[Top] [All Lists]

Re: [ontolog-forum] Current Semantic Web Layer Cake

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
Date: Wed, 08 Aug 2007 02:45:32 -0400
Message-id: <46B9668C.3090201@xxxxxxxxxxx>
Jon,    (01)

That is an important issue, but it's not what I was talking about:    (02)

 > I am referring to the conception of logic as a normative science,
 > which is part of what Peirce meant by defining logic as formal
 > semiotic.    (03)

I was talking about an extremely narrow point.  Consider the
following three notations:    (04)

  1. The first-order subset of Peirce's algebra of logic of 1885.    (05)

  2. The first-order subset of Frege's Begriffsschrift of 1879.    (06)

  3. Any of the three concrete notations in Annex A, B, or C of
     the Final Draft International Standard of Common Logic of 2007.    (07)

My claim was that any statement s1 expressed in notation #1,
can be translated to a statement s2 in notation #2 (and vice-versa)
in such a way that s1 and s2 have exactly the same truth values
in all possible models (in Tarski's sense) or states of affairs
(in Peirce's sense).    (08)

Furthermore, s1 can be translated to a statement s31 in notation #3,
and s2 can be translated to a statement s32 in notation #3 in such
a way that s1, s2, s31, and s32 have the same truth values in all
possible models or states of affairs.    (09)

That is what I meant by interoperability:  any person with any
philosophical views of any kind can, if he or she wishes, map
any statement from #1 to #2, or from #2 to #1, or from #1 to #3,
or from #2 to #3 -- and back to the original language -- in such
a way that the truth values in the source and target languages
are identical.    (010)

John    (011)

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    (012)

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