[Top] [All Lists]

Re: [ontolog-forum] First-Order Semantics

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Waclaw Kusnierczyk <Waclaw.Marcin.Kusnierczyk@xxxxxxxxxxx>
Date: Sat, 16 Jun 2007 00:37:44 +0200
Message-id: <467314B8.40704@xxxxxxxxxxx>
Christopher Menzel wrote:
> On Jun 14, 2007, at 9:57 PM, John F. Sowa wrote:
>> Kathy and Pat,
>> I agree with Pat's explanation, but I think it could be made
>> somewhat clearer by distinguishing the base domain D from
>> the domain D' of *all* relations over D for second-order logic
>> (and then a domain D'' of *all* relations over D', etc.).
>> PH> The key semantic difference between the other logics is
>>> that they all impose conditions on the domain, requiring
>>> it to contain some entities as a result of containing others.
>>> So for example, classical second-order logic semantics
>>> requires that the domain is contain all relations
>>> over the base domain.
>> I would rephrase the last sentence in the following way:
>>     So for example, classical second-order logic semantics
>>     starts with the given base domain D and introduces
>>     another domain D' of *all* relations over D.
>> I just wanted to give different names D, D', D'', etc.
>> to distinguish the base domain D from any domains that
>> may be introduced by implicit assumptions.
>> CL allows the domain D to contain relations, but it doesn't
>> require D to contain *all possible* relations.
> Indeed the mathematical facts require that it *not* contain them.   
> There are (as of course John and Pat know) 2^card(D) relations over  
> any set (taking relations here to be sets of n-tuples).      (01)

Only if n=1.    (02)

vQ    (03)

Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/  
Subscribe/Config: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/  
Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx
Shared Files: http://ontolog.cim3.net/file/
Community Wiki: http://ontolog.cim3.net/wiki/ 
To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx    (04)

<Prev in Thread] Current Thread [Next in Thread>