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\label{modelReconstructionOne}
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\fbox{\begin{tt}\begin{tabular}{l}(PICK-UP MOVING RED GREEN)@\symbol{123}[[0,1],[14,22])\symbol{125}\\ 
\ \\ 
(SUPPORTED?\ RED)@\symbol{123}[[0:22])\symbol{125}\\ 
(SUPPORTED?\ MOVING)@\symbol{123}[[1:13]), [[24:26])\symbol{125}\\ 
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(a)\\ *[2ex]
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\ \\ 
(SUPPORTED?\ MOVING)@\symbol{123}[[14:23])\symbol{125}\\ 
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(b)
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\label{eventClassificationOne}
\end{figure}
}

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\label{blockDiagramOne}
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\end{center}

\label{Allen}
\end{figure}
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\samepage \begin{figure}% latex2html id marker 694
\begin{eqnarray*}
x=y&\stackrel{\triangle}{=}&\overline{x=y}\\ 
\mbox{\sc Supported}(x)&\stackrel{\triangle}{=}&\overline{\neg\mbox{\sc Grounded} (x)}\\ 
\mbox{\sc RigAtt} (x,y)&\stackrel{\triangle}{=}&(\exists r)\mbox{\sc Rigid} (x,y,r)\\ 
\mbox{\sc Supports}(x,y)&\stackrel{\triangle}{=}&
\overline{\left[\begin{array}{l}
\neg\mbox{\sc Grounded} (y)\wedge\\ 
\neg\mbox{\sc Stable}
\left(\begin{array}{l}
{\cal P}\setminus{\{x\}},
\left\langle\begin{array}{l}
\mbox{\sc Grounded}\cup{\{z|\neg\RIGIDLYATTACHEDF^{*}(z,y)\}},\\ 
\mbox{\sc Rigid},\\ 
\mbox{\sc Revolute},\\ 
\mbox{\sc SameLayer}
\end{array}\right\rangle
\end{array}\right)
\end{array}\right]}\\ 
\mbox{\sc Contacts}(x,y)&\stackrel{\triangle}{=}&
\overline{\mbox{\sc Touches}(x,y)\wedge\mbox{\sc SameLayer} (x,y)}\\ 
\mbox{\sc Attached}(x,y)&\stackrel{\triangle}{=}&
\overline{(\exists r)\mbox{\sc Rigid} (x,y,r)\vee\mbox{\sc Revolute} (x,y,r)}
\end{eqnarray*}

\label{primitiveEventTypes}
\end{figure}
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\samepage \setbox\sizebox=\hbox{$\mbox{\sc PickUp}(w,x,y)$}\lthtmltypeout{latex2htmlSize :tex2html_wrap_inline8824: \the\ht\sizebox::\the\dp\sizebox.}\box\sizebox
}

{\newpage
\clearpage
\samepage \begin{figure}% latex2html id marker 804
\begin{eqnarray*}
\mbox{\sc PickUp}(x,y,z)&\stackrel{\triangle}{=}&
\left(\begin{array}{l}
\neg\Diamond x=y\wedge
\neg\Diamond z=x\wedge
\neg\Diamond z=y\wedge\\ 
\mbox{\sc Supported}(y)\wedge
\neg\Diamond\mbox{\sc Attached}(x,z)\wedge\\ 
\left\{\begin{array}{l}
\left[\begin{array}{l}
\neg\Diamond\mbox{\sc Attached}(x,y)\wedge
\neg\Diamond\mbox{\sc Supports}(x,y)\wedge\\ 
\mbox{\sc Supports}(z,y)\wedge\\ 
\neg\Diamond\mbox{\sc Supported}(x)\wedge
\neg\Diamond\mbox{\sc Attached}(y,z)\wedge\\ 
\neg\Diamond\mbox{\sc Supports}(y,x)\wedge
\neg\Diamond\mbox{\sc Supports}(y,z)\wedge\\ 
\neg\Diamond\mbox{\sc Supports}(x,z)\wedge
\neg\Diamond\mbox{\sc Supports}(z,x)
\end{array}\right];\\ 
\left[\mbox{\sc Attached}(x,y)\vee\mbox{\sc Attached}(y,z)\right];\\ 
\left[\begin{array}{l}
\mbox{\sc Attached}(x,y)\wedge
\mbox{\sc Supports}(x,y)\wedge\\ 
\neg\Diamond\mbox{\sc Supports}(z,y)\wedge\\ 
\neg\Diamond\mbox{\sc Supported}(x)\wedge
\neg\Diamond\mbox{\sc Attached}(y,z)\wedge\\ 
\neg\Diamond\mbox{\sc Supports}(y,x)\wedge
\neg\Diamond\mbox{\sc Supports}(y,z)\wedge\\ 
\neg\Diamond\mbox{\sc Supports}(x,z)\wedge
\neg\Diamond\mbox{\sc Supports}(z,x)
\end{array}\right]
\end{array}\right\}
\end{array}\right)\\ 
\mbox{\sc PutDown}(x,y,z)&\stackrel{\triangle}{=}&
\left(\begin{array}{l}
\neg\Diamond x=y\wedge
\neg\Diamond z=x\wedge
\neg\Diamond z=y\wedge\\ 
\mbox{\sc Supported}(y)\wedge
\neg\Diamond\mbox{\sc Attached}(x,z)\wedge\\ 
\left\{\begin{array}{l}
\left[\begin{array}{l}
\mbox{\sc Attached}(x,y)\wedge
\mbox{\sc Supports}(x,y)\wedge\\ 
\neg\Diamond\mbox{\sc Supports}(z,y)\wedge\\ 
\neg\Diamond\mbox{\sc Supported}(x)\wedge
\neg\Diamond\mbox{\sc Attached}(y,z)\wedge\\ 
\neg\Diamond\mbox{\sc Supports}(y,x)\wedge
\neg\Diamond\mbox{\sc Supports}(y,z)\wedge\\ 
\neg\Diamond\mbox{\sc Supports}(x,z)\wedge
\neg\Diamond\mbox{\sc Supports}(z,x)
\end{array}\right];\\ 
\left[\mbox{\sc Attached}(x,y)\vee\mbox{\sc Attached}(y,z)\right];\\ 
\left[\begin{array}{l}
\neg\Diamond\mbox{\sc Attached}(x,y)\wedge
\neg\Diamond\mbox{\sc Supports}(x,y)\wedge\\ 
\mbox{\sc Supports}(z,y)\wedge\\ 
\neg\Diamond\mbox{\sc Supported}(x)\wedge
\neg\Diamond\mbox{\sc Attached}(y,z)\wedge\\ 
\neg\Diamond\mbox{\sc Supports}(y,x)\wedge
\neg\Diamond\mbox{\sc Supports}(y,z)\wedge\\ 
\neg\Diamond\mbox{\sc Supports}(x,z)\wedge
\neg\Diamond\mbox{\sc Supports}(z,x)
\end{array}\right]
\end{array}\right\}
\end{array}\right)\\ 
\mbox{\sc Stack}(w,x,y,z)&\stackrel{\triangle}{=}&
\left[\begin{array}{l}
\neg\Diamond z=w\wedge
\neg\Diamond z=x\wedge
\neg\Diamond z=y\wedge\\ 
\mbox{\sc PutDown}(w,x,y)\wedge
\mbox{\sc Supports}(z,y)\wedge\\ 
\neg\mbox{\sc Attached}(z,y)
\end{array}\right]\\ 
\mbox{\sc Unstack}(w,x,y,z)&\stackrel{\triangle}{=}&
\left[\begin{array}{l}
\neg\Diamond z=w\wedge
\neg\Diamond z=x\wedge
\neg\Diamond z=y\wedge\\ 
\mbox{\sc PickUp}(w,x,y)\wedge
\mbox{\sc Supports}(z,y)\wedge
\neg\mbox{\sc Attached}(z,y)
\end{array}\right]\\ 
\mbox{\sc Move}(w,x,y,z)&\stackrel{\triangle}{=}&
\neg\Diamond y=z\wedge\left[\mbox{\sc PickUp}(w,x,y);\mbox{\sc PutDown}(w,x,z)\right]\\ 
\mbox{\sc Assemble}(w,x,y,z)&\stackrel{\triangle}{=}&
\mbox{\sc PutDown}(w,y,z)\wedge_{{\{<\}}}\mbox{\sc Stack}(w,x,y,z)\\ 
\mbox{\sc Disassemble}(w,x,y,z)&\stackrel{\triangle}{=}&
\mbox{\sc Unstack}(w,x,y,z)\wedge_{{\{<\}}}\mbox{\sc PickUp}(x,y,z)\\ 
\end{eqnarray*}

\label{compoundEventTypes}
\end{figure}
}

{\newpage
\clearpage
\samepage \begin{figure}\begin{center}
\begin{tabular}{cccc}
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/stack00-3-image}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/stack00-11-image}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/stack00-12-image}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/stack00-23-image}}}\\ 
Frame 3&
Frame 11&
Frame 12&
Frame 23\\ 
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/stack00-24-image}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/stack00-26-image}}}\\ 
Frame 24&
Frame 26
\end{tabular}
\end{center}

\label{videoThreeA}
\end{figure}
}

{\newpage
\clearpage
\samepage \begin{figure}\begin{center}
\begin{tabular}{cccc}
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/unstack00-1-image}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/unstack00-10-image}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/unstack00-11-image}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/unstack00-24-image}}}\\ 
Frame 1&
Frame 10&
Frame 11&
Frame 24\\ 
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/unstack00-25-image}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/unstack00-29-image}}}\\ 
Frame 25&
Frame 29
\end{tabular}
\end{center}

\label{videoThreeB}
\end{figure}
}

{\newpage
\clearpage
\samepage \begin{figure}\begin{center}
\begin{tabular}{cccc}
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/move00-0-image}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/move00-8-image}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/move00-9-image}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/move00-16-image}}}\\ 
Frame 0&
Frame 8&
Frame 9&
Frame 16\\ 
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/move00-17-image}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/move00-33-image}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/move00-34-image}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/move00-45-image}}}\\ 
Frame 17&
Frame 33&
Frame 34&
Frame 45\\ 
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/move00-46-image}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/move00-47-image}}}\\ 
Frame 46&
Frame 47
\end{tabular}
\end{center}

\label{videoThreeC}
\end{figure}
}

{\newpage
\clearpage
\samepage \begin{figure}\begin{center}
\begin{tabular}{cccc}
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/assemble00-0-image}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/assemble00-9-image}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/assemble00-10-image}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/assemble00-17-image}}}\\ 
Frame 0&
Frame 9&
Frame 10&
Frame 17\\ 
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/assemble00-18-image}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/assemble00-32-image}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/assemble00-33-image}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/assemble00-40-image}}}\\ 
Frame 18&
Frame 32&
Frame 33&
Frame 40\\ 
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/assemble00-41-image}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/assemble00-46-image}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/assemble00-47-image}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/assemble00-56-image}}}\\ 
Frame 41&
Frame 46&
Frame 47&
Frame 56\\ 
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/assemble00-57-image}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/assemble00-67-image}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/assemble00-68-image}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/assemble00-80-image}}}\\ 
Frame 57&
Frame 67&
Frame 68&
Frame 80
\end{tabular}
\end{center}

\label{videoThreeD}
\end{figure}
}

{\newpage
\clearpage
\samepage \begin{figure}\begin{center}
\begin{tabular}{cccc}
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/disassemble00-18-image}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/disassemble00-19-image}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/disassemble00-22-image}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/disassemble00-23-image}}}\\ 
Frame 18&
Frame 19&
Frame 22&
Frame 23\\ 
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/disassemble00-49-image}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/disassemble00-50-image}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/disassemble00-56-image}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/disassemble00-57-image}}}\\ 
Frame 49&
Frame 50&
Frame 56&
Frame 57\\ 
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/disassemble00-62-image}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/disassemble00-63-image}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/disassemble00-87-image}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/disassemble00-88-image}}}\\ 
Frame 62&
Frame 63&
Frame 87&
Frame 88
\end{tabular}
\end{center}

\label{videoThreeE}
\end{figure}
}

{\newpage
\clearpage
\samepage \setbox\sizebox=\hbox{$\mbox{\sc Unstack}$}\lthtmltypeout{latex2htmlSize :tex2html_wrap_inline8890: \the\ht\sizebox::\the\dp\sizebox.}\box\sizebox
}

{\newpage
\clearpage
\samepage \setbox\sizebox=\hbox{$\mbox{\sc Move}$}\lthtmltypeout{latex2htmlSize :tex2html_wrap_inline8892: \the\ht\sizebox::\the\dp\sizebox.}\box\sizebox
}

{\newpage
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{\newpage
\clearpage
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{\newpage
\clearpage
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}

{\newpage
\clearpage
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{\newpage
\clearpage
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{\newpage
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{\newpage
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\stepcounter{section}
{\newpage
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{\newpage
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{\newpage
\clearpage
\samepage \begin{eqnarray*}[q_1,r_1]=[q_2,r_2]&\stackrel{\triangle}{=}&(q_1=q_2)\wedge(r_1=r_2)\\ {}
[q_1,r_1]<[q_2,r_2]&\stackrel{\triangle}{=}&r_1<q_2\\ {}
[q_1,r_1]>[q_2,r_2]&\stackrel{\triangle}{=}&q_1>r_2\\ 
[q_1,r_1]\;\mbox{\small\sf m} \;[q_2,r_2]&\stackrel{\triangle}{=}&r_1=q_2\\ 
[q_1,r_1]\;\mbox{\small\sf mi} \;[q_2,r_2]&\stackrel{\triangle}{=}&q_1=r_2\\ 
[q_1,r_1]\;\mbox{\small\sf o} \;[q_2,r_2]&\stackrel{\triangle}{=}&q_1<q_2<r_1<r_2\\ 
[q_1,r_1]\;\mbox{\small\sf oi} \;[q_2,r_2]&\stackrel{\triangle}{=}&r_1>r_2>q_1>q_2\\ 
[q_1,r_1]\;\mbox{\small\sf s} \;[q_2,r_2]&\stackrel{\triangle}{=}&(q_1=q_2)\wedge(r_1<r_2)\\ 
[q_1,r_1]\;\mbox{\small\sf si} \;[q_2,r_2]&\stackrel{\triangle}{=}&(q_1=q_2)\wedge(r_1>r_2)\\ 
[q_1,r_1]\;\mbox{\small\sf f} \;[q_2,r_2]&\stackrel{\triangle}{=}&(q_1>q_2)\wedge(r_1=r_2)\\ 
[q_1,r_1]\;\mbox{\small\sf fi} \;[q_2,r_2]&\stackrel{\triangle}{=}&(q_1<q_2)\wedge(r_1=r_2)\\ 
[q_1,r_1]\;\mbox{\small\sf d} \;[q_2,r_2]&\stackrel{\triangle}{=}&(q_1>q_2)\wedge(r_1<r_2)\\ 
[q_1,r_1]\;\mbox{\small\sf di} \;[q_2,r_2]&\stackrel{\triangle}{=}&(q_1<q_2)\wedge(r_1>r_2)
\end{eqnarray*}
}

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{\newpage
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\samepage \begin{eqnarray}_{\alpha_1}[q_1,r_1]_{\beta_1}=_{\alpha_2}[q_2,r_2]_{\beta_2}&\stackrel{\triangle}{=}&
(q_1=q_2)\wedge(\alpha_1=\alpha_2)\wedge(r_1=r_2)\wedge(\beta_1=\beta_2)\\ 
\label{ltdef}
_{\alpha_1}[q_1,r_1]_{\beta_1}<_{\alpha_2}[q_2,r_2]_{\beta_2}&\stackrel{\triangle}{=}&
r_1\leq_{(\neg\beta_1\wedge\neg\alpha_2)}q_2\\ 
\label{gtdef}
_{\alpha_1}[q_1,r_1]_{\beta_1}>_{\alpha_2}[q_2,r_2]_{\beta_2}&\stackrel{\triangle}{=}&
q_1\geq_{(\neg\alpha_1\wedge\neg\beta_2)}r_2\\ 
\label{mdef}
_{\alpha_1}[q_1,r_1]_{\beta_1}\;\mbox{\small\sf m} \;_{\alpha_2}[q_2,r_2]_{\beta_2}&
\stackrel{\triangle}{=}&(r_1=q_2)\wedge(\beta_1\not=\alpha_2)\\ 
\label{midef}
_{\alpha_1}[q_1,r_1]_{\beta_1}\;\mbox{\small\sf mi} \;_{\alpha_2}[q_2,r_2]_{\beta_2}&
\stackrel{\triangle}{=}&(q_1=r_2)\wedge(\alpha_1\not=\beta_2)\\ 
\label{odef}
_{\alpha_1}[q_1,r_1]_{\beta_1}\;\mbox{\small\sf o} \;_{\alpha_2}[q_2,r_2]_{\beta_2}&
\stackrel{\triangle}{=}&
q_1\leq_{(\alpha_1\wedge\neg\alpha_2)}q_2\leq_{(\beta_1\wedge\alpha_2)}r_1
\leq_{(\neg\beta_1\wedge\beta_2)}r_2\\ 
\label{oidef}
_{\alpha_1}[q_1,r_1]_{\beta_1}\;\mbox{\small\sf oi} \;_{\alpha_2}[q_2,r_2]_{\beta_2}&
\stackrel{\triangle}{=}&
r_1\geq_{(\beta_1\wedge\neg\beta_2)}r_2\geq_{(\alpha_1\wedge\beta_2)}q_1
\geq_{(\neg\alpha_1\wedge\alpha_2)}q_2\\ 
\label{sdef}
_{\alpha_1}[q_1,r_1]_{\beta_1}\;\mbox{\small\sf s} \;_{\alpha_2}[q_2,r_2]_{\beta_2}&
\stackrel{\triangle}{=}&(q_1=q_2)\wedge(\alpha_1=\alpha_2)\wedge
[r_1\leq_{(\neg\beta_1\wedge\beta_2)}r_2]\\ 
\label{sidef}
_{\alpha_1}[q_1,r_1]_{\beta_1}\;\mbox{\small\sf si} \;_{\alpha_2}[q_2,r_2]_{\beta_2}&
\stackrel{\triangle}{=}&(q_1=q_2)\wedge(\alpha_1=\alpha_2)\wedge
[r_1\geq_{(\beta_1\wedge\neg\beta_2)}r_2]\\ 
\label{fdef}
_{\alpha_1}[q_1,r_1]_{\beta_1}\;\mbox{\small\sf f} \;_{\alpha_2}[q_2,r_2]_{\beta_2}&
\stackrel{\triangle}{=}&[q_1\geq_{(\neg\alpha_1\wedge\alpha_2)}q_2]\wedge
(r_1=r_2)\wedge(\beta_1=\beta_2)\\ 
\label{fidef}
_{\alpha_1}[q_1,r_1]_{\beta_1}\;\mbox{\small\sf fi} \;_{\alpha_2}[q_2,r_2]_{\beta_2}&
\stackrel{\triangle}{=}&[q_1\leq_{(\alpha_1\wedge\neg\alpha_2)}q_2]\wedge
(r_1=r_2)\wedge(\beta_1=\beta_2)\\ 
\label{ddef}
_{\alpha_1}[q_1,r_1]_{\beta_1}\;\mbox{\small\sf d} \;_{\alpha_2}[q_2,r_2]_{\beta_2}&
\stackrel{\triangle}{=}&[q_1\geq_{(\neg\alpha_1\wedge\alpha_2)}q_2]\wedge
[r_1\leq_{(\neg\beta_1\wedge\beta_2)}r_2]\\ 
\label{didef}
_{\alpha_1}[q_1,r_1]_{\beta_1}\;\mbox{\small\sf di} \;_{\alpha_2}[q_2,r_2]_{\beta_2}&
\stackrel{\triangle}{=}&[q_1\leq_{(\alpha_1\wedge\neg\alpha_2)}q_2]\wedge
[r_1\geq_{(\beta_1\wedge\neg\beta_2)}r_2]
\end{eqnarray}
}

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\samepage \begin{equation}\label{spandef}
{\{_{\alpha}[q,r]_{\beta}|
(i\leq_{\gamma}q\leq_{\delta}j)\wedge
(k\leq_{\epsilon}r\leq_{\zeta}l)\}}
\end{equation}
}

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{\newpage
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\samepage \begin{displaymath}\begin{array}{ll}
(1)&(i\not=\infty)\wedge
(j\not=-\infty)\wedge
(k\not=\infty)\wedge
(l\not=-\infty)\wedge\\ 
(2)&[(i=-\infty)\rightarrow\neg\gamma]\wedge
[(j=\infty)\rightarrow\neg\delta]\wedge
[(k=-\infty)\rightarrow\neg\epsilon]\wedge
[(l=\infty)\rightarrow\neg\zeta]\wedge\\ 
(3)&(j\leq l)\wedge
(k\geq i)\wedge\\ 
(4)&(i\leq j)\wedge
(k\leq l)\wedge\\ 
(5)&[(i\not=j)\vee(\gamma\wedge\delta)]\wedge
[(k\not=l)\vee(\epsilon\wedge\zeta)]\wedge\\ 
(6)&[(i\not=l)\vee(\alpha\wedge\beta)]\wedge\\ 
(7)&\{[(j=l)\wedge\neg\zeta]\rightarrow\neg\delta\}
\wedge
\{[(k=i)\wedge\neg\gamma]\rightarrow\neg\epsilon\}
\wedge\\ 
(8)&\{[(j=l)\wedge(\neg\alpha\vee\neg\beta)]\rightarrow\neg\delta\}
\wedge
\{[(k=i)\wedge(\neg\alpha\vee\neg\beta)]\rightarrow\neg\epsilon\}
\end{array}
\end{displaymath}
}

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{\newpage
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\samepage \begin{displaymath}\langle_{\alpha}[_{\gamma}[i,j]_{\delta},_{\epsilon}[k,l]_{\zeta}]_{\beta}\rangle\stackrel{\triangle}{=}
\left\{\begin{array}{l}
{\{_{\alpha}[_{\gamma'}[i,j']_{\delta'},_{\epsilon'}[k',l]_{\zeta'}]_{\beta}\}}\\ 
\;\;\;\mbox{\rm where}\;
\begin{array}[t]{rcl}
j'&=&\min(j,l)\\ 
k'&=&\max(k,i)\\ 
\gamma'&=&\gamma\wedge(i\not=-\infty)\\ 
\delta'&=&\delta\wedge[\min(j,l)\not=\infty]\wedge
[(j<l)\vee(\zeta\wedge\alpha\wedge\beta)]\\ 
\epsilon'&=&\epsilon\wedge[\max(k,i)\not=-\infty]\wedge
[(k>i)\vee(\gamma\wedge\beta\wedge\alpha)]\\ 
\zeta'&=&\zeta\wedge(l\not=\infty)
\end{array}\\ 
\;\;\;\mbox{\rm when}\;
\begin{array}[t]{l}
(i\leq j')\wedge
(k'\leq l)\wedge\\ {}
[(i=j')\rightarrow(\gamma'\wedge\delta')]\wedge
[(k'=l)\rightarrow(\epsilon'\wedge\zeta')]\wedge\\ {}
[(i=l)\rightarrow(\alpha\wedge\beta)]\wedge\\ 
(i\not=\infty)\wedge
(j'\not=-\infty)\wedge
(k'\not=\infty)\wedge
(l\not=-\infty)
\end{array}\\ 
{\{\}}\;\;\;\mbox{\rm otherwise}
\end{array}\right.
\end{displaymath}
}

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{\newpage
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\samepage \begin{displaymath}\begin{array}{l}
_{\alpha_1}[_{\gamma_1}[i_1,j_1]_{\delta_1},_{\epsilon_1}[k_1,l_1]_{\zeta_1}]_{\beta_1}\cap
_{\alpha_2}[_{\gamma_2}[i_2,j_2]_{\delta_2},_{\epsilon_2}[k_2,l_2]_{\zeta_2}]_{\beta_2}\stackrel{\triangle}{=}\\ 
\;\;\;\left\{\begin{array}{l}
\langle_{\alpha_1}[_{\gamma}[\max(i_1,i_2),\min(j_1,j_2)]_{\delta},_{\epsilon}[\max(k_1,k_2),\min(l_1,l_2)]_{\zeta}]_{\beta_1}\rangle\\ 
\;\;\;\mbox{\rm where}\;
\begin{array}[t]{rcl}
\gamma&=&\left\{\begin{array}{ll}
\gamma_1&i_1>i_2\\ 
\gamma_1\wedge\gamma_2&i_1=i_2\\ 
\gamma_2&i_1<i_2
\end{array}\right.\\ 
\delta&=&\left\{\begin{array}{ll}
\delta_1&j_1<j_2\\ 
\delta_1\wedge\delta_2&j_1=j_2\\ 
\delta_2&j_1>j_2
\end{array}\right.\\ 
\epsilon&=&\left\{\begin{array}{ll}
\epsilon_1&k_1>k_2\\ 
\epsilon_1\wedge\epsilon_2&k_1=k_2\\ 
\epsilon_2&k_1<k_2
\end{array}\right.\\ 
\zeta&=&\left\{\begin{array}{ll}
\zeta_1&l_1<l_2\\ 
\zeta_1\wedge\zeta_2&l_1=l_2\\ 
\zeta_2&l_1>l_2
\end{array}\right.
\end{array}\\ 
\;\;\;\mbox{\rm when}\;(\alpha_1=\alpha_2)\wedge(\beta_1=\beta_2)\\ 
{\{\}}\;\;\;\mbox{\rm otherwise}
\end{array}\right.
\end{array}
\end{displaymath}
}

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{\newpage
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\samepage \begin{displaymath}\neg_{\alpha}[_{\gamma}[i,j]_{\delta},_{\epsilon}[k,l]_{\zeta}]_{\beta}\stackrel{\triangle}{=}
\left(\begin{array}{l}
\langle_{\alpha}[_{\mbox{\tiny\bf T}}[-\infty,\infty]_{\mbox{\tiny\bf T}},_{\mbox{\tiny\bf T}}[-\infty,k]_{\neg\epsilon}]_{\beta}\rangle\cup\\ 
\langle_{\alpha}[_{\mbox{\tiny\bf T}}[-\infty,\infty]_{\mbox{\tiny\bf T}},_{\neg\zeta}[l,\infty]_{\mbox{\tiny\bf T}}]_{\beta}\rangle\cup\\ 
\langle_{\alpha}[_{\mbox{\tiny\bf T}}[-\infty,i]_{\neg\gamma},_{\mbox{\tiny\bf T}}[-\infty,\infty]_{\mbox{\tiny\bf T}}]_{\beta}\rangle\cup\\ 
\langle_{\alpha}[_{\neg\delta}[j,\infty]_{\mbox{\tiny\bf T}},_{\mbox{\tiny\bf T}}[-\infty,\infty]_{\mbox{\tiny\bf T}}]_{\beta}\rangle\cup\\ 
\langle_{\neg\alpha}[_{\mbox{\tiny\bf T}}[-\infty,\infty]_{\mbox{\tiny\bf T}},_{\mbox{\tiny\bf T}}[-\infty,\infty]_{\mbox{\tiny\bf T}}]_{\beta}\rangle\cup\\ 
\langle_{\alpha}[_{\mbox{\tiny\bf T}}[-\infty,\infty]_{\mbox{\tiny\bf T}},_{\mbox{\tiny\bf T}}[-\infty,\infty]_{\mbox{\tiny\bf T}}]_{\neg\beta}\rangle\cup\\ 
\langle_{\neg\alpha}[_{\mbox{\tiny\bf T}}[-\infty,\infty]_{\mbox{\tiny\bf T}},_{\mbox{\tiny\bf T}}[-\infty,\infty]_{\mbox{\tiny\bf T}}]_{\neg\beta}\rangle
\end{array}\right)
\end{displaymath}
}

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{\newpage
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\samepage \begin{displaymath}\begin{array}{l}
\mbox{\sc Span}(_{\alpha_1}[q_1,r_1]_{\beta_1},_{\alpha_2}[q_2,r_2]_{\beta_2})
\stackrel{\triangle}{=}\\ 
\;\;\;\;\;_{\{[\alpha_1\wedge(q_1\leq q_2)]\vee[\alpha_2\wedge(q_1\geq q_2)]\}}[\min(q_1,q_2),\max(r_1,r_2)]_{\{[\beta_1\wedge(r_1\geq r_2)]\vee[\beta_2\wedge(r_1\leq r_2)]\}}
\end{array}
\end{displaymath}
}

{\newpage
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\samepage \begin{displaymath}\mbox{\sc Span}(I_1,I_2)\stackrel{\triangle}{=}
\bigcup_{\sI_1\in I_1}\bigcup_{\sI_2\in I_2}\mbox{\sc Span}(\I_1,\I_2)
\end{displaymath}
}

{\newpage
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\samepage \begin{displaymath}\begin{array}{l}
\mbox{\sc Span}(_{\alpha_1}[_{\gamma_1}[i_1,j_1]_{\delta_1},_{\epsilon_1}[k_1,l_1]_{\zeta_1}]_{\beta_1},_{\alpha_2}[_{\gamma_2}[i_2,j_2]_{\delta_2},_{\epsilon_2}[k_2,l_2]_{\zeta_2}]_{\beta_2})\stackrel{\triangle}{=}\\ 
\;\;\;\left(\begin{array}{l}
\langle_{\alpha_1}[_{\gamma_1}[i_1,j]_{\delta},_{\epsilon}[k,l_1]_{\zeta_1}]_{\beta_1}\rangle\cup\\ 
\langle_{\alpha_1}[_{\gamma_1}[i_1,j]_{\delta},_{\epsilon}[k,l_2]_{\zeta_2}]_{\beta_2}\rangle\cup\\ 
\langle_{\alpha_2}[_{\gamma_2}[i_2,j]_{\delta},_{\epsilon}[k,l_1]_{\zeta_1}]_{\beta_1}\rangle\cup\\ 
\langle_{\alpha_2}[_{\gamma_2}[i_2,j]_{\delta},_{\epsilon}[k,l_2]_{\zeta_2}]_{\beta_2}\rangle
\end{array}\right)\\ 
\;\;\;\mbox{\rm where}
\begin{array}[t]{rcl}
j&=&\min(j_1,j_2)\\ 
k&=&\max(k_1,k_2)\\ 
\delta&=&[\delta_1\wedge(j_1\leq j_2)]\vee[\delta_2\wedge(j_1\geq j_2)]\\ 
\epsilon&=&[\epsilon_1\wedge(k_1\geq k_2)]\vee[\epsilon_2\wedge(k_1\leq k_2)]
\end{array}
\end{array}
\end{displaymath}
}

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{\newpage
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\samepage \begin{eqnarray*}{\cal D}(=,\mbox{\bf i})&\stackrel{\triangle}{=}&
{\{\mbox{\bf i}\}}\\ 
{\cal D}(<,_{\alpha_1}[_{\gamma_1}[i_1,j_1]_{\delta_1},_{\epsilon_1}[k_1,l_1]_{\zeta_1}]_{\beta_1})&\stackrel{\triangle}{=}&
\bigcup_{\alpha_2,\beta_2\in{\{\mbox{\tiny\bf T},\mbox{\tiny\bf F}\}}}
\langle_{\alpha_2}[_{(\neg\beta_1\wedge\neg\alpha_2\wedge\epsilon_1)}[k_1,\infty]_{\mbox{\tiny\bf T}},_{\mbox{\tiny\bf T}}[-\infty,\infty]_{\mbox{\tiny\bf T}}]_{\beta_2}\rangle\\ 
{\cal D}(>,_{\alpha_1}[_{\gamma_1}[i_1,j_1]_{\delta_1},_{\epsilon_1}[k_1,l_1]_{\zeta_1}]_{\beta_1})&\stackrel{\triangle}{=}&
\bigcup_{\alpha_2,\beta_2\in{\{\mbox{\tiny\bf T},\mbox{\tiny\bf F}\}}}
\langle_{\alpha_2}[_{\mbox{\tiny\bf T}}[-\infty,\infty]_{\mbox{\tiny\bf T}},_{\mbox{\tiny\bf T}}[-\infty,j_1]_{(\neg\alpha_1\wedge\neg\beta_2\wedge\delta_1)}]_{\beta_2}\rangle\\ 
{\cal D}(\mbox{\small\sf m},_{\alpha_1}[_{\gamma_1}[i_1,j_1]_{\delta_1},_{\epsilon_1}[k_1,l_1]_{\zeta_1}]_{\beta_1})&\stackrel{\triangle}{=}&
\bigcup_{\beta_2\in{\{\mbox{\tiny\bf T},\mbox{\tiny\bf F}\}}}
\langle_{\neg\beta_1}[_{\epsilon_1}[k_1,l_1]_{\zeta_1},_{\mbox{\tiny\bf T}}[-\infty,\infty]_{\mbox{\tiny\bf T}}]_{\beta_2}\rangle\\ 
{\cal D}(\mbox{\small\sf mi},_{\alpha_1}[_{\gamma_1}[i_1,j_1]_{\delta_1},_{\epsilon_1}[k_1,l_1]_{\zeta_1}]_{\beta_1})&\stackrel{\triangle}{=}&
\bigcup_{\alpha_2\in{\{\mbox{\tiny\bf T},\mbox{\tiny\bf F}\}}}
\langle_{\alpha_2}[_{\mbox{\tiny\bf T}}[-\infty,\infty]_{\mbox{\tiny\bf T}},_{\gamma_1}[i_1,j_1]_{\delta_1}]_{\neg\alpha_1}\rangle\\ 
{\cal D}(\mbox{\small\sf o},_{\alpha_1}[_{\gamma_1}[i_1,j_1]_{\delta_1},_{\epsilon_1}[k_1,l_1]_{\zeta_1}]_{\beta_1})&\stackrel{\triangle}{=}&\\ 
\lefteqn{\hspace{-1.5in}\bigcup_{\alpha_2,\beta_2\in{\{\mbox{\tiny\bf T},\mbox{\tiny\bf F}\}}}
\langle_{\alpha_2}[_{(\alpha_1\wedge\neg\alpha_2\wedge\gamma_1)}[i_1,l_1]_{(\beta_1\wedge\alpha_2\wedge\zeta_1)},_{(\neg\beta_1\wedge\beta_2\wedge\epsilon_1)}[k_1,\infty]_{\mbox{\tiny\bf T}}]_{\beta_2}\rangle}\\ 
{\cal D}(\mbox{\small\sf oi},_{\alpha_1}[_{\gamma_1}[i_1,j_1]_{\delta_1},_{\epsilon_1}[k_1,l_1]_{\zeta_1}]_{\beta_1})&\stackrel{\triangle}{=}&\\ 
\lefteqn{\hspace{-1.5in}\bigcup_{\alpha_2,\beta_2\in{\{\mbox{\tiny\bf T},\mbox{\tiny\bf F}\}}}
\langle_{\alpha_2}[_{\mbox{\tiny\bf T}}[-\infty,j_1]_{(\neg\alpha_1\wedge\alpha_2\wedge\delta_1)},_{(\alpha_1\wedge\beta_2\wedge\gamma_1)}[i_1,l_1]_{(\beta_1\wedge\neg\beta_2\wedge\zeta_1)}]_{\beta_2}\rangle}\\ 
{\cal D}(\mbox{\small\sf s},_{\alpha_1}[_{\gamma_1}[i_1,j_1]_{\delta_1},_{\epsilon_1}[k_1,l_1]_{\zeta_1}]_{\beta_1})&\stackrel{\triangle}{=}&
\bigcup_{\beta_2\in{\{\mbox{\tiny\bf T},\mbox{\tiny\bf F}\}}}
\langle_{\alpha_1}[_{\gamma_1}[i_1,j_1]_{\delta_1},_{(\neg\beta_1\wedge\beta_2\wedge\epsilon_1)}[k_1,\infty]_{\mbox{\tiny\bf T}}]_{\beta_2}\rangle\\ 
{\cal D}(\mbox{\small\sf si},_{\alpha_1}[_{\gamma_1}[i_1,j_1]_{\delta_1},_{\epsilon_1}[k_1,l_1]_{\zeta_1}]_{\beta_1})&\stackrel{\triangle}{=}&
\bigcup_{\beta_2\in{\{\mbox{\tiny\bf T},\mbox{\tiny\bf F}\}}}
\langle_{\alpha_1}[_{\gamma_1}[i_1,j_1]_{\delta_1},_{\mbox{\tiny\bf T}}[-\infty,l_1]_{(\beta_1\wedge\neg\beta_2\wedge\zeta_1)}]_{\beta_2}\rangle\\ 
{\cal D}(\mbox{\small\sf f},_{\alpha_1}[_{\gamma_1}[i_1,j_1]_{\delta_1},_{\epsilon_1}[k_1,l_1]_{\zeta_1}]_{\beta_1})&\stackrel{\triangle}{=}&
\bigcup_{\alpha_2\in{\{\mbox{\tiny\bf T},\mbox{\tiny\bf F}\}}}
\langle_{\alpha_2}[_{\mbox{\tiny\bf T}}[-\infty,j_1]_{(\neg\alpha_1\wedge\alpha_2\wedge\delta_1)},_{\epsilon_1}[k_1,l_1]_{\zeta_1}]_{\beta_1}\rangle\\ 
{\cal D}(\mbox{\small\sf fi},_{\alpha_1}[_{\gamma_1}[i_1,j_1]_{\delta_1},_{\epsilon_1}[k_1,l_1]_{\zeta_1}]_{\beta_1})&\stackrel{\triangle}{=}&
\bigcup_{\alpha_2\in{\{\mbox{\tiny\bf T},\mbox{\tiny\bf F}\}}}
\langle_{\alpha_2}[_{(\alpha_1\wedge\neg\alpha_2\wedge\gamma_1)}[i_1,\infty]_{\mbox{\tiny\bf T}},_{\epsilon_1}[k_1,l_1]_{\zeta_1}]_{\beta_1}\rangle\\ 
{\cal D}(\mbox{\small\sf d},_{\alpha_1}[_{\gamma_1}[i_1,j_1]_{\delta_1},_{\epsilon_1}[k_1,l_1]_{\zeta_1}]_{\beta_1})&\stackrel{\triangle}{=}&\\ 
\lefteqn{\hspace{-1.5in}\bigcup_{\alpha_2,\beta_2\in{\{\mbox{\tiny\bf T},\mbox{\tiny\bf F}\}}}
\langle_{\alpha_2}[_{\mbox{\tiny\bf T}}[-\infty,j_1]_{(\neg\alpha_1\wedge\alpha_2\wedge\delta_1)},_{(\neg\beta_1\wedge\beta_2\wedge\epsilon_1)}[k_1,\infty]_{\mbox{\tiny\bf T}}]_{\beta_2}\rangle}\\ 
{\cal D}(\mbox{\small\sf di},_{\alpha_1}[_{\gamma_1}[i_1,j_1]_{\delta_1},_{\epsilon_1}[k_1,l_1]_{\zeta_1}]_{\beta_1})&\stackrel{\triangle}{=}&\\ 
\lefteqn{\hspace{-1.5in}\bigcup_{\alpha_2,\beta_2\in{\{\mbox{\tiny\bf T},\mbox{\tiny\bf F}\}}}
\langle_{\alpha_2}[_{(\alpha_1\wedge\neg\alpha_2\wedge\gamma_1)}[i_1,\infty]_{\mbox{\tiny\bf T}},_{\mbox{\tiny\bf T}}[-\infty,l_1]_{(\beta_1\wedge\neg\beta_2\wedge\zeta_1)}]_{\beta_2}\rangle}
\end{eqnarray*}
}

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{\newpage
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\stepcounter{subsection}
{\newpage
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\samepage \setbox\sizebox=\hbox{${\cal I}(I,r,J)$}\lthtmltypeout{latex2htmlSize :tex2html_wrap_inline10384: \the\ht\sizebox::\the\dp\sizebox.}\box\sizebox
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{\newpage
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\samepage \setbox\sizebox=\hbox{$\mbox{\bf k}=\mbox{\sc Span}(\mbox{\bf i},\mbox{\bf j})$}\lthtmltypeout{latex2htmlSize :tex2html_wrap_inline10390: \the\ht\sizebox::\the\dp\sizebox.}\box\sizebox
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{\newpage
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{\newpage
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}

{\newpage
\clearpage
\samepage \begin{displaymath}{\cal I}(\mbox{\bf i},r,\mbox{\bf j})\stackrel{\triangle}{=}
\bigcup_{\mbox{\scriptsize\bf i}'\in{\cal D}(r^{-1},\mbox{\scriptsize\bf j})}
\bigcup_{\mbox{\scriptsize\bf i}''\in\mbox{\scriptsize\bf i}'\cap\mbox{\scriptsize\bf i}}
\bigcup_{\mbox{\scriptsize\bf j}'\in{\cal D}(r,\mbox{\scriptsize\bf i})}
\bigcup_{\mbox{\scriptsize\bf j}''\in\mbox{\scriptsize\bf j}'\cap\mbox{\scriptsize\bf j}}
\mbox{\sc Span}(\mbox{\bf i}'',\mbox{\bf j}'')
\end{displaymath}
}

{\newpage
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{\newpage
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\samepage \setbox\sizebox=\hbox{$|{\cal I}(\cdot,r,\cdot)|\leq4|{\cal D}(r,\cdot)|^2$}\lthtmltypeout{latex2htmlSize :tex2html_wrap_inline10424: \the\ht\sizebox::\the\dp\sizebox.}\box\sizebox
}

{\newpage
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{\newpage
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\stepcounter{subsection}
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{\newpage
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{\newpage
\clearpage
\samepage \begin{eqnarray*}{\cal E}(M,p(c_1,\ldots,c_n))&\stackrel{\triangle}{=}&{\{\I|p(c_1,\ldots,c_n)@\mbox{\bf i}\in M\}}\\ 
{\cal E}(M,\Phi\vee\Psi)&\stackrel{\triangle}{=}&{\cal E}(M,\Phi)\cup{\cal E}(M,\Psi)\\ 
{\cal E}(M,\neg\Phi)&\stackrel{\triangle}{=}&
\begin{array}[t]{l}
\displaystyle
\bigcup_{\mbox{\scriptsize\bf i}'_1\in\neg\sI_1}\cdots
\bigcup_{\mbox{\scriptsize\bf i}'_n\in\neg\sI_n}\mbox{\bf i}'_1\cap\cdots\cap\mbox{\bf i}'_n\\ 
\mbox{\rm where}\;{\cal E}(M,\Phi)={\{\I_1,\ldots,\I_n\}}
\end{array}\\ 
{\cal E}(M,\Phi\wedge_R\Psi)&\stackrel{\triangle}{=}&
\bigcup_{\mbox{\scriptsize\bf i}\in{\cal E}(M,\Phi)}\bigcup_{\mbox{\scriptsize\bf j}\in{\cal E}(M,\Psi)}
\bigcup_{r\in R}{\cal I}(\mbox{\bf i},r,\mbox{\bf j})\\ 
{\cal E}(M,\Diamond_R\Phi)&\stackrel{\triangle}{=}&
\bigcup_{\mbox{\scriptsize\bf i}\in{\cal E}(M,\Phi)}\bigcup_{r\in R}{\cal D}(r,\mbox{\bf i})
\end{eqnarray*}
}

\stepcounter{section}
{\newpage
\clearpage
\samepage \begin{figure}\begin{center}
\begin{tabular}{cccc}
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/stack00-3-image-and-most-preferred-model}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/stack00-11-image-and-most-preferred-model}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/stack00-12-image-and-most-preferred-model}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/stack00-23-image-and-most-preferred-model}}}\\ 
Frame 3&
Frame 11&
Frame 12&
Frame 23\\ 
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/stack00-24-image-and-most-preferred-model}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/stack00-26-image-and-most-preferred-model}}}\\ 
Frame 24&
Frame 26
\end{tabular}
\end{center}

\label{modelReconstructionThreeA}
\end{figure}
}

{\newpage
\clearpage
\samepage \begin{figure}\begin{center}
\begin{tabular}{cccc}
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/unstack00-1-image-and-most-preferred-model}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/unstack00-10-image-and-most-preferred-model}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/unstack00-11-image-and-most-preferred-model}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/unstack00-24-image-and-most-preferred-model}}}\\ 
Frame 1&
Frame 10&
Frame 11&
Frame 24\\ 
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/unstack00-25-image-and-most-preferred-model}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/unstack00-29-image-and-most-preferred-model}}}\\ 
Frame 25&
Frame 29
\end{tabular}
\end{center}

\label{modelReconstructionThreeB}
\end{figure}
}

{\newpage
\clearpage
\samepage \begin{figure}\begin{center}
\begin{tabular}{cccc}
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/move00-0-image-and-most-preferred-model}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/move00-8-image-and-most-preferred-model}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/move00-9-image-and-most-preferred-model}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/move00-16-image-and-most-preferred-model}}}\\ 
Frame 0&
Frame 8&
Frame 9&
Frame 16\\ 
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/move00-17-image-and-most-preferred-model}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/move00-33-image-and-most-preferred-model}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/move00-34-image-and-most-preferred-model}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/move00-45-image-and-most-preferred-model}}}\\ 
Frame 17&
Frame 33&
Frame 34&
Frame 45\\ 
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/move00-46-image-and-most-preferred-model}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/move00-47-image-and-most-preferred-model}}}\\ 
Frame 46&
Frame 47
\end{tabular}
\end{center}

\label{modelReconstructionThreeC}
\end{figure}
}

{\newpage
\clearpage
\samepage \begin{figure}\begin{center}
\begin{tabular}{cccc}
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/assemble00-0-image-and-most-preferred-model}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/assemble00-9-image-and-most-preferred-model}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/assemble00-10-image-and-most-preferred-model}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/assemble00-17-image-and-most-preferred-model}}}\\ 
Frame 0&
Frame 9&
Frame 10&
Frame 17\\ 
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/assemble00-18-image-and-most-preferred-model}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/assemble00-32-image-and-most-preferred-model}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/assemble00-33-image-and-most-preferred-model}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/assemble00-40-image-and-most-preferred-model}}}\\ 
Frame 18&
Frame 32&
Frame 33&
Frame 40\\ 
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/assemble00-41-image-and-most-preferred-model}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/assemble00-46-image-and-most-preferred-model}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/assemble00-47-image-and-most-preferred-model}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/assemble00-56-image-and-most-preferred-model}}}\\ 
Frame 41&
Frame 46&
Frame 47&
Frame 56\\ 
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/assemble00-57-image-and-most-preferred-model}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/assemble00-67-image-and-most-preferred-model}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/assemble00-68-image-and-most-preferred-model}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/assemble00-80-image-and-most-preferred-model}}}\\ 
Frame 57&
Frame 67&
Frame 68&
Frame 80
\end{tabular}
\end{center}

\label{modelReconstructionThreeD}
\end{figure}
}

{\newpage
\clearpage
\samepage \begin{figure}\begin{center}
\begin{tabular}{cccc}
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/disassemble00-18-image-and-most-preferred-model}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/disassemble00-19-image-and-most-preferred-model}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/disassemble00-22-image-and-most-preferred-model}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/disassemble00-23-image-and-most-preferred-model}}}\\ 
Frame 18&
Frame 19&
Frame 22&
Frame 23\\ 
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/disassemble00-49-image-and-most-preferred-model}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/disassemble00-50-image-and-most-preferred-model}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/disassemble00-56-image-and-most-preferred-model}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/disassemble00-57-image-and-most-preferred-model}}}\\ 
Frame 49&
Frame 50&
Frame 56&
Frame 57\\ 
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/disassemble00-62-image-and-most-preferred-model}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/disassemble00-63-image-and-most-preferred-model}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/disassemble00-87-image-and-most-preferred-model}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/disassemble00-88-image-and-most-preferred-model}}}\\ 
Frame 62&
Frame 63&
Frame 87&
Frame 88
\end{tabular}
\end{center}

\label{modelReconstructionThreeE}
\end{figure}
}

{\newpage
\clearpage
\samepage \begin{figure}\begin{center}
\fbox{\begin{tt}\begin{tabular}{l}(PUT-DOWN MOVING RED BLUE)@\symbol{123}[[0,12],[24,30])\symbol{125}\\ 
(STACK MOVING RED BLUE GREEN)@\symbol{123}[[0,12],[24,30])\symbol{125}\\ 
\ \\ 
(SUPPORTED?\ MOVING)@\symbol{123}[[13:24])\symbol{125}\\ 
(SUPPORTED?\ RED)@\symbol{123}[[0:30])\symbol{125}\\ 
(SUPPORTED?\ BLUE)@\symbol{123}[[0:30])\symbol{125}\\ 
(SUPPORTS?\ MOVING RED)@\symbol{123}[[0:12])\symbol{125}\\ 
(SUPPORTS?\ RED MOVING)@\symbol{123}[[13:24])\symbol{125}\\ 
(SUPPORTS?\ RED BLUE)@\symbol{123}[[19:20]), [[21:22])\symbol{125}\\ 
(SUPPORTS?\ GREEN MOVING)@\symbol{123}[[19:20]), [[21:22])\symbol{125}\\ 
(SUPPORTS?\ GREEN RED)@\symbol{123}[[19:20]), [[21:22])\symbol{125}\\ 
(SUPPORTS?\ GREEN BLUE)@\symbol{123}[[0:30])\symbol{125}\\ 
(SUPPORTS?\ BLUE MOVING)@\symbol{123}[[13:24])\symbol{125}\\ 
(SUPPORTS?\ BLUE RED)@\symbol{123}[[12:30])\symbol{125}\\ 
(CONTACTS?\ RED BLUE)@\symbol{123}[[12:19]), [[20:21]), [[22:30])\symbol{125}\\ 
(CONTACTS?\ GREEN BLUE)@\symbol{123}[[0:30])\symbol{125}\\ 
(ATTACHED?\ MOVING RED)@\symbol{123}[[0:24])\symbol{125}\\ 
(ATTACHED?\ RED BLUE)@\symbol{123}[[19:20]), [[21:22])\symbol{125}\\ 
\end{tabular}\end{tt}}
\end{center}

\label{eventClassificationThreeA}
\end{figure}
}

{\newpage
\clearpage
\samepage \begin{figure}\begin{center}
\fbox{\begin{tt}\begin{tabular}{l}(PICK-UP MOVING RED BLUE)@\symbol{123}[[0,11],[25,33])\symbol{125}\\ 
(UNSTACK MOVING RED BLUE GREEN)@\symbol{123}[[0,11],[25,33])\symbol{125}\\ 
\ \\ 
(SUPPORTED?\ MOVING)@\symbol{123}[[11:23])\symbol{125}\\ 
(SUPPORTED?\ RED)@\symbol{123}[[0:36])\symbol{125}\\ 
(SUPPORTED?\ BLUE)@\symbol{123}[[0:36])\symbol{125}\\ 
(SUPPORTS?\ MOVING RED)@\symbol{123}[[23:36])\symbol{125}\\ 
(SUPPORTS?\ RED MOVING)@\symbol{123}[[11:23])\symbol{125}\\ 
(SUPPORTS?\ RED BLUE)@\symbol{123}[[13:14])\symbol{125}\\ 
(SUPPORTS?\ GREEN MOVING)@\symbol{123}[[13:14])\symbol{125}\\ 
(SUPPORTS?\ GREEN RED)@\symbol{123}[[13:14])\symbol{125}\\ 
(SUPPORTS?\ GREEN BLUE)@\symbol{123}[[0:36])\symbol{125}\\ 
(SUPPORTS?\ BLUE MOVING)@\symbol{123}[[11:23])\symbol{125}\\ 
(SUPPORTS?\ BLUE RED)@\symbol{123}[[0:25])\symbol{125}\\ 
(CONTACTS?\ MOVING RED)@\symbol{123}[[34:36])\symbol{125}\\ 
(CONTACTS?\ RED BLUE)@\symbol{123}[[0:13]), [[14:24])\symbol{125}\\ 
(CONTACTS?\ GREEN BLUE)@\symbol{123}[[0:13]), [[14:36])\symbol{125}\\ 
(ATTACHED?\ MOVING RED)@\symbol{123}[[11:33])\symbol{125}\\ 
(ATTACHED?\ RED BLUE)@\symbol{123}[[13:14])\symbol{125}\\ 
(ATTACHED?\ GREEN BLUE)@\symbol{123}[[13:14])\symbol{125}\\ 
\end{tabular}\end{tt}}
\end{center}

\label{eventClassificationThreeB}
\end{figure}
}

{\newpage
\clearpage
\samepage \begin{figure}\begin{center}
\fbox{\begin{tt}\begin{tabular}{l}(PICK-UP MOVING RED GREEN)@\symbol{123}[[0,9],[17,46])\symbol{125}\\ 
(PUT-DOWN MOVING RED BLUE)@\symbol{123}[[17,35],[46,52])\symbol{125}\\ 
(MOVE MOVING RED GREEN BLUE)@\symbol{123}[[0,9],[46,52])\symbol{125}\\ 
\ \\ 
(SUPPORTED?\ MOVING)@\symbol{123}[[9:15])\symbol{125}\\ 
(SUPPORTED?\ RED)@\symbol{123}[[0:52])\symbol{125}\\ 
(SUPPORTED?\ BLUE)@\symbol{123}[[35:46])\symbol{125}\\ 
(SUPPORTS?\ MOVING RED)@\symbol{123}[[17:46])\symbol{125}\\ 
(SUPPORTS?\ MOVING BLUE)@\symbol{123}[[35:46])\symbol{125}\\ 
(SUPPORTS?\ RED MOVING)@\symbol{123}[[9:15])\symbol{125}\\ 
(SUPPORTS?\ RED BLUE)@\symbol{123}[[35:46])\symbol{125}\\ 
(SUPPORTS?\ GREEN MOVING)@\symbol{123}[[9:15])\symbol{125}\\ 
(SUPPORTS?\ GREEN RED)@\symbol{123}[[0:17])\symbol{125}\\ 
(SUPPORTS?\ BLUE RED)@\symbol{123}[[46:52])\symbol{125}\\ 
(CONTACTS?\ RED GREEN)@\symbol{123}[[0:17])\symbol{125}\\ 
(CONTACTS?\ RED BLUE)@\symbol{123}[[46:52])\symbol{125}\\ 
(ATTACHED?\ MOVING RED)@\symbol{123}[[9:46])\symbol{125}\\ 
(ATTACHED?\ RED BLUE)@\symbol{123}[[35:46])\symbol{125}\\ 
\end{tabular}\end{tt}}
\end{center}

\label{eventClassificationThreeC}
\end{figure}
}

{\newpage
\clearpage
\samepage \begin{figure}\begin{center}
\fbox{\begin{tt}\begin{tabular}{l}(PUT-DOWN MOVING RED GREEN)@\symbol{123}[[57,68],[68,87])\symbol{125}\\ 
(PUT-DOWN MOVING GREEN BLUE)@\symbol{123}[[18,35],[41,47])\symbol{125}\\ 
(STACK MOVING RED GREEN BLUE)@\symbol{123}[[57,68],[68,87])\symbol{125}\\ 
(ASSEMBLE MOVING RED GREEN BLUE)@\symbol{123}[[18,35],[68,87])\symbol{125}\\ 
\ \\ 
(SUPPORTED?\ MOVING)@\symbol{123}[[10:18]), [[47:57])\symbol{125}\\ 
(SUPPORTED?\ RED)@\symbol{123}[[57:87])\symbol{125}\\ 
(SUPPORTED?\ GREEN)@\symbol{123}[[11:87])\symbol{125}\\ 
(SUPPORTED?\ BLUE)@\symbol{123}[[35:41])\symbol{125}\\ 
(SUPPORTS?\ MOVING RED)@\symbol{123}[[57:68])\symbol{125}\\ 
(SUPPORTS?\ MOVING GREEN)@\symbol{123}[[11:41])\symbol{125}\\ 
(SUPPORTS?\ MOVING BLUE)@\symbol{123}[[35:41])\symbol{125}\\ 
(SUPPORTS?\ RED MOVING)@\symbol{123}[[10:18]), [[47:57])\symbol{125}\\ 
(SUPPORTS?\ RED GREEN)@\symbol{123}[[11:16])\symbol{125}\\ 
(SUPPORTS?\ GREEN RED)@\symbol{123}[[68:87])\symbol{125}\\ 
(SUPPORTS?\ GREEN BLUE)@\symbol{123}[[35:41])\symbol{125}\\ 
(SUPPORTS?\ BLUE GREEN)@\symbol{123}[[41:87])\symbol{125}\\ 
(CONTACTS?\ RED GREEN)@\symbol{123}[[68:87])\symbol{125}\\ 
(CONTACTS?\ GREEN BLUE)@\symbol{123}[[41:87])\symbol{125}\\ 
(ATTACHED?\ MOVING RED)@\symbol{123}[[11:16]), [[49:68])\symbol{125}\\ 
(ATTACHED?\ MOVING GREEN)@\symbol{123}[[11:41])\symbol{125}\\ 
(ATTACHED?\ GREEN BLUE)@\symbol{123}[[35:41])\symbol{125}\\ 
\end{tabular}\end{tt}}
\end{center}

\label{eventClassificationThreeD}
\end{figure}
}

{\newpage
\clearpage
\samepage \begin{figure}\begin{center}
\fbox{\begin{tt}\begin{tabular}{l}(PICK-UP MOVING RED GREEN)@\symbol{123}[[0,19],[23,50])\symbol{125}\\ 
(PICK-UP MOVING GREEN BLUE)@\symbol{123}[[22,58],[62,87])\symbol{125}\\ 
(UNSTACK MOVING RED GREEN BLUE)@\symbol{123}[[0,19],[23,50])\symbol{125}\\ 
(DISASSEMBLE MOVING RED GREEN BLUE)@\symbol{123}[[0,19],[62,87])\symbol{125}\\ 
\ \\ 
(SUPPORTED?\ MOVING)@\symbol{123}[[19:22])\symbol{125}\\ 
(SUPPORTED?\ RED)@\symbol{123}[[0:50])\symbol{125}\\ 
(SUPPORTED?\ GREEN)@\symbol{123}[[0:87])\symbol{125}\\ 
(SUPPORTED?\ BLUE)@\symbol{123}[[58:62])\symbol{125}\\ 
(SUPPORTS?\ MOVING RED)@\symbol{123}[[23:50])\symbol{125}\\ 
(SUPPORTS?\ MOVING GREEN)@\symbol{123}[[58:87])\symbol{125}\\ 
(SUPPORTS?\ MOVING BLUE)@\symbol{123}[[58:62])\symbol{125}\\ 
(SUPPORTS?\ RED MOVING)@\symbol{123}[[19:22])\symbol{125}\\ 
(SUPPORTS?\ GREEN MOVING)@\symbol{123}[[19:22])\symbol{125}\\ 
(SUPPORTS?\ GREEN RED)@\symbol{123}[[0:23])\symbol{125}\\ 
(SUPPORTS?\ GREEN BLUE)@\symbol{123}[[58:62])\symbol{125}\\ 
(SUPPORTS?\ BLUE GREEN)@\symbol{123}[[0:58])\symbol{125}\\ 
(CONTACTS?\ RED GREEN)@\symbol{123}[[0:23])\symbol{125}\\ 
(CONTACTS?\ GREEN BLUE)@\symbol{123}[[0:58])\symbol{125}\\ 
(ATTACHED?\ MOVING RED)@\symbol{123}[[19:50])\symbol{125}\\ 
(ATTACHED?\ MOVING GREEN)@\symbol{123}[[58:87])\symbol{125}\\ 
(ATTACHED?\ GREEN BLUE)@\symbol{123}[[58:62])\symbol{125}\\ 
\end{tabular}\end{tt}}
\end{center}

\label{eventClassificationThreeE}
\end{figure}
}

{\newpage
\clearpage
\samepage \begin{figure}\begin{center}
\begin{tabular}{cccc}
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/pick-up01-5-image-and-most-preferred-model}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/pick-up01-10-image-and-most-preferred-model}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/pick-up01-11-image-and-most-preferred-model}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/pick-up01-17-image-and-most-preferred-model}}}\\ 
Frame 5&
Frame 10&
Frame 11&
Frame 17\\ 
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/pick-up01-18-image-and-most-preferred-model}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/pick-up01-22-image-and-most-preferred-model}}}\\ 
Frame 18&
Frame 22
\end{tabular}
\end{center}

\label{modelReconstructionFourA}
\end{figure}
}

{\newpage
\clearpage
\samepage \begin{figure}\begin{center}
\begin{tabular}{cccc}
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/pick-up02-6-image-and-most-preferred-model}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/pick-up02-7-image-and-most-preferred-model}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/pick-up02-8-image-and-most-preferred-model}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/pick-up02-18-image-and-most-preferred-model}}}\\ 
Frame 6&
Frame 7&
Frame 8&
Frame 18\\ 
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/pick-up02-19-image-and-most-preferred-model}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/pick-up02-24-image-and-most-preferred-model}}}\\ 
Frame 19&
Frame 24
\end{tabular}
\end{center}

\label{modelReconstructionFourB}
\end{figure}
}

{\newpage
\clearpage
\samepage \begin{figure}\begin{center}
\begin{tabular}{cccc}
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/sequential00-4-image-and-most-preferred-model}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/sequential00-8-image-and-most-preferred-model}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/sequential00-9-image-and-most-preferred-model}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/sequential00-18-image-and-most-preferred-model}}}\\ 
Frame 4&
Frame 8&
Frame 9&
Frame 18\\ 
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/sequential00-19-image-and-most-preferred-model}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/sequential00-44-image-and-most-preferred-model}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/sequential00-45-image-and-most-preferred-model}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/sequential00-51-image-and-most-preferred-model}}}\\ 
Frame 19&
Frame 44&
Frame 45&
Frame 51\\ 
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/sequential00-52-image-and-most-preferred-model}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/sequential00-69-image-and-most-preferred-model}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/sequential00-70-image-and-most-preferred-model}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/sequential00-77-image-and-most-preferred-model}}}\\ 
Frame 52&
Frame 69&
Frame 70&
Frame 77\\ 
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/sequential00-78-image-and-most-preferred-model}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/sequential00-102-image-and-most-preferred-model}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/sequential00-103-image-and-most-preferred-model}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/sequential00-109-image-and-most-preferred-model}}}\\ 
Frame 78&
Frame 102&
Frame 103&
Frame 109\\ 
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/sequential00-110-image-and-most-preferred-model}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/sequential00-111-image-and-most-preferred-model}}}\\ 
Frame 110&
Frame 111
\end{tabular}
\end{center}

\label{modelReconstructionFourC}
\end{figure}
}

{\newpage
\clearpage
\samepage \begin{figure}\begin{center}
\begin{tabular}{cccc}
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/simultaneous00-0-image-and-most-preferred-model}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/simultaneous00-5-image-and-most-preferred-model}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/simultaneous00-6-image-and-most-preferred-model}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/simultaneous00-10-image-and-most-preferred-model}}}\\ 
Frame 0&
Frame 5&
Frame 6&
Frame 10\\ 
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/simultaneous00-11-image-and-most-preferred-model}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/simultaneous00-15-image-and-most-preferred-model}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/simultaneous00-16-image-and-most-preferred-model}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/simultaneous00-21-image-and-most-preferred-model}}}\\ 
Frame 11&
Frame 15&
Frame 16&
Frame 21
\end{tabular}
\end{center}

\label{modelReconstructionFourD}
\end{figure}
}

{\newpage
\clearpage
\samepage \begin{figure}\begin{center}
\begin{tabular}{rccc}
\raisebox{32pt}{(a)}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/none01-4-image-and-most-preferred-model}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/none01-11-image-and-most-preferred-model}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/none01-12-image-and-most-preferred-model}}}\\ 
&
Frame 4&
Frame 11&
Frame 12\\ 
&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/none01-18-image-and-most-preferred-model}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/none01-19-image-and-most-preferred-model}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/none01-21-image-and-most-preferred-model}}}\\ 
&
Frame 18&
Frame 19&
Frame 21\\ \hline\\ [-5pt]
\raisebox{32pt}{(b)}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/none00-0-image-and-most-preferred-model}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/none00-6-image-and-most-preferred-model}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/none00-7-image-and-most-preferred-model}}}\\ 
&
Frame 0&
Frame 6&
Frame 7\\ 
&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/none00-12-image-and-most-preferred-model}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/none00-13-image-and-most-preferred-model}}}&
\mbox{\scalebox{\ifnum 30=100 1 \else .30\fi}
{\includegraphics{siskind2001a/none00-18-image-and-most-preferred-model}}}\\ 
&
Frame 12&
Frame 13&
Frame 18
\end{tabular}
\end{center}

\label{modelReconstructionTwo}
\end{figure}
}

{\newpage
\clearpage
\samepage \begin{figure}\begin{center}
\fbox{\begin{tt}\begin{tabular}{l}(PICK-UP MOVING RED GREEN)@\symbol{123}[[0,11],[18,30])\symbol{125}\\ 
\ \\ 
(SUPPORTED?\ RED)@\symbol{123}[[0:30])\symbol{125}\\ 
(SUPPORTED?\ GREEN)@\symbol{123}[[11:18])\symbol{125}\\ 
(SUPPORTS?\ MOVING RED)@\symbol{123}[[11:30])\symbol{125}\\ 
(SUPPORTS?\ MOVING GREEN)@\symbol{123}[[11:18])\symbol{125}\\ 
(SUPPORTS?\ RED GREEN)@\symbol{123}[[11:18])\symbol{125}\\ 
(SUPPORTS?\ GREEN RED)@\symbol{123}[[0:11])\symbol{125}\\ 
(CONTACTS?\ RED GREEN)@\symbol{123}[[0:11])\symbol{125}\\ 
(ATTACHED?\ MOVING RED)@\symbol{123}[[11:30])\symbol{125}\\ 
(ATTACHED?\ RED GREEN)@\symbol{123}[[11:18])\symbol{125}\\ 
\end{tabular}\end{tt}}
\end{center}

\label{eventClassificationFourA}
\end{figure}
}

{\newpage
\clearpage
\samepage \begin{figure}\begin{center}
\fbox{\begin{tt}\begin{tabular}{l}(PICK-UP MOVING RED GREEN)@\symbol{123}[[0,8],[19,30])\symbol{125}\\ 
\ \\ 
(SUPPORTED?\ MOVING)@\symbol{123}[[8:19])\symbol{125}\\ 
(SUPPORTED?\ RED)@\symbol{123}[[0:30])\symbol{125}\\ 
(SUPPORTED?\ BLUE)@\symbol{123}[[0:30])\symbol{125}\\ 
(SUPPORTS?\ MOVING RED)@\symbol{123}[[19:30])\symbol{125}\\ 
(SUPPORTS?\ RED MOVING)@\symbol{123}[[8:19])\symbol{125}\\ 
(SUPPORTS?\ GREEN MOVING)@\symbol{123}[[8:19])\symbol{125}\\ 
(SUPPORTS?\ GREEN RED)@\symbol{123}[[0:19])\symbol{125}\\ 
(SUPPORTS?\ YELLOW BLUE)@\symbol{123}[[0:30])\symbol{125}\\ 
(CONTACTS?\ RED GREEN)@\symbol{123}[[0:10]), [[16:19])\symbol{125}\\ 
(CONTACTS?\ BLUE YELLOW)@\symbol{123}[[0:30])\symbol{125}\\ 
(ATTACHED?\ MOVING RED)@\symbol{123}[[8:30])\symbol{125}\\ 
(ATTACHED?\ RED GREEN)@\symbol{123}[[10:16])\symbol{125}\\ 
\end{tabular}\end{tt}}
\end{center}

\label{eventClassificationFourB}
\end{figure}
}

{\newpage
\clearpage
\samepage \begin{figure}\begin{center}
\fbox{\begin{tt}\begin{tabular}{l}(PICK-UP MOVING RED GREEN)@\symbol{123}[[52,70],[78,102]),\\ 
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [[0,9],[19,44])\symbol{125}\\ 
(PUT-DOWN MOVING RED GREEN)@\symbol{123}[[19,44],[52,70]),\\ 
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [[78,102],[110,117])\symbol{125}\\ 
\ \\ 
(SUPPORTED?\ MOVING)@\symbol{123}[[9:18]), [[44:52]),\\ 
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [[70:77]), [[102:110])\symbol{125}\\ 
(SUPPORTED?\ RED)@\symbol{123}[[0:117])\symbol{125}\\ 
(SUPPORTS?\ MOVING RED)@\symbol{123}[[18:44]), [[78:102])\symbol{125}\\ 
(SUPPORTS?\ RED MOVING)@\symbol{123}[[9:18]), [[44:52]),\\ 
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [[70:77]), [[102:110])\symbol{125}\\ 
(SUPPORTS?\ GREEN MOVING)@\symbol{123}[[9:18]), [[44:52]),\\ 
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [[70:77]), [[102:110])\symbol{125}\\ 
(SUPPORTS?\ GREEN RED)@\symbol{123}[[0:19]), [[44:78]), [[102:117])\symbol{125}\\ 
(CONTACTS?\ RED GREEN)@\symbol{123}[[0:9]), [[13:18]), [[46:70]),\\ 
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [[106:117])\symbol{125}\\ 
(ATTACHED?\ MOVING RED)@\symbol{123}[[9:52]), [[70:110])\symbol{125}\\ 
(ATTACHED?\ RED GREEN)@\symbol{123}[[9:13]), [[70:76]), [[104:106])\symbol{125}\\ 
\end{tabular}\end{tt}}
\end{center}

\label{eventClassificationFourC}
\end{figure}
}

{\newpage
\clearpage
\samepage \begin{figure}\begin{center}
\fbox{\begin{tt}\begin{tabular}{l}(PICK-UP MOVING RED GREEN)@\symbol{123}[[0,6],[16,22])\symbol{125}\\ 
(PICK-UP MOVING YELLOW BLUE)@\symbol{123}[[0,12],[17,22])\symbol{125}\\ 
\ \\ 
(SUPPORTED?\ MOVING)@\symbol{123}[[6:16])\symbol{125}\\ 
(SUPPORTED?\ MOVING)@\symbol{123}[[12:15])\symbol{125}\\ 
(SUPPORTED?\ RED)@\symbol{123}[[0:22])\symbol{125}\\ 
(SUPPORTED?\ YELLOW)@\symbol{123}[[0:22])\symbol{125}\\ 
(SUPPORTS?\ MOVING RED)@\symbol{123}[[16:22])\symbol{125}\\ 
(SUPPORTS?\ MOVING YELLOW)@\symbol{123}[[17:22])\symbol{125}\\ 
(SUPPORTS?\ RED MOVING)@\symbol{123}[[6:16])\symbol{125}\\ 
(SUPPORTS?\ GREEN MOVING)@\symbol{123}[[6:16])\symbol{125}\\ 
(SUPPORTS?\ GREEN RED)@\symbol{123}[[0:16])\symbol{125}\\ 
(SUPPORTS?\ BLUE MOVING)@\symbol{123}[[12:15])\symbol{125}\\ 
(SUPPORTS?\ BLUE YELLOW)@\symbol{123}[[0:17])\symbol{125}\\ 
(SUPPORTS?\ YELLOW MOVING)@\symbol{123}[[12:15])\symbol{125}\\ 
(CONTACTS?\ RED GREEN)@\symbol{123}[[0:15])\symbol{125}\\ 
(CONTACTS?\ BLUE YELLOW)@\symbol{123}[[0:17])\symbol{125}\\ 
(ATTACHED?\ MOVING RED)@\symbol{123}[[6:22])\symbol{125}\\ 
(ATTACHED?\ MOVING YELLOW)@\symbol{123}[[12:22])\symbol{125}\\ 
\end{tabular}\end{tt}}
\end{center}

\label{eventClassificationFourD}
\end{figure}
}

{\newpage
\clearpage
\samepage \begin{figure}\begin{center}
\begin{tabular}{c}
\fbox{\begin{tt}\begin{tabular}{l}(SUPPORTED?\ RED)@\symbol{123}[[0:19])\symbol{125}\\ 
(SUPPORTED?\ MOVING)@\symbol{123}[[13:31])\symbol{125}\\ 
(SUPPORTS?\ RED MOVING)@\symbol{123}[[13:31])\symbol{125}\\ 
(SUPPORTS?\ MOVING RED)@\symbol{123}[[0:13])\symbol{125}\\ 
(SUPPORTS?\ GREEN RED)@\symbol{123}[[12:19])\symbol{125}\\ 
(SUPPORTS?\ GREEN MOVING)@\symbol{123}[[13:19])\symbol{125}\\ 
(ATTACHED?\ RED MOVING)@\symbol{123}[[0:31])\symbol{125}\\ 
(ATTACHED?\ RED GREEN)@\symbol{123}[[13:19])\symbol{125}\\ 
\end{tabular}\end{tt}}\\ 
(a)\\ *[2ex]
\fbox{\begin{tt}\begin{tabular}{l}(SUPPORTED?\ RED)@\symbol{123}[[0:25])\symbol{125}\\ 
(SUPPORTED?\ GREEN)@\symbol{123}[[7:13])\symbol{125}\\ 
(SUPPORTS?\ MOVING RED)@\symbol{123}[[7:13])\symbol{125}\\ 
(SUPPORTS?\ MOVING GREEN)@\symbol{123}[[7:13])\symbol{125}\\ 
(SUPPORTS?\ RED GREEN)@\symbol{123}[[7:13])\symbol{125}\\ 
(SUPPORTS?\ GREEN RED)@\symbol{123}[[0:7]), [[13:25])\symbol{125}\\ 
(CONTACTS?\ RED GREEN)@\symbol{123}[[0:7]), [[13:25])\symbol{125}\\ 
(ATTACHED?\ MOVING RED)@\symbol{123}[[7:13])\symbol{125}\\ 
(ATTACHED?\ RED GREEN)@\symbol{123}[[7:13])\symbol{125}\\ 
\end{tabular}\end{tt}}\\ 
(b)
\end{tabular}
\end{center}

\label{eventClassificationTwo}
\end{figure}
}

{\newpage
\clearpage
\samepage \begin{table}\begin{center}
\begin{tabular}{l|ccccccc}
&
{\em pick up\/} &
{\em put down\/} &
{\em stack\/} &
{\em unstack\/} &
{\em move\/} &
{\em assemble\/} &
{\em disassemble\/}\\ \hline
{\em pick up\/} & 5/5 & & & & & & \\ 
{\em put down\/} & & 5/5 & & & & & \\ 
{\em stack\/} & & 5/5 & 5/5 & & & & \\ 
{\em unstack\/} & 5/5 & & & 4/5 & & & \\ 
{\em move\/} & 4/5 & 5/5 & & & 4/5 & & \\ 
{\em assemble\/} & & 5/10 & 1/5 & & & 1/5 & \\ 
{\em disassemble\/} & 10/10 & & & 5/5 & & & 5/5
\end{tabular}
\end{center}

\label{evaluation}
\end{table}
}

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\end{document}
