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Directory:Jon Awbrey/Papers/Inquiry Driven Systems : Part 6 (view source)

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For the domain <math>S = I = \{ {}^{\backprime\backprime} \text{A} {}^{\prime\prime}, {}^{\backprime\backprime} \text{B} {}^{\prime\prime}, {}^{\backprime\backprime} \text{i} {}^{\prime\prime}, {}^{\backprime\backprime} \text{u} {}^{\prime\prime} \}\!</math> of four elements one needs to use two logical features.  One possibility is to classify each element according to its syntactic category, as being a noun or a pronoun, and according to its semantic category, as denoting the self or the other.
 
For the domain <math>S = I = \{ {}^{\backprime\backprime} \text{A} {}^{\prime\prime}, {}^{\backprime\backprime} \text{B} {}^{\prime\prime}, {}^{\backprime\backprime} \text{i} {}^{\prime\prime}, {}^{\backprime\backprime} \text{u} {}^{\prime\prime} \}\!</math> of four elements one needs to use two logical features.  One possibility is to classify each element according to its syntactic category, as being a noun or a pronoun, and according to its semantic category, as denoting the self or the other.
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Tables&nbsp;62.1, 62.2, and 62.3 show several ways of representing these categories in terms of feature-value pairs and propositional codes.  In each Table, Column&nbsp;1 describes the category in question, Column&nbsp;2 gives the mnemonic form of a propositional expression for that category, and Column&nbsp;3 gives the abbreviated form of that expression, using a notation for propositional calculus where parentheses circumscribing a term or expression are interpreted as forming its logical negation.
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Tables 62.1 through 62.3 show several ways of representing these categories in terms of feature value pairs and propositional codes.  In each Table, Column 1 describes the category in question, Column 2 gives the mnemonic form of a propositional expression for that category, and Column 3 gives the abbreviated form of that expression, using a notation for propositional calculus where parentheses circumscribing a term or expression are interpreted as forming its logical negation.
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Table 62.1  Analytic Codes for Object Features  
 
Table 62.1  Analytic Codes for Object Features  
 
Category Mnemonic Code  
 
Category Mnemonic Code  
 
  Self self s
 
  Self self s
−
  Other (self) (s)  
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  Other (self) (s)
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<pre>
 
Table 62.2  Analytic Codes for Semantic Features  
 
Table 62.2  Analytic Codes for Semantic Features  
 
Category Mnemonic Code  
 
Category Mnemonic Code  
 
  1st Person my m
 
  1st Person my m
 
  2nd Person (my) (m)  
 
  2nd Person (my) (m)  
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<pre>
 
Table 62.3  Analytic Codes for Syntactic Features  
 
Table 62.3  Analytic Codes for Syntactic Features  
 
Category Mnemonic Code  
 
Category Mnemonic Code  
 
  Noun name n
 
  Noun name n
 
  Pronoun (name) (n)  
 
  Pronoun (name) (n)  
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Tables 63 and 64 list the codes for each element of the world domain W = { A, B, "A", "B", "i", "u"}, giving all features relative to the interpreters A and B, respectively.  
 
Tables 63 and 64 list the codes for each element of the world domain W = { A, B, "A", "B", "i", "u"}, giving all features relative to the interpreters A and B, respectively.  
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Table 63.  Analytic Codes for Interpreter A  
 
Table 63.  Analytic Codes for Interpreter A  
 
Name Vector Conjunct Mnemonic Code  
 
Name Vector Conjunct Mnemonic Code  
Line 6,772: Line 6,790:  
"i" 10Y y1 (y2) my (name) m (n)
 
"i" 10Y y1 (y2) my (name) m (n)
 
"u" 00Y (y1)(y2) (my)(name) (m)(n)  
 
"u" 00Y (y1)(y2) (my)(name) (m)(n)  
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Table 64.  Analytic Codes for Interpreter B  
 
Table 64.  Analytic Codes for Interpreter B  
 
Name Vector Conjunct Mnemonic Code  
 
Name Vector Conjunct Mnemonic Code  
Line 6,781: Line 6,803:  
"i" 10Y y1 (y2) my (name) m (n)
 
"i" 10Y y1 (y2) my (name) m (n)
 
"u" 00Y (y1)(y2) (my)(name) (m)(n)  
 
"u" 00Y (y1)(y2) (my)(name) (m)(n)  
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Tables 65.1 and 66.1 transcribe the sign relations A and B, respectively, into the forms of the AIR just suggested.  Tables 65.2 and 66.2 extract the denotative components of A and B, respectively, and isolate the transitions from signs to objects as ordered pairs of the form <s, o>.  Tables 65.3 and 66.3 extract the connotative components of A and B, respectively, and represent the transitions from signs to interpretants in terms of differential features, in other words, as propositions in the differential extension of the syntactic domain.  
 
Tables 65.1 and 66.1 transcribe the sign relations A and B, respectively, into the forms of the AIR just suggested.  Tables 65.2 and 66.2 extract the denotative components of A and B, respectively, and isolate the transitions from signs to objects as ordered pairs of the form <s, o>.  Tables 65.3 and 66.3 extract the connotative components of A and B, respectively, and represent the transitions from signs to interpretants in terms of differential features, in other words, as propositions in the differential extension of the syntactic domain.  
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Table 65.1  AIR1 (A):  Analytic Representation of A  
 
Table 65.1  AIR1 (A):  Analytic Representation of A  
 
Object Sign Interpretant  
 
Object Sign Interpretant  
Line 6,794: Line 6,824:  
(s) (m)(n) (m) n  
 
(s) (m)(n) (m) n  
 
(s) (m)(n) (m)(n)  
 
(s) (m)(n) (m)(n)  
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Table 65.2  AIR1 (Den A):  Denotative Component of A  
 
Table 65.2  AIR1 (Den A):  Denotative Component of A  
 
Object Sign Transition  
 
Object Sign Transition  
Line 6,801: Line 6,835:  
(s) (m) n <(m) n , (s)>
 
(s) (m) n <(m) n , (s)>
 
(s) (m)(n) <(m)(n), (s)>  
 
(s) (m)(n) <(m)(n), (s)>  
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</pre>
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Table 65.3  AIR1 (Con A):  Connotative Component of A  
 
Table 65.3  AIR1 (Con A):  Connotative Component of A  
 
Sign Interpretant Transition  
 
Sign Interpretant Transition  
Line 6,812: Line 6,850:  
(m)(n) (m) n (dm) dn  
 
(m)(n) (m) n (dm) dn  
 
(m)(n) (m)(n) (dm)(dn)  
 
(m)(n) (m)(n) (dm)(dn)  
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</pre>
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<pre>
 
Table 66.1  AIR1 (B):  Analytic Representation of B  
 
Table 66.1  AIR1 (B):  Analytic Representation of B  
 
Object Sign Interpretant  
 
Object Sign Interpretant  
Line 6,823: Line 6,865:  
s m (n) m  n  
 
s m (n) m  n  
 
s m (n) m (n)   
 
s m (n) m (n)   
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</pre>
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Table 66.2  AIR1 (Den B):  Denotative Component of B  
 
Table 66.2  AIR1 (Den B):  Denotative Component of B  
 
Object Sign Transition  
 
Object Sign Transition  
Line 6,830: Line 6,876:  
s m  n < m  n ,  s >
 
s m  n < m  n ,  s >
 
s m (n) < m (n),  s >  
 
s m (n) < m (n),  s >  
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</pre>
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Table 66.3  AIR1 (Con B):  Connotative Component of B  
 
Table 66.3  AIR1 (Con B):  Connotative Component of B  
 
Sign Interpretant Transition  
 
Sign Interpretant Transition  
Line 6,841: Line 6,891:  
m (n) m  n (dm) dn  
 
m (n) m  n (dm) dn  
 
m (n) m (n) (dm)(dn)  
 
m (n) m (n) (dm)(dn)  
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</pre>
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<br>
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<pre>
 
Table 67.1  AIR2 (A):  Analytic Representation of A  
 
Table 67.1  AIR2 (A):  Analytic Representation of A  
 
Object Sign Interpretant  
 
Object Sign Interpretant  
Line 6,852: Line 6,906:  
<!>X <!>Y <n>Y
 
<!>X <!>Y <n>Y
 
<!>X <!>Y <!>Y  
 
<!>X <!>Y <!>Y  
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</pre>
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<pre>
 
Table 67.2  AIR2 (Den A):  Denotative Component of A  
 
Table 67.2  AIR2 (Den A):  Denotative Component of A  
 
Object Sign Transition  
 
Object Sign Transition  
Line 6,859: Line 6,917:  
<!>X <n>Y <<n>Y, <!>X>
 
<!>X <n>Y <<n>Y, <!>X>
 
<!>X <!>Y <<!>Y, <!>X>  
 
<!>X <!>Y <<!>Y, <!>X>  
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</pre>
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<br>
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<pre>
 
Table 67.3  AIR2 (Con A):  Connotative Component of A  
 
Table 67.3  AIR2 (Con A):  Connotative Component of A  
 
Sign Interpretant Transition  
 
Sign Interpretant Transition  
Line 6,870: Line 6,932:  
<!>Y <n>Y <dn>dY
 
<!>Y <n>Y <dn>dY
 
<!>Y <!>Y <d!>dY  
 
<!>Y <!>Y <d!>dY  
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</pre>
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<br>
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<pre>
 
Table 68.1  AIR2 (B):  Analytic Representation of B  
 
Table 68.1  AIR2 (B):  Analytic Representation of B  
 
Object Sign Interpretant  
 
Object Sign Interpretant  
Line 6,881: Line 6,947:  
<*>X <m>Y <*>Y
 
<*>X <m>Y <*>Y
 
<*>X <m>Y <m>Y  
 
<*>X <m>Y <m>Y  
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</pre>
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<br>
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<pre>
 
Table 68.2  AIR2 (Den B):  Denotative Component of B  
 
Table 68.2  AIR2 (Den B):  Denotative Component of B  
 
Object Sign Transition  
 
Object Sign Transition  
Line 6,888: Line 6,958:  
<*>X <*>Y <<*>Y, <*>X>
 
<*>X <*>Y <<*>Y, <*>X>
 
<*>X <m>Y <<m>Y, <*>X>  
 
<*>X <m>Y <<m>Y, <*>X>  
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</pre>
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<br>
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<pre>
 
Table 68.3  AIR2 (Con B):  Connotative Component of B  
 
Table 68.3  AIR2 (Con B):  Connotative Component of B  
 
Sign Interpretant Transition  
 
Sign Interpretant Transition  
Jon Awbrey
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