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<HTML lang=en>
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<HEAD>
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<TITLE> Christian Urban </TITLE>
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<BASE HREF="http://www4.in.tum.de/~urbanc/Cut/">
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</HEAD>
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<BODY TEXT="#000000"
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BGCOLOR="#000080"
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LINK="#0000EF"
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VLINK="#51188E"
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ALINK="#FF0000">
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<TABLE WIDTH="100%"
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COLS="2"
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BGCOLOR="#000080"
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BORDER="0"
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FRAME="none"
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CELLPADDING="10"
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CELLSPACING="2"
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RULES="COLS,ROWS">
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<!-- left column -->
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<TR>
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<TD BGCOLOR="#FFFFFF"
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WIDTH="24%"
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VALIGN="TOP"
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ROWSPAN="4">
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<B>Links</B><BR>
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<A HREF="http://www4.in.tum.de/~urbanc/index.html">Home</A><BR>
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<A HREF="http://www4.in.tum.de/~urbanc/Cut/cutapplet.html">Applet Home</A><BR><BR><p>
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<B>Java Versions</B><BR>
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<A HREF="http://www4.in.tum.de/~urbanc/Cut/CL.html">CL</A><BR>
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<A HREF="http://www4.in.tum.de/~urbanc/Cut/LJT.html">LJT</A><BR>
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<A HREF="http://www4.in.tum.de/~urbanc/Cut/ND.html">ND</A><BR><BR>
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<B>Plugin Versions</B><BR>
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<A HREF="http://www4.in.tum.de/~urbanc/Cut/CL-plugin.html">CL</A><BR>
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<A HREF="http://www4.in.tum.de/~urbanc/Cut/LJT-plugin.html">LJT</A><BR>
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<A HREF="http://www4.in.tum.de/~urbanc/Cut/ND-plugin.html">ND</A><BR>
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<BR>
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<BR>
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<A HREF="http://isabelle.in.tum.de/nominal/">
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<IMG SRC="ribbon.gif" ALT="" style="width: 114px; height: 100px;" align="left">
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</A>
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</TD>
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<!-- right column -->
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<TD BGCOLOR="#FFFFFF" WIDTH="75%">
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<A NAME="Home"></A>
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<H2>Cut-Elimination in Herbelin's calculus for intuitionistic logic</H2>
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Recommended reading for this applet is a paper by Dyckhoff and Urban,
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[<A HREF="http://www-theory.dcs.st-and.ac.uk/~rd/publications/MJES/DyckhoffUrbanWestApp01.rev.ps">ps</A>,
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<A HREF="http://www-theory.dcs.st-and.ac.uk/~rd/publications/MJES/DyckhoffUrbanWestApp01.rev.ps">pdf</A>].
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Mayor difference between the standard sequent calculus and Herbelin's sequent calculus
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is that in the cut-free fragment "there are no semantically
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trivial permutations of the inference rules, where by 'semantically trivial' we mean
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'interpreted in NJ as true equations between to (normal) deductions'"
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(from [<A HREF="http://www-theory.dcs.st-and.ac.uk/~rd/publications/SLPaper.corr.ps">ps</A>]).
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</TD>
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</TR>
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<TR>
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<TD BGCOLOR="#FFFFFF" WIDTH="75%">
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<B>How to use it?</B>
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If your browser is working correctly, then you will see a window
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with two examples (more added if you suggest some). When pressing on
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one of the buttons, a new window will pop up. What follows
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is a brief explanation of all the features available in this window.
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</TD>
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</TR>
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<TR>
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<TD BGCOLOR="#FFFFFF" WIDTH="75%">
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<B>Buttons and Keys</B>
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<UL>
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<LI> The buttons
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<IMG SRC="http://www4.in.tum.de/~urbanc/Cut/x.jpg">
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`fire' cuts (not all cuts necessarily have such buttons).
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<LI> If you use the <B>left mouse button</B> for pressing on those buttons,
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then the new proof will appear inside the window. Whereas if you use
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the <B>right mouse button</B>, a new window will pop up and
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the new proof will be displayed in this window. Use the right mouse
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button if you want to compare a proof and its reduct.
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<LI> The keys <B>Page-up</B> and <B>Page-down</B> zoom in or out of a proof
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respectively.
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</UL>
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</TD>
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</TR>
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<TR>
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<TD BGCOLOR="#FFFFFF" WIDTH="75%">
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<B>Menu Functions</B>
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<UL>
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<LI> <B>Zoom in</B> and <B>Zoom out</B> work like Page-up and Page-down,
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respectively.
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<LI> <B>Unicode</B> If this radiobutton is switched on, logic symbols
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are displayed in unicode, otherwise in ascii. (This is for the
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poor guys who have a browser and/or operating system which cannot handle
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unicode.)
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<LI> <B>Labels</B> As mentioned earlier the sequents are composed of
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two sets of labelled
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formulae, not multisets of formulae as in the standard formulation
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of sequent calculus. Enabling this radiobutton causes that labels are
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drawn. Use this when you are unsure where implicit contractions are.
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<LI> <B>Compact printing</B> In the paper referred above weakening
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is done only in axioms. If this radiobutton is switched on (default),
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then, in order to save space, formulae are weakened as soon as possible.
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</UL>
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</TD>
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</TR>
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</TABLE>
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<center>
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<!--"CONVERTED_APPLET"-->
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<!-- HTML CONVERTER -->
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<OBJECT classid="clsid:CAFEEFAC-0013-0001-0000-ABCDEFFEDCBA"
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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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<PARAM NAME = CODE VALUE = "MyApplet.class" >
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<PARAM NAME = ARCHIVE VALUE = MyApplet.zip >
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<PARAM NAME="type" VALUE="application/x-java-applet;jpi-version=1.3.1">
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<PARAM NAME="scriptable" VALUE="false">
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<PARAM NAME = "calculi" VALUE ="B">
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<COMMENT>
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<EMBED type="application/x-java-applet;jpi-version=1.3.1" CODE = "Cut/MyApplet.class" ARCHIVE = MyApplet.zip WIDTH = 1 HEIGHT = 1 calculi = "B" scriptable=false pluginspage="http://java.sun.com/products/plugin/1.3.1/plugin-install.html"><NOEMBED>
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<p><blink><FONT COLOR="#800000">
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Applet should appear in a new window, but you don't have Java enabled in your browser.
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</FONT></blink><p>
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</NOEMBED>
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</EMBED>
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</COMMENT>
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</OBJECT>
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<!--
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<APPLET CODE = "Cut/MyApplet.class" ARCHIVE = MyApplet.zip WIDTH = 1 HEIGHT = 1>
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<PARAM NAME = "calculi" VALUE ="B">
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<p><blink><FONT COLOR="#800000">
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Applet should appear in a new window, but you don't have Java enabled in your browser.
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</FONT></blink><p>
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</APPLET>
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-->
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<!--"END_CONVERTED_APPLET"-->
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</center>
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<P><!-- Created: Tue Jul 3 21:01:42 BST 2001 -->
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<!-- hhmts start -->
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Last modified: Sat Mar 3 05:17:20 CET 2007
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<!-- hhmts end -->
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</BODY>
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</HTML>
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