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<TITLE> Christian Urban </TITLE>
<BASE HREF="http://www4.in.tum.de/~urbanc/Cut/">
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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>
<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>
<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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<BR>
<A HREF="http://isabelle.in.tum.de/nominal/">
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<A NAME="Home"></A>
<H2>Cut-Elimination in Classical Logic</H2>
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>
<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>
<param name="calculi" value="A">
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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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Last modified: Sat Mar 3 05:17:31 CET 2007
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