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

[David Whitten]

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


I thought maybe I needed to say "man is a human" and "woman is a human"
can't occur at the same time (or at least is abnormal) to exclude Subset #1
and Subset #2, but instead I get a syntax error:

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 and the human is not provably a man then
the human is a man.
if a human is provably a woman and the human is provably a man then it is
abnormal.
if a human is provably a man then the human is not a woman.
if a human is provably a woman then the human is not a man.

ImportanceTypeSentenceProblemDescription/Suggestion

errorraceAxioms cannot be parsed.

Correct the axioms.errorsentence7if a human is provably <> a woman and the
human is provably a man then it is abnormal.

This is the first sentence that was not ACE. The sign <> indicates the
position where parsing failed.warningword5MackUndefined word. Interpreted
as a singular proper name.



On Tue, Aug 11, 2015 at 4:32 AM, Norbert E. Fuchs <fuchs at ifi.uzh.ch> wrote:

>
> 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> 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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>
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