Christian Urban

Links Home Applet Home Java Versions CL LJT ND Plugin Versions CL LJT ND | ## Cut-Elimination in Herbelin's calculus for intuitionistic logic Recommended reading for this applet is a paper by Dyckhoff and Urban, [ps, pdf]. Mayor difference between the standard sequent calculus and Herbelin's sequent calculus is that in the cut-free fragment "there are no semantically trivial permutations of the inference rules, where by 'semantically trivial' we mean 'interpreted in NJ as true equations between to (normal) deductions'" (from [ps]).
How to use it? If your browser is working correctly, then you will see a window with two examples (more added if you suggest some). 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 `fire' cuts (not all cuts necessarily have such buttons). 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. 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. Compact printing In the paper referred above weakening is done only in axioms. If this radiobutton is switched on (default), then, in order to save space, formulae are weakened as soon as possible.

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Last modified: Sat Mar 3 05:17:09 CET 2007