[Top] [All Lists]

Re: [ontolog-forum] Role of definitions (Remember the poor human)

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
Date: Tue, 13 Feb 2007 11:51:05 -0500
Message-id: <45D1EC79.1090800@xxxxxxxxxxx>
Pat, Chris, and Barry,    (01)

I agree that there is a dilemma:    (02)

  1. The usual versions of FOL do not distinguish which,
     if any, axioms are intended to be define a term (type,
     relation, or function) and which merely use a term that
     is defined elsewhere.    (03)

  2. As Barry said, where should anyone "turn to find out
     what a term means?"    (04)

I also believe that the distinction is important for more
than poor humans.  For both theoretical and computational
reasons, it's important to recognize that some axioms (or
whatever else one might want to call the statements of
an ontology) are more deeply "entrenched" than others.    (05)

In particular, definitions usually have the force of necessary
conditions, while other axioms may be contingent.  That is
the reason why the developers of description logics say
that DLs have a modal effect:  assertions stated in DLs are
intended to be at least necessary conditions, and, often
but not always, sufficient conditions.    (06)

FOL, by itself, cannot make any assertions about the levels
of entrenchment of any statements in the same theory.  But
if one has multiple metalevels, then such distinctions can
be asserted in a first-order metalanguage about a first-order
object language.  That distinction is the basis for Dunn's
semantics for modal logic, and it can be extended to multi-
modal reasoning by distinguishing multiple levels of
entrenchment by assertions at the metalevel.  See    (07)

    http://www.jfsowa.com/pubs/laws.htm    (08)

To support levels of entrenchment, or at least the two-level
split of definition vs. contingent assertion, it is not
necessary to have a full-blown modal logic.   At the very
least, it could be done by splitting the specifications
in two or more parts, while labeling one part "definition".    (09)

For reasoning in the logic, the statements in both parts
can be used together.  For metalevel reasoning about the
ontology, either formal or informal, that split could be
considered.    (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>