<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Verdée, Peter</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Degrees of inconsistency. Carefully combining classical and paraconsistent negation.</style></title></titles><dates><year><style  face="normal" font="default" size="100%">Submitted</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;This paper is devoted to combining the negation of Classical Logic (&lt;strong&gt;CL&lt;/strong&gt;) and the negation of Graham Priest's &lt;strong&gt;LP&lt;/strong&gt; in a way that is faithful to central properties of the combined logics. We give a number of desiderata for a logic &lt;strong&gt;L&lt;/strong&gt; which combines both negations. These desiderata include the following: (a) &lt;strong&gt;L&lt;/strong&gt; should be truth functional, (b) &lt;strong&gt;L&lt;/strong&gt; should be strictly non-explosive for the paraconsisent negation ˜ (i.e. if &lt;em&gt;A&lt;/em&gt; and ˜&lt;em&gt;A&lt;/em&gt; both have a non-trivial set of consequences, then this should also be the case for the set containing both) and (c) &lt;strong&gt;L&lt;/strong&gt; should be a conservative extension of &lt;strong&gt;CL&lt;/strong&gt; and of &lt;strong&gt;LP&lt;/strong&gt;. The desiderata are motivated by a particular property-theoretic perspective on paraconsistency. Next we devise the logic &lt;strong&gt;CLP&lt;/strong&gt;. We present an axiomatization of this logic and three semantical characterizations (a non-deterministic semantics, an in nitely valued set-theoretic semantics and an in nitely valued semantics with integer numbers as values). We prove that &lt;strong&gt;CLP&lt;/strong&gt; is the only logic satisfying all postulated desiderata. The in nitely valued semantics of &lt;strong&gt;CLP&lt;/strong&gt; can be seen as giving rise to an interpretation in which inconsistencies and inconsistent properties come in degrees: not every sentence which involves inconsistencies is equally inconsistent.&lt;/p&gt;</style></abstract></record></records></xml>