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

To: "John F. Sowa" <sowa@xxxxxxxxxxx>
Cc: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Pat Hayes <phayes@xxxxxxx>
Date: Tue, 13 Feb 2007 14:18:23 -0600
Message-id: <p06230902c1f7caf73608@[]>
>Pat, Chris, and Barry,
>I agree that there is a dilemma:
>   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.    (01)

This distinction, and the idea that only some of these sentences 
constitute a 'definition' which has a different logical status than 
other sentences, is exactly what I was urging we should put behind 
us. Let me ask you, if you think otherwise, to explain what exactly 
constitutes, in strict logical terms, the difference between formal 
sentences that this terminology apparently assumes. These are all 
sentences of CL, let us say for concreteness.    (02)

>   2. As Barry said, where should anyone "turn to find out
>      what a term means?"    (03)

I think this is a completely different topic. I agree that we need to 
find ways to do this task of communication with users about meanings 
of terms.    (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)

I disagree. For both theoretical and computational reasons it is 
important to realize that this distinction has no merit or logical 
force whatsoever :-) There are no definitions in the strict sense in 
a first-order framework. This fact is something to treasure and 
preserve as long as possible. For example, adding the power to make 
definitions to IKL would make the entire logic paradoxical, and 
re-create the Russell paradox in CL. Until someone finds a genuine 
use case for such definitions I suggest we continue to get along 
without them.    (06)

>In particular, definitions usually have the force of necessary
>conditions, while other axioms may be contingent.    (07)

But this distinction has no meaning except in a modal logic. And very 
few modal logics can do justice to the intuitive distinction in any 
case. (Which variety or flavor of modality would you suggest for 
capturing contingency, and why?)    (08)

>  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.
>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
>     http://www.jfsowa.com/pubs/laws.htm
>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)

This is like saying that to color a flag one does not need actual 
colors. What is achieved by this labelling? What semantic force does 
it have? What use is it? (None, I suggest.)    (010)

Pat    (011)

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