<html><head><meta http-equiv="Content-Type" content="text/html charset=utf-8"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space;" class=""><div><div class=""><br class=""></div><div class=""><div dir="ltr" class="">On Tuesday, 26 May 2015 14:28:46 UTC+2, Norbert E. Fuchs wrote:<blockquote class="gmail_quote" style="margin: 0;margin-left: 0.8ex;border-left: 1px #ccc solid;padding-left: 1ex;"> <br class="">> On 25 May 2015, at 11:18 , Norbert E. Fuchs <<a href="javascript:" target="_blank" gdf-obfuscated-mailto="BekG93zmJJgJ" rel="nofollow" class="">fu...@ifi.uzh.ch</a>> wrote: <br class="">> <br class="">> ... I tried – but until now was not completely successful – to get default reasoning with the help of modality ... <br class=""><br class=""></blockquote><div class=""><br class=""></div><div class="">Well, modality obviously is not the way to go since it does not actually implement non-monotonicity. </div><div class=""><br class=""></div><div class="">In the meantime I extended my reasoner RACE [1] for Attempto Controlled English ACE by non-monotonic reasoning based on the standard combination of strong negation (logical negation) and weak negation (negation as failure) both of which are offered by ACE, and have been previously used in Tobias Kuhn's AceRules [2]. </div><div class=""><br class=""></div><div class="">Here is an example demonstrating what I have achieved so far. </div><div class=""><br class=""></div><div class=""> <i class="">Axioms:</i> </div><div class=""> Beaky is a bird that flies. </div><div class=""> Tweety is a bird. </div><div class=""> If a bird is abnormal then it does not fly. </div><div class=""> If a bird is sick then it is abnormal. </div><div class=""> If a bird does not provably fly then it is abnormal.</div><div class=""><br class=""></div><div class=""> <i class="">Query:</i> </div><div class=""> Which bird does not fly?</div><div class=""><br class=""></div><div class="">The proof succeeds and provides the following report:</div><div class=""><br class=""></div><div class=""> The following minimal subset of the axioms answer the query:</div><div class=""><br class=""></div><div class=""> 2: Tweety is a bird.</div><div class=""> 3: If a bird is abnormal then it does not fly.</div><div class=""> 5: If a bird does not provably fly then it is abnormal.</div><div class=""> Substitution: which = Tweety</div><div class=""><br class=""></div><div class="">Notice that my implementation restricts the use of weak negation to the preconditions of if-then sentences – which seems reasonable. Further notice that the syntax of weak negation (... does/do/is/are not provably ..., ... it is not provable that ...) explicitly indicates the possibility of non-monotonic reasoning. </div><div class=""><br class=""></div><div class=""><br class=""></div><div class="">I'd appreciate your comments. Feel free to experiment with my implementation via RACE's web-interface [1].</div><div class=""><br class=""></div><div class=""><br class=""></div><div class="">[1] <a href="http://attempto.ifi.uzh.ch/race/" class="">http://attempto.ifi.uzh.ch/race/</a></div><div class=""><br class=""></div><div class="">[2] <a href="http://attempto.ifi.uzh.ch/site/resources/" class="">http://attempto.ifi.uzh.ch/site/resources/</a></div></div></div></div><br class=""></body></html>