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Directory:Jon Awbrey/Papers/Inquiry Driven Systems (view source)
Revision as of 19:04, 17 December 2008
, 19:04, 17 December 2008→1.3.4.14. Application of OF : Generic Level: reset formula display as TeX array
\text{For Icons:} &
\text{For Icons:} &
\operatorname{Sign} (\operatorname{Obj}) & = &
\operatorname{Sign} (\operatorname{Obj}) & = &
\operatorname{Inst} (\operatorname{Prop} (\operatorname{Obj})), \\
\operatorname{Inst} (\operatorname{Prop} (\operatorname{Obj})) \\
\text{For Indices:} &
\text{For Indices:} &
\operatorname{Sign} (\operatorname{Obj}) & = &
\operatorname{Sign} (\operatorname{Obj}) & = &
\operatorname{Prop} (\operatorname{Inst} (\operatorname{Obj})). \\
\operatorname{Prop} (\operatorname{Inst} (\operatorname{Obj})) \\
\end{array}</math>
\end{array}</math>
|}
|}
\text{For Icons:} &
\text{For Icons:} &
\operatorname{Obj} (\operatorname{Sign}) & = &
\operatorname{Obj} (\operatorname{Sign}) & = &
\operatorname{Inst} (\operatorname{Prop} (\operatorname{Sign})), \\
\operatorname{Inst} (\operatorname{Prop} (\operatorname{Sign})) \\
\text{For Indices:} &
\text{For Indices:} &
\operatorname{Obj} (\operatorname{Sign}) & = &
\operatorname{Obj} (\operatorname{Sign}) & = &
\operatorname{Prop} (\operatorname{Inst} (\operatorname{Sign})). \\
\operatorname{Prop} (\operatorname{Inst} (\operatorname{Sign})) \\
\end{array}</math>
\end{array}</math>
|}
|}
|
|
<math>\begin{array}{lllllll}
<math>\begin{array}{lllllll}
x \lessdot & = &
x \lessdot & = &
x \operatorname{'s~Property} & = &
x \operatorname{'s~Property} & = &
\operatorname{Property~of}\ x & = &
\operatorname{Property~of}\ x & = &
\operatorname{Object~above}\ x, \\
\operatorname{Object~above}\ x \\
x \gtrdot & = &
x \gtrdot & = &
x \operatorname{'s~Instance} & = &
x \operatorname{'s~Instance} & = &
\operatorname{Instance~of}\ x & = &
\operatorname{Instance~of}\ x & = &
\operatorname{Object~below}\ x. \\
\operatorname{Object~below}\ x \\
\end{array}</math>
\end{array}</math>
|}
|}
x \lessdot & = &
x \lessdot & = &
x\ \operatorname{is~the~Instance~of~what?} & = &
x\ \operatorname{is~the~Instance~of~what?} & = &
x \operatorname{'s~Property}, \\
x \operatorname{'s~Property} \\
x \gtrdot & = &
x \gtrdot & = &
x\ \operatorname{is~the~Property~of~what?} & = &
x\ \operatorname{is~the~Property~of~what?} & = &
x \operatorname{'s~Instance}. \\
x \operatorname{'s~Instance} \\
\end{array}</math>
\end{array}</math>
|}
|}
<math>\begin{array}{lllll}
<math>\begin{array}{lllll}
x \operatorname{'s~Icon} & = &
x \operatorname{'s~Icon} & = &
x \cdot M_{OS}, \\
x \cdot M_{OS} \\
x \operatorname{'s~Index} & = &
x \operatorname{'s~Index} & = &
x \cdot N_{OS}. \\
x \cdot N_{OS} \\
\end{array}</math>
\end{array}</math>
|}
|}
Equating the results of these equations yields the analysis of ''M'' and ''N'' as forms of composition within the genre of properties and instances:
Equating the results of these equations yields the analysis of <math>M\!</math> and <math>N\!</math> as forms of composition within the genre of properties and instances:
{| align="center" cellpadding="8"
| ''x''’s Icon
|
<math>\begin{array}{lllll}
x \operatorname{'s~Icon} & = &
x \cdot M_{OS} & = &
x \lessdot \gtrdot \\
x \operatorname{'s~Index} & = &
x \cdot N_{OS} & = &
x \gtrdot \lessdot \\
\end{array}</math>
|}
|}
On the assumption (to be examined more closely later) that any object ''x'' can be taken as a sign, the converse relations appear to be manifestly identical to the originals:
On the assumption (to be examined more closely later) that any object <math>x\!</math> can be taken as a sign, the converse relations appear to be manifestly identical to the originals:
:{|
:{|