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+Applet for Cut-Elimination and Normalisation
+ +Warning: +These pages are still under construction and designed for the conoscenti +only. If you encounter any problems, email me. Some general information +about the applet is given below.+ +The applet is outcome of my interest in cut-elimination. It helps to +explore reduction trees in a slight variant of the sequent calculus LK, +and also reduction trees in Herbelin's calculus LJT (as presented +here) +and in the standard formulation of natural deduction for intuitionistic +logic. Given for example the following classical sequent proof
+ +
++ +you can produce by simply pressing the buttons L and R the following +two cut-free proofs.
+ +
+
++ +If you ever have done cut-elimination by hand, then you +know how useful this applet is.
+
+
The applet is particularly useful for doing
+some calculations finding out what the (proof-theoretical) semantics for classical logic
+should look like. Some informal notes are
+here.
+
+ + +The applet needs at least Java 1.2 including the +Swing libraries. Some browsers support these requirements +directly, and if you are one of the lucky to have such a browser +you can access the three calculi by pressing on one of the +following links. + +
-
+
- CL - cut-elimination +in classical logic +
- LJT - cut-elimination in +intuitionistic logic +
- ND - normalisation in
+intuitionistic natural deduction
+
+ +If not, then your browser can most probably run the applet with +the help of a Java plugin. In this case follow the links below. + +
-
+
- CL - cut-elimination +in classical logic +
- LJT - cut-elimination in +intuitionistic logic +
- ND - normalisation in
+intuitionistic natural deduction
+
+ +