>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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