[Attempto] Should I allow for non-monotonic reasoning?

[Norbert E. Fuchs]

On Tuesday, 26 May 2015 14:28:46 UTC+2, Norbert E. Fuchs wrote:

> On 25 May 2015, at 11:18 , Norbert E. Fuchs <fu... at ifi.uzh.ch <javascript:>> wrote: 
> 
> ... I tried – but until now was not completely successful – to get default reasoning with the help of modality ... 


Well, modality obviously is not the way to go since it does not actually implement non-monotonicity. 

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]. 

Here is an example demonstrating what I have achieved so far. 

  Axioms: 
  Beaky is a bird that flies. 
  Tweety is a bird. 
  If a bird is abnormal then it does not fly. 
  If a bird is sick then it is abnormal. 
  If a bird does not provably fly then it is abnormal.

  Query: 
  Which bird does not fly?

The proof succeeds and provides the following report:

  The following minimal subset of the axioms answer the query:

  2: Tweety is a bird.
  3: If a bird is abnormal then it does not fly.
  5: If a bird does not provably fly then it is abnormal.
  Substitution: which = Tweety

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. 


I'd appreciate your comments. Feel free to experiment with my implementation via RACE's web-interface [1].


[1] http://attempto.ifi.uzh.ch/race/

[2] http://attempto.ifi.uzh.ch/site/resources/

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