<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>27</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Batens, Diderik</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A Paraconsistent Proof Procedure Based on Classical Logic</style></title></titles><dates><year><style  face="normal" font="default" size="100%">2003</style></year></dates><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Apparently Ex Falso Quodlibet (or Explosion) cannot be isolated within CL (Classical Logic); if Explosion has to go, then so have other inference rules, for example either Addition or Disjunctive Syllogism. This cer- tainly holds according to the standard abstract view on logic. However, as I shall show, it does not hold if a logic is defined by a procedure-a set of instructions to obtain a proof (if there is one) of a given conclusion from a given premise set. In this paper I present a procedure pCL¡ that defines a logic CL¡|a function assigning a consequence set to any premise set. Anything deriv- able by CL from a consistent premise set ¡ is derivable from ¡ by CL¡. If ¡ is (CL-)inconsistent, pCL¡ enables one to demonstrate this (by de- riving a contradiction from ¡). The logic CL¡ validates applications of Disjunctive Syllogism as well as applications of Addition. Nevertheless, this logic is paraconsistent as well as (in a specific sense) relevant. pCL¡ derives from an intuitively attractive proof search procedure. A characteristic semantics for CL¡ will be presented and the central prop- erties of the logic will be mentioned. CL¡ shows that (and clarifies how) adherents of CL may obtain non-trivial consequence sets for inconsistent theories.&lt;/p&gt;</style></abstract></record></records></xml>