[Attempto] AceRules help regarding generalized quantifiers

[Norbert E. Fuchs]

On 30 Dec 2008, at 15:56, Stephan Mueller wrote:

> Hello,
>
> I've been using AceRules trying to put together a small set of ACE
> rules and execute them in courteous mode. However, I do have a problem
> with generalized quantifiers, as it is illustrated in the following
> example:
>
> Input: "If someone X has at least 1 order then X is a customer. John
> has exactly 2 orders."
>
> Output: "John has exactly 2 orders."
>
> In this example, I would additionally expect the output "John is a
> customer" which I only get when not using the generalized quantifiers
> and specifying the exact amount of orders ("If someone X has 2 orders
> then X is a customer. John has 2 orders.")
>
> Are these constructs not supported in AceRules or is there another way
> to formulated rules involving quantities? Any help is appreciated.
>
> Thanks,
> Stephan

On 31 Dec 2008, at 13:17, Tobias Kuhn wrote:

> Hi Stephan,
>
> Such generalized quantifiers are not interpreted by AceRules.  
> "exactly 2" is accepted, but there is
> no relation to "at least 2" or "less than 5" for AceRules. This is  
> because the underlying rule
> formalisms do not support such cardinality statements. It might be  
> that there are extensions thereof
> that would support such things. I am not really up to date. I  
> haven't been working on such rule
> problems recently.
>
> What you have to consider is that the forward-chaining approach may  
> easily break if such cardinality
> statement are processed in some way. Your statement "John has  
> exactly 2 orders" should also imply
>
>   John has less than 3 orders.
>   John has less than 4 orders.
>   John has less than 10 orders.
>
> ... and so on. Thus, you get an infinite answer set and the rule  
> engine won't terminate.
>
> In case you want to change AceRules to handle such things in one way  
> or another, have a look at the
> file "courteous_interpreter/answerset_generator.pl" of the AceRules  
> source code.
>
> For the list: a pre-release of the AceRules source code can be  
> downloaded here:
>
>   http://attempto.ifi.uzh.ch/site/downloads/files/acerules-081124_unofficial.zip
>
>
> Cheers,
> Tobias

Stephan

Since you wrote *Any help is appreciated.", I would like to point you  
to the first-order theorem prover RACE, another tool that the Attempto  
group provides.

Though RACE interprets "exactly" differently to AceRules, it provides  
the deduction

If someone X has at least 1 order then X is a customer. John has 2  
orders. |- John is a customer.

Here is a screen-shot of the result shown by the RACE web-client  (http://attempto.ifi.uzh.ch/race/ 
):

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The relation between "at least 1" and "2" is implemented by RACE's  
built-in auxiliary axioms. Variations of these axioms could also  
express the relation between "at least 1" and "exactly 2".

The source code of RACE is not yet available, but besides the web- 
interface there is a web-service (http://attempto.ifi.uzh.ch/site/docs/race_webservice.html 
).

Best regards.

    ---- nef