[Attempto] Non-monotonic reasoning in RACE

[Norbert E. Fuchs]

> On 11 Aug 2015, at 13:47 , David Whitten <whitten at netcom.com> wrote:
> 
> I don't know what I have done wrong.
> 
> I tried using the web interface for race, but don't know why (below) subset #1 (Mary) and set#2 (at least 1 woman) are included.
> 
> I had the axiom set:
> 
> Every man is a human. Every woman is a human. 
> Mary is a human that is a woman. John is a human that is a man. Mack is a human.
> if a human is not provably a woman then the human is a man.
> 
> I had the query:
> 
> Who is a man and is a human?
> 
> RACE said: overall time: 0.552 sec; RACE time: 0.04 sec
> Axioms: Every man is a human. Every woman is a human. Mary is a human that is a woman. John is a human that is a man. Mack is a human. if a human is not provably a woman then the human is a man.
> 
> Query: Who is a man and is a human?
> 
> Parameters: 
> 
> The following minimal subsets of the axioms answer the query:
> 
> 	• Subset 1
> 		• 3: Mary is a human that is a woman.
> 		• 6: If a human is not provably a woman then the human is a man.
> 		• Substitution: who = (at least 1) woman
> 	• Subset 2
> 		• 3: Mary is a human that is a woman.
> 		• 6: If a human is not provably a woman then the human is a man.
> 		• Substitution: who = Mary
> 	• Subset 3
> 		• 4: John is a human that is a man.
> 		• Substitution: who = John
> 	• Subset 4
> 		• 5: Mack is a human.
> 		• 6: If a human is not provably a woman then the human is a man.
> 		• Substitution: who = Mack
> 

David

I had suggested non-redundant axioms

  Every man is a human. Every woman is a human. Mary is a woman. John is a man. Mack is a human. If a human is not provably a woman then the human is a man.

and asked you for patience while I was about to remove a bug that prevented your example from executing. In the meantime I removed the bug and now get the expected result seen here in a screen-shot of RACE's web-interface.





Also, I extended RACE to handle the combination of logical negation ("not") and negation-as-failure ("not provable"). Here is an example of  "... not provable ... not ..." 



while the combination "... not ... not provable P ..." is not accepted as being semantically identically to "P".



Any comments or suggestions?

Best regards.

   --- nef


 
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