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Cut-Elimination in Classical Logic

+ +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 +[ps.gz, + pdf]. +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. +
+How to use it?  +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. +
+Buttons and Keys +
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  • The buttons +        and +        are for + commuting cuts, which can slide up either in the right or left proof branch. +
  • Pressing on     +  ,      or +        + `fires' a logical cut. The latter two buttons correspond to the two possible + nestings of multiplicative logical cuts. +
  • If you use the left mouse button for pressing on those buttons, + then the new proof will appear inside the window. Whereas if you use + the right mouse button, 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). +
  • The keys Page-up and Page-down zoom in or out of a proof + respectively. +
+
+Menu Functions + +
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  • Zoom in and Zoom out work like Page-up and Page-down, + respectively. +
  • Unicode  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.) +
  • Labels  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. +
  • Auxiliary Substitution  If you have read the paper referred + above, you know what this does. +
  • Gentzen's D.N.Transl. and Kolmogorov's D.N.Transl. + perform double negation translations on the current proof. +
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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 + + +