$ )1.0/*-)4

representation of those relations. In the next section we show that Peirces sign

'04)*#&$1 /)$ @0 ()..07 *& /)*02&'#/)4 '04)*#&$1 @0*?00$ 1#2$ )1.0/*1+ )1 ?044 )1

*& '04)*#&$1 #$B&4B07 @5 *,0 &/*),07'&$ 1*'-/*-'0+ #$/4-7#$2 #*1 .'&/011

#$*0'.'0*)*#&$C

N'R A ).C).%.#="=8$# $/ %89# ).;"=8$#%

M,0 OP '04)*#&$1 &% *,0 1#2$+ *,)* )'0 *,0(104B01 1#2$+ )'0" 3+ 8I+ iI+ 88+ i8+ K8+ 3

iI+ 3i8+ 3K8+ 3K8iIC =$ #$*0'.'0*)*#&$ &% *,010+ (&'0 /&(.40: $&*#&$1 &%

*,0 1#2$ '0A-#'01 /5/4#/ .'&/011#$2C M& *,#1 0$7 ?0 ()E0 -10 &% ) '01-4* %'&(

;3)'@& 0* )4C+ WPOO>+ .'&B#$2 *,)* .'&/011#$2 &% ) 1#$240 1#2$+ )$7 ) 10'#01 &% 1#2$1

/)$ @0 (&70407 #$ )$ #1&(&'.,#/ %)1,#&$C M,0 /5/401 0$)@407 @5 ) .'&/011+ *,)*

,)1 *,'00 *5.01+ %#'1* &' #$#*#)4+ #$*0'(07#)*0+ )$7 %#$)4+ /)$ @0 )11&/#)*07 ?#*, *,0

*,'00 40B041 &% #$*0'.'0*)*#&$+ #((07#)*0+ 75$)(#/+ )$7 %#$)4+ '01.0/*#B045C H04&?

?0 '0B#1#* &-' .'&/011 (&704+ 70.#/*07 #$ G#2C O\;@>+ #$ &'70' *& '0B0)4 #*1

.&*0$*#)4 %&' )$ )1.0/*-)4 '0.'010$*)*#&$ &% *,0 OP '04)*#&$1 &% *,0 1#2$C D0 '0%0'


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*& 1#2$ )1.0/*1 @5 (0)$1 &% *,0#' 60#'/0)$ *0'(+ %&' 0:)(.40+ *,0 A-)4#1#2$ 1#2$

aspect by the term qualisign.

D0 @02#$ &-' )$)451#1 ?#*, *,0 %#'1* 0B0$* #$ 1#2$ .'&/011#$2+ ?,#/, #1 *,0

70%#$#*#&$ &% *,0 #$.-* %&' .'&/011#$2C =1 ) /&$10A-0$/0 &% *,0 .&11#@#4#*5 &% *,0

1#2$ *& @0 )$ &@L0/*+ *,0 '0.'010$*)*#&$ &% *,0 #$.-* @5 *,0 A-)4#1#2$ 1#2$ )1.0/*

;3> (-1* @0 )$ 0:.'011#&$ &% *,0 #((07#)*0 &@L0/* &% #$*0'.'0*)*#&$ ;8I>+ )1 ?044C

300 G#2C OYC

189:). 3X@ 3#2$ '04)*#&$1 ()..07 *& /)*02&'#/)4 '04)*#&$1 @0*?00$ 1#2$ )1.0/*1+

)$7 *& '04)*#&$1 @0*?00$ 1*)201 &% AWdAOC G&' #$1*)$/0+ 8I /)$ @0 ()..07 *& )

'04)*#&$ @0*?00$ ',0(0+ #/&$+ )$7 A-)4#1#2$+ )$7 *& *,0 '04)*#&$ ;X>Oa;W>Oa;O>OC

8$ $&-!#'/+ *,0 '0.'010$*)*#&$ &% ) '04)*#&$ @0*?00$ *,0 #$.-* 1*)*0 )$7 0%%0/*+ @5

*,0 1#$1#2$ 1#2$ )1.0/* ;3>+ #1 )41& )$ 0:.'011#&$ &% *,0 0B0$* #$B&4B07 #$ *,0

#((07#)*0 #$*0'.'0*)$* ;88>C =$ 0:.'011#&$ &% *,0 )@&B0 '04)*#&$+ *,#1 *#(0 %'&(

*,0 .0'1.0/*#B0 &% /&$1*#*-0$/5+ @5 *,0 #/&$ 1#2$ )1.0/*+ )(&-$*1 *& ) (&'0

70B04&.07 0:.'011#&$ &% *,0 1#2$a&@L0/* ;8I>+ )1 ?044 )1 ) '0.'010$*)*#&$ &% *,0

#$#*#)4 B)4-0 &% #$%&'()*#&$ )-2(0$*)*#&$ ;3aiI>C G#$)445+ *,0 '0.'010$*)*#&$ &%

*,0 )@&B0 '04)*#&$ @5 *,0 #$70: 1#2$ )1.0/*+ )1 ) .$*0' *& /&(.40(0$*)'5

#$%&'()*#&$ )@&-* *,0 #$.-* 1*)*0 )$7 0%%0/*+ #1 )41& )$ 0:.'011#&$ &% )

70B04&.(0$* #$ *,0 .'&/011 &% #$%&'()*#&$ )-2(0$*)*#&$+ @&*, )1 ) B)4-0 ;3

iI>+ )$7 )$ 0B0$* ;88>C

8$ (8$!-(*!#&'+ *,0 #$.-* 1#2$ #1 '0.'010$*07 @5 *,0 402#1#2$ 1#2$ )1.0/*+

?,#/, #1 )41& )$ 0:.'011#&$ &% *,0 #$#*#)4 B)4-0 #$ *,0 .'&/011 &% #$%&'()*#&$


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)-2(0$*)*#&$ &% *,0 ,)@#*-)4 '04)*#&$ #$B&4B07 #$ *,0 #$.-* 1#2$ ;iI>C =

'0.'010$*)*#&$ &% *,0 #$.-* @5 *,0 ',0(0 1#2$ )1.0/*+ #1 )$ 0:.'011#&$ &% *,0

1#2$a&@L0/* )1 )$ )@1*')/* 1*)*0 ;8I>C M,#1 1*)*0 @0#$2 *,0 1-@L0/* &%

#$*0'.'0*)*#&$+ *,0 ',0(0 #1 )41& )$ 0:.'011#&$ &% *,0 #$#*#)4 B)4-0 &% *,)* .'&/011

;3K8>C

8$ *&%.1,%,'!(!#&'+ *,0 '0.'010$*)*#&$ &% *,0 1#2$a&@L0/* #1 )-2(0$*07

%'&( #((07#)*0 *& 7ynamical. This is witnessed by a representation of the signs

&@L0/* ;/%C 402#1#2$c iI> )$7 #$*0'.'0*)$* ;/%C ',0(0c 3K8>C 8% *,0 /-''0$*

.'&/011#$2 /5/40 #1 ) %#$)4 &$0+ *,0 )@&B0 '0.'010$*)*#&$ &% *,0 #$*0'.'0*)$* /)$

@0 -107 )1 ) '0.'010$*)*#&$ &% *,0 %#$)4 &' $&'()4 #$*0'.'0*)$* ;3K8>c &*,0'?#10+

(&'0 /5/40;1> ()5 @0 '0A-#'07 ,0$/0 *,)* '0.'010$*)*#&$ (-1* @0 )$ 0:.'011#&$

&% *,0 75$)(#/ #$*0'.'0*)$* ;3i8>C

8$ .-,)#*(!#&'+ )-2(0$*07 '0.'010$*)*#&$1 &% *,0 1#2$a&@L0/* ;3K8+ iI>

)'0 /&(@#$07 #$*& ) 1#$240 '0.'010$*)*#&$C M,#1 #1 0:.'01107 )1 *,0 %#$)4 #$.-*

'0.'010$*)*#&$ ;3K8iI>+ #% *,0 /-''0$* /5/40 #1 ) %#$)4 &$0C 8% #* #1 $&*+ *,0 )@&B0

'0.'010$*)*#&$ #1 &%%0'07 )1 #$.-* %&' %-'*,0' .'&/011#$2 @5 *,0 $0:* /5/40 ;3

i8>CXP

= ()..#$2 &% *,0 '0()#$#$2 %&-' '04)*#&$1 ;i8+ 3K8+ K8+ 3K8iI> *&

B0'*#/01 &% *,0 &/*),07'&$ /)$ @0 70%#$07 )1 %&44&?1C 8% *,0 /-''0$* /5/40 #1 $&*

*,0 %#$)4 &$0 ;#C0C+ %-'*,0' .'&/011#$2 #1 '0A-#'07>+ *,0 /-''0$* )-2(0$*)*#&$ &%

*,0 #$*0'.'0*)$* ;3i8> ()5 @0/&(0 ) 1#2$a&@L0/* ;/%C A-)4#1#2$> #$ *,0 $0:* /5/40+

#$ &'70' %&' ) 20$0')*#&$ &% *,0 %#$)4 #$*0'.'0*)$* ;3K8>C I*,0'?#10+ *,0 1#2$a

&@L0/* (-1* #$B&4B0 #$%&'()*#&$ )@&-* ) %#$)4 )..'&:#()*#&$ &% *,0 0:.'011#&$ &%

*,0 75$)(#/ #$*0'.'0*)$*C M,#1 #$%&'()*#&$ /)$ @0 '0.'010$*07 )1 )$ )@1*')/*

state, by the rheme sign aspect (DI), and as ) habitual event, by the legisign

1#2$ )1.0/* ;K8>C M,0 .'&/011 ()5 *0'(#$)*0+ @5 20$0')*#$2 ) '0.'010$*)*#&$ &%

*,0 '04)*#&$ @0*?00$ *,0 1#2$+ #*1 &@L0/*+ )$7 #$*0'.'0*)$*+ %&44&?#$2 ;) %#$)4>

#$%&'()*#&$ )-2(0$*)*#&$ ;3K8iI>C

30In the SDI, the DO is involved.


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=//&'7#$2 *& *,0 )@&B0 )$)451#1+ *,0 '04)*#&$1+ i8+ 3K8+ K8+ 3K8iI+ /)$

be mapped to a single sign aspect of Peirces classification, as well as to a single

$&70 &% *,0 /-**#$2 .4)$0 &% *,0 &/*),07'&$C M,0 )@&B0 ()..#$2 /)$ @0

0:*0$707 *& ) /)*02&'#/)4 '04)*#&$C M& *,#1 0$7 ?0 &@10'B0 *,)*+ @5 B#'*-0 &% *,0

#$B&4B0(0$* &% *,0 )@&B0 %&-' '04)*#&$1 #$ *,0 #$%&'()*#&$ )-2(0$*)*#&$

.'&/011+ *,&10 '04)*#&$1 ()5 '0.'010$* .'&.0'*#01 &% *,0 #$*0'.'0*#$2 151*0(

#*104%C D0 )41& $&*#/0 *,)* *,0 &/*),07'&$ ()5 '0.'010$* '04)*#&$1 #$B&4B07 #$

)/*#&$reaction phenomena in three ways: as a firstness (cf. action), a

secondness (cf. cutting plane), and a thirdness (cf. reaction). From this, we may

/&$/4-70 *,)* ) /)*02&'#/)4 '04)*#&$ &% *,0 )@&B0 %&-' $&*#&$1 /)$ @0 70%#$07 @5

/&(.40*#$2 *,0#' ()..#$2 @5 ) %#'1* )$7 ) *,#'7 040(0$*+ '0.'010$*07 @5 *,0

nodes action, and reaction, respectively. See Fig.O_C

M,#1 /&(.40*01 &-' )$)451#1 &% ) '04)*#&$ @0*?00$ ) K0?*&$#)$ (&704 &%

)/*#&$reaction phenomena and Peirces theory of signs. Our model is restricted

*& '04)*#&$)4 #$*0'.'0*)*#&$ ;/%C 10/&$7$011>C = '0.'010$*)*#&$ &% 1#2$

#$*0'.'0*)*#&$ )1 ) %#'1*$011+ )$7 ) *,#'7$011 )'0 @05&$7 &-' 1/&.0CXO

189:). 3M@ = ()..#$2 &% i8+ 3i8+ K8+ 3K8iI+ *& '04)*#&$1 &% *,0 &/*),07'&$+

0C2C+ 3DI is mapped to the relation actionA-)4#1#2$reaction

31Through representing the relation involved in firstness and thirdness, by a single node, the

octahedron may be conceived to be a representation of the lattice multiplication q3*q2*q1.


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X (:


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H0$10+ ZC ORY\C i)1 351*0( 70' M,0&'0*#1/,0$ 30(#&*#EC :,%#&$#$;O>+ WSW_C

H#'E,&%%+ lC+ Q H)'*00+ MC ORYPC G&),-' (..1#,) (1/,8-(C K0? n&'E" Z/l')?a[#44C

H-'/,+ C j7#$@-'2, J$#B0'1#*5 6'011C

K0?*&$+ 8C ORRR^O\_YC C", I-#'*#.#(C H0'E0405" J$#B0'1#*5 &% 9)4#%&'$#) 6'011C

60#'/0+ 9C O_\TORPRC ;&/#* L&!,8&&=C [&-2,*&$ m#@')'5+ [)'B)'7 -$#B0'1#*5"

J$.-@4#1,07 ()$-1/'#.* &$ (#/'&%#4(C

60#'/0+ 9C ORXWC D&11,*!,) .(.,-$ &5 D"(-1,$ :('),-$ I,#-*,C 9)(@'#720" [)'B)'7

J$#B0'1#*5 6'011C

60#'/0+ 9C ORRW+ ORR_C C", M$$,'!#(1 I,#-*,J :,1,*!,) I"#1&$&."#*(1 E-#!#'/$N A

3&17%,$C H4&&(#$2*&$" 60#'/0 j7#*#&$ 6'&L0/*+ 8$7#)$) J$#B0'1#*5 6'011C

3)$70'1+ lC ORYP. Peirces sixtya1#: 1#2$1F C-('$(*!#&'$ &5 !", D"(-1,$ :F I,#-*,

:&*#,!++ \ ;O>+ XO\C

3)'@&+ `C ORR\C m)**#/0 0(@077#$2C 8$ 6C jE4-$7+ lC j44#1+ Q lC Z)$$ ;j71C>+

Conceptual structures: Knowledge representation as interlingua (ICCS96)

;]&4C OOOT+ ..C WRXXPY>C

3)'@&+ `C+ G)'E)1+ `C+ Q B)$ H'00(0$+ =C WPOOC O'&41,)/, #' P&-%(!#&'J Q

D&%.7!(!#&'(1 C",&-+ &5 H'!,-.-,!(!#&'C H0'4#$" 3.'#$20' ;0H&&E"

,**."^^7:C7C&'2^OPCOPPY^RY_aXa\SWaOYP_Ra_>C

B)$ H'00(0$+ =C WPOWC O'&41,)/, #' P&-%(!#&'J C", I,#-*,('N $,%#&!#*

8(*=/-&7')C C


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]#*)$5#+ 6C WPP\C Z0)$#$2%-4 #$%&'()*#&$C HMMM C-('$(*!#&'$ &' H'5&-%(!#&'

C",&-++ TW ;OP>+ S\OYS\W\C

D)4*,0'+ jC ORYRC Allgemeine Zeichenlehre: Einf rung in die Grundlagen de

:,%#&!#=C 3*-**2)'*" i0-*/,0 ]0'4)21a=$1*)4*C

D0#11+ 6C+ Q H-'E1+ =C ORST. Peirces sixtya1#: 1#2$1C C", R&7-'(1 &5 I"#1&$&."++ KA

;OS>+ X_XX__C

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