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Re: An inconsistency or not?

From: Jeremy Wong <50263336@student.cityu.edu.hk>
Date: Thu, 31 Mar 2005 10:47:03 +0800
To: Chris Purcell <cjp39@cam.ac.uk>
Cc: semantic-web@w3.org, 장민수 <minsu@etri.re.kr>
Message-id: <004e01c5359b$ec0c9de0$6502a8c0@miko947ymju833>

The ways you and I reason the axioms and facts are different. You pay 
attention to deduction, while I pay attention to validity checking. "Either 
situation is possible" means that an OWL tool can assume John and Johnny the 
same and another OWL tool can assume John and Johnny different individuals.


Jeremy

----- Original Message ----- 
From: "Chris Purcell" <cjp39@cam.ac.uk>
To: "Jeremy Wong" <50263336@student.cityu.edu.hk>
Cc: <semantic-web@w3.org>; "장민수" <minsu@etri.re.kr>
Sent: Thursday, March 31, 2005 10:27 AM
Subject: Re: An inconsistency or not?


>> Good point! You cannot say that my argument is invalid. I cannot say that 
>> your argument is invalid.
>
> Your argument is logically false given the stated premises. I'm not sure 
> how more invalid you want.
>
>> In reference to section 5.2 of OWL Reference, OWL tools should assume in 
>> principle that 2 URI references (John and Johnny) either the same or 
>> different individuals is possible.
>
> From the docs:
>
> Unless an explicit statement is being made that two URI references
> refer to the same or to different individuals, OWL tools should in 
> principle
> assume either situation is possible.
>
> However, in this case they cannot be different individuals, as this leads 
> to a contradiction. We therefore deduce the two references are the same 
> individual. One can consider the two statements (Harry hasFather 
> John/Johnny) to be an explicit statement of identity.
>
> This exact tool (functional properties) is used on the SemWeb to establish 
> identity without requiring predefined URIs. For instance, in FOAF, the 
> foaf:mbox property is defined as *inverse* functional, allowing one to 
> establish identity solely based on someone's (personal) e-mail address.
>
>>> You assert:
>>>
>>>     card({...}) = 2
>>>
>>> This is only true if John != Johnny, which we do not know. Your argument 
>>> is invalid.
>>>
>>>> It is my second reply. Consider the interpretation of the cardinality 
>>>> restriction..
>>>>
>>>> {x ∈ O | card({y ∈ O∪LV : <x,y> ∈ ER(p)}) = n}
>>>>
>>>> Substitute n = 1, x = Harry, p = hasFather into the interpretation..
>>>>
>>>> {Harry ∈ O | card({y ∈ O∪LV : <Harry,y> ∈ ER(hasFather)}) = 1}
>>>>
>>>> Then..
>>>>
>>>> {y ∈ {S(John),S(Johnny)} | card({John ∈ O∪LV : <Harry,y> ∈ 
>>>> ER(hasFather)}) = 2 <> 1}
>>>>
>>>> Therefore the restriction (class axiom?), restriction(hasFather 
>>>> cardinality(1)), is not satisified. Hence the collection of axioms is 
>>>> not consistent.
>
> 
Received on Thursday, 31 March 2005 02:49:56 UTC

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