<HTML lang=en><HEAD><TITLE> Christian Urban </TITLE><BASE HREF="http://www4.in.tum.de/~urbanc/"></HEAD><BODY TEXT="#000000" BGCOLOR="#000080" LINK="#0000EF" VLINK="#51188E" ALINK="#FF0000"><TABLE WIDTH="100%" COLS="2" BGCOLOR="#000080" BORDER="0" FRAME="none" CELLPADDING="10" CELLSPACING="2" RULES="COLS,ROWS"><!-- left column --><TR><TD BGCOLOR="#FFFFFF" WIDTH="24%" VALIGN="TOP" ROWSPAN="2"><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><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><BR><BR><A HREF="http://isabelle.in.tum.de/nominal/"><IMG SRC="ribbon.gif" ALT="" style="width: 114px; height: 100px;" align="left"></A></TD><!-- right column --><TD BGCOLOR="#FFFFFF" WIDTH="75%"><H2>What is the Semantics for Classical Logic?</H2>In the intuitionistic case, the answer to this question is well-understood -essentially a semantics is given to all proofs in normal form and all otherproofs inherit this semantics from the normal forms they reduce to. This implies that:<blockquote>(1) reductions preserving the semantics of a proof. </blockquote>It is widely known that this assumption causes any reasonable semantics for classical logic to collaps. In the literature Lafont's example isoften cited for this observation.<p> <center><IMG SRC="Cut/lafont1.jpg" ALT="" ALIGN=CENTER></center><p><center><IMG SRC="Cut/lafont2.jpg" ALT="" ALIGN=CENTER><IMG SRC="Cut/lafont3.jpg" ALT="" ALIGN=CENTER></center><p></TD></TR></TABLE><P><!-- Created: Tue Jul 3 21:01:42 BST 2001 --><!-- hhmts start -->Last modified: Sat Mar 3 05:17:53 CET 2007<!-- hhmts end --></BODY></HTML>