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1 <HTML lang=en> |
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2 <HEAD> |
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3 <TITLE> Christian Urban </TITLE> |
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4 <BASE HREF="http://www4.in.tum.de/~urbanc/Cut/"> |
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5 </HEAD> |
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6 |
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7 <BODY TEXT="#000000" |
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8 BGCOLOR="#000080" |
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9 LINK="#0000EF" |
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10 VLINK="#51188E" |
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11 ALINK="#FF0000"> |
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12 |
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13 <TABLE WIDTH="100%" |
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16 BORDER="0" |
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17 FRAME="none" |
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18 CELLPADDING="10" |
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19 CELLSPACING="2" |
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20 RULES="COLS,ROWS"> |
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21 |
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22 <!-- left column --> |
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23 <TR> |
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24 <TD BGCOLOR="#FFFFFF" |
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25 WIDTH="24%" |
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26 VALIGN="TOP" |
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27 ROWSPAN="4"> |
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28 |
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29 <B>Links</B><BR> |
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30 <A HREF="http://www4.in.tum.de/~urbanc/cutapplet.html">Home</A><BR> |
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31 <A HREF="http://www4.in.tum.de/~urbanc/Cut/index.html">Applet Home</A><BR><BR><p> |
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32 |
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33 <B>Java Versions</B><BR> |
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34 <A HREF="http://www4.in.tum.de/~urbanc/Cut/CL.html">CL</A><BR> |
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35 <A HREF="http://www4.in.tum.de/~urbanc/Cut/LJT.html">LJT</A><BR> |
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36 <A HREF="http://www4.in.tum.de/~urbanc/Cut/ND.html">ND</A><BR><BR> |
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37 |
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38 <B>Plugin Versions</B><BR> |
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39 <A HREF="http://www4.in.tum.de/~urbanc/Cut/CL-plugin.html">CL</A><BR> |
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40 <A HREF="http://www4.in.tum.de/~urbanc/Cut/LJT-plugin.html">LJT</A><BR> |
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41 <A HREF="http://www4.in.tum.de/~urbanc/Cut/ND-plugin.html">ND</A><BR> |
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42 |
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43 <BR> |
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44 <BR> |
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45 |
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46 <A HREF="http://isabelle.in.tum.de/nominal/"> |
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47 <IMG SRC="ribbon.gif" ALT="" style="width: 114px; height: 100px;" align="left"> |
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48 </A> |
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49 </TD> |
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50 |
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51 |
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52 <!-- right column --> |
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53 <TD BGCOLOR="#FFFFFF" WIDTH="75%"> |
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54 <A NAME="Home"></A> |
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55 <H2>Cut-Elimination in Classical Logic</H2> |
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56 |
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57 If you use this applet it is strongly(!) recommended to have read the the paper on |
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58 strong normalisation of cut-elimination in classical logic by Urban and Bierman |
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59 [<A HREF="http://www4.in.tum.de/~urbanc/Publications/fi-01.ps.gz">ps.gz</A>, |
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60 <A HREF="http://www4.in.tum.de/~urbanc/Publications/fi-01.pdf">pdf</A>]. |
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61 Mayor difference between the standard sequent calculus and the sequent calculus |
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62 implemented by the applet is that the rules contraction and weakening are completely |
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63 implicit. This means that sequents consist of two sets of (labelled) formulae, |
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64 as opposed to lists or multisets of formulae. Although this is very simple, it |
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65 needs some time to get used to. |
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66 </TD> |
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67 </TR> |
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68 |
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69 <TR> |
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70 <TD BGCOLOR="#FFFFFF" WIDTH="75%"> |
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71 <B>How to use it?</B> |
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72 If your browser is playing game with Java, then you will see a window |
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73 with a number of examples. When pressing on one of the buttons, a new |
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74 window will pop up. What follows is a brief explanation of all |
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75 the features available in this window. |
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76 </TD> |
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77 </TR> |
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78 |
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79 <TR> |
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80 <TD BGCOLOR="#FFFFFF" WIDTH="75%"> |
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81 <B>Buttons and Keys</B> |
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82 <UL> |
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83 <LI> The buttons |
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84 <IMG SRC="http://www4.in.tum.de/~urbanc/Cut/l.jpg"> and |
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85 <IMG SRC="http://www4.in.tum.de/~urbanc/Cut/r.jpg"> are for |
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86 commuting cuts, which can slide up either in the right or left proof branch. |
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87 <LI> Pressing on <IMG SRC="http://www4.in.tum.de/~urbanc/Cut/x.jpg"> |
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88 , <IMG SRC="http://www4.in.tum.de/~urbanc/Cut/x1.jpg"> or |
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89 <IMG SRC="http://www4.in.tum.de/~urbanc/Cut/x2.jpg"> |
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90 `fires' a logical cut. The latter two buttons correspond to the two possible |
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91 nestings of multiplicative logical cuts. |
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92 <LI> If you use the <B>left mouse button</B> for pressing on those buttons, |
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93 then the new proof will appear inside the window. Whereas if you use |
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94 the <B>right mouse button</B>, a new window will pop up and |
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95 the new proof will be displayed in this window. Use the right mouse |
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96 button if you want to compare a proof and its reduct(s). |
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97 <LI> The keys <B>Page-up</B> and <B>Page-down</B> zoom in or out of a proof |
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98 respectively. |
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99 </UL> |
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100 </TD> |
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101 </TR> |
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102 |
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103 <TR> |
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104 <TD BGCOLOR="#FFFFFF" WIDTH="75%"> |
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105 <B>Menu Functions</B> |
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106 |
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107 <UL> |
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108 <LI> <B>Zoom in</B> and <B>Zoom out</B> work like Page-up and Page-down, |
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109 respectively. |
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110 <LI> <B>Unicode</B> If this radiobutton is switched on, logic symbols |
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111 are displayed in unicode, otherwise in ascii. (This is for the |
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112 poor guys who have a browser and/or operating system which cannot handle |
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113 unicode.) |
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114 <LI> <B>Labels</B> As mentioned earlier the sequents are composed of |
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115 two sets of labelled |
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116 formulae, not multisets of formulae as in the standard formulation |
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117 of sequent calculus. Enabling this radiobutton causes that labels are |
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118 drawn. Use this when you are unsure where implicit contractions are. |
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119 <LI> <B>Auxiliary Substitution</B> If you have read the paper referred |
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120 above, you know what this does. |
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121 <LI> <B>Gentzen's D.N.Transl.</B> and <B>Kolmogorov's D.N.Transl.</B> |
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122 perform double negation translations on the current proof. |
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123 </UL> |
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124 </TD> |
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125 </TR> |
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126 |
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127 </TABLE> |
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128 <center> |
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129 <!--"CONVERTED_APPLET"--> |
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130 <!-- HTML CONVERTER --> |
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131 <OBJECT classid="clsid:CAFEEFAC-0013-0001-0000-ABCDEFFEDCBA" |
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132 WIDTH = 1 HEIGHT = 1 codebase="http://java.sun.com/products/plugin/1.3.1/jinstall-131-win32.cab#Version=1,3,1,0"> |
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133 <PARAM NAME = CODE VALUE = "MyApplet.class" > |
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134 <PARAM NAME = ARCHIVE VALUE = MyApplet.zip > |
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135 |
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136 <PARAM NAME="type" VALUE="application/x-java-applet;jpi-version=1.3.1"> |
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137 <PARAM NAME="scriptable" VALUE="false"> |
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138 <PARAM NAME = "calculi" VALUE ="A"> |
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139 <COMMENT> |
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140 <EMBED type="application/x-java-applet;jpi-version=1.3.1" CODE = "MyApplet.class" ARCHIVE = MyApplet.zip WIDTH = 1 HEIGHT = 1 calculi = "A" scriptable=false pluginspage="http://java.sun.com/products/plugin/1.3.1/plugin-install.html"><NOEMBED> |
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141 <p><blink><FONT COLOR="#800000"> |
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142 Applet should appear in a new window, but you don't have Java enabled in your browser. |
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143 </FONT></blink><p> |
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144 </NOEMBED> |
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145 </EMBED> |
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146 </COMMENT> |
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147 </OBJECT> |
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148 |
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149 <!-- |
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150 <APPLET CODE = "MyApplet.class" ARCHIVE = MyApplet.zip WIDTH = 1 HEIGHT = 1> |
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151 <PARAM NAME = "calculi" VALUE ="A"> |
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152 <p><blink><FONT COLOR="#800000"> |
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153 Applet should appear in a new window, but you don't have Java enabled in your browser. |
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154 </FONT></blink><p> |
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155 |
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156 </APPLET> |
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157 --> |
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158 |
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159 |
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160 <!--"END_CONVERTED_APPLET"--> |
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161 |
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162 |
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163 </center> |
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164 <P><!-- Created: Tue Jul 3 21:01:42 BST 2001 --> |
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165 <!-- hhmts start --> |
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166 Last modified: Sat Mar 3 05:17:41 CET 2007 |
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167 <!-- hhmts end --> |
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168 </BODY> |
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169 </HTML> |