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<TITLE> Christian Urban </TITLE>+ −
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<B>Links</B><BR>+ −
<A HREF="http://www4.in.tum.de/~urbanc/index.html">Home</A><BR>+ −
<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>+ −
<A HREF="http://www4.in.tum.de/~urbanc/Cut/CL.html">CL</A><BR>+ −
<A HREF="http://www4.in.tum.de/~urbanc/Cut/LJT.html">LJT</A><BR>+ −
<A HREF="http://www4.in.tum.de/~urbanc/Cut/ND.html">ND</A><BR><BR>+ −
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<B>Plugin Versions</B><BR>+ −
<A HREF="http://www4.in.tum.de/~urbanc/Cut/CL-plugin.html">CL</A><BR>+ −
<A HREF="http://www4.in.tum.de/~urbanc/Cut/LJT-plugin.html">LJT</A><BR>+ −
<A HREF="http://www4.in.tum.de/~urbanc/Cut/ND-plugin.html">ND</A><BR>+ −
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<A HREF="http://isabelle.in.tum.de/nominal/">+ −
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<A NAME="Home"></A>+ −
<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 + −
strong normalisation of cut-elimination in classical logic by Urban and Bierman+ −
[<A HREF="http://www4.in.tum.de/~urbanc/Publications/fi-01.ps.gz">ps.gz</A>,+ −
<A HREF="http://www4.in.tum.de/~urbanc/Publications/fi-01.pdf">pdf</A>].+ −
Mayor difference between the standard sequent calculus and the sequent calculus + −
implemented by the applet is that the rules contraction and weakening are completely + −
implicit. This means that sequents consist of two sets of (labelled) formulae,+ −
as opposed to lists or multisets of formulae. Although this is very simple, it + −
needs some time to get used to. + −
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<B>How to use it?</B> + −
If your browser is playing game with Java, then you will see a window + −
with a number of examples. When pressing on one of the buttons, a new + −
window will pop up. What follows is a brief explanation of all + −
the features available in this window. + −
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<B>Buttons and Keys</B>+ −
<UL>+ −
<LI> The buttons + −
<IMG SRC="http://www4.in.tum.de/~urbanc/Cut/l.jpg"> and + −
<IMG SRC="http://www4.in.tum.de/~urbanc/Cut/r.jpg"> are for + −
commuting cuts, which can slide up either in the right or left proof branch.+ −
<LI> Pressing on <IMG SRC="http://www4.in.tum.de/~urbanc/Cut/x.jpg"> + −
, <IMG SRC="http://www4.in.tum.de/~urbanc/Cut/x1.jpg"> or + −
<IMG SRC="http://www4.in.tum.de/~urbanc/Cut/x2.jpg"> + −
`fires' a logical cut. The latter two buttons correspond to the two possible + −
nestings of multiplicative logical cuts.+ −
<LI> If you use the <B>left mouse button</B> for pressing on those buttons,+ −
then the new proof will appear inside the window. Whereas if you use + −
the <B>right mouse button</B>, a new window will pop up and + −
the new proof will be displayed in this window. Use the right mouse + −
button if you want to compare a proof and its reduct(s).+ −
<LI> The keys <B>Page-up</B> and <B>Page-down</B> zoom in or out of a proof+ −
respectively. + −
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<B>Menu Functions</B>+ −
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<UL>+ −
<LI> <B>Zoom in</B> and <B>Zoom out</B> work like Page-up and Page-down, + −
respectively.+ −
<LI> <B>Unicode</B> If this radiobutton is switched on, logic symbols + −
are displayed in unicode, otherwise in ascii. (This is for the + −
poor guys who have a browser and/or operating system which cannot handle + −
unicode.)+ −
<LI> <B>Labels</B> As mentioned earlier the sequents are composed of + −
two sets of labelled + −
formulae, not multisets of formulae as in the standard formulation + −
of sequent calculus. Enabling this radiobutton causes that labels are + −
drawn. Use this when you are unsure where implicit contractions are. + −
<LI> <B>Auxiliary Substitution</B> If you have read the paper referred+ −
above, you know what this does.+ −
<LI> <B>Gentzen's D.N.Transl.</B> and <B>Kolmogorov's D.N.Transl.</B> + −
perform double negation translations on the current proof. + −
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<applet archive=MyApplet.zip code="MyApplet.class" width=1 height=1>+ −
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<P><!-- Created: Tue Jul 3 21:01:42 BST 2001 -->+ −
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Last modified: Sat Mar 3 05:17:31 CET 2007+ −
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