Christian Urban

Links Home Applet Home Java Versions CL LJT ND Plugin Versions CL LJT ND | ## 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 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 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.

Last modified: Sat Mar 3 05:17:41 CET 2007