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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 Classical Logic</H2>
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If you use this applet it is strongly(!) recommended to have read the the paper on
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strong normalisation of cut-elimination in classical logic by Urban and Bierman
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[<A HREF="http://www4.in.tum.de/~urbanc/Publications/fi-01.ps.gz">ps.gz</A>,
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<A HREF="http://www4.in.tum.de/~urbanc/Publications/fi-01.pdf">pdf</A>].
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Mayor difference between the standard sequent calculus and the sequent calculus
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implemented by the applet is that the rules contraction and weakening are completely
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implicit. This means that sequents consist of two sets of (labelled) formulae,
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as opposed to lists or multisets of formulae. Although this is very simple, it
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needs some time to get used to.
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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 playing game with Java, then you will see a window
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with a number of examples. When pressing on one of the buttons, a new
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window will pop up. What follows is a brief explanation of all
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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/l.jpg"> and
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<IMG SRC="http://www4.in.tum.de/~urbanc/Cut/r.jpg"> are for
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commuting cuts, which can slide up either in the right or left proof branch.
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<LI> Pressing on <IMG SRC="http://www4.in.tum.de/~urbanc/Cut/x.jpg">
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, <IMG SRC="http://www4.in.tum.de/~urbanc/Cut/x1.jpg"> or
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<IMG SRC="http://www4.in.tum.de/~urbanc/Cut/x2.jpg">
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`fires' a logical cut. The latter two buttons correspond to the two possible
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nestings of multiplicative logical cuts.
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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(s).
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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>Auxiliary Substitution</B> If you have read the paper referred
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above, you know what this does.
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<LI> <B>Gentzen's D.N.Transl.</B> and <B>Kolmogorov's D.N.Transl.</B>
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perform double negation translations on the current proof.
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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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<applet archive=MyApplet.zip code="MyApplet.class" width=1 height=1>
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<param name="calculi" value="A">
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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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</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 05:17:31 CET 2007
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<!-- hhmts end -->
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</BODY>
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</HTML>
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