[Top] [All Lists]

Re: [ontolog-forum] First-Order Semantics

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
Date: Thu, 14 Jun 2007 22:57:50 -0400
Message-id: <4672002E.5000203@xxxxxxxxxxx>
Kathy and Pat,    (01)

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.).    (02)

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.    (03)

I would rephrase the last sentence in the following way:    (04)

    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.    (05)

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.    (06)

CL allows the domain D to contain relations, but it doesn't
require D to contain *all possible* relations.    (07)

John    (08)

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    (09)

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