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Re: An inconsistency or not?

From: Chris Purcell <cjp39@cam.ac.uk>
Date: Thu, 31 Mar 2005 03:27:45 +0100
Message-Id: <754027b4b2913c587c9e0b3e6e71aa19@cam.ac.uk>
Cc: (wrong string) <minsu@etri.re.kr>
To: Jeremy Wong <50263336@student.cityu.edu.hk>

> 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 02:27:49 UTC

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