John, (01)
I apologize for misunderstanding your complaint. If I understand correctly,
you object that ISO 1087-1 condoned the notion 'primitive concept', without
providing a formal definition of it. (02)
I don't know that 'primitive concept' is a term used in any standard. ISO
1087-1 merely says that some terms may not really be 'defineable' (or at least
'defined') using one of its (semi-)formal definition styles. (03)
I do think the term 'primitive concept' is "commonly understood" to mean "a
concept that does not have a formal definition (in some given body of
knowledge)". Whether such a concept might have a formal definition in terms
of some other concepts that may or may not be included in the same body of
knowledge is not relevant. (Further, the quoted common understanding strikes
me as a valid formal definition. It does mean that a concept can only be
'primitive' in a given body of knowledge.) (04)
"primitive concept" has the same meaning as "undefined term", but only
mathematicians do not attach pejorative connotations to the latter term. (05)
ISO 704 does use the term 'description' and explicitly says it refers to
statements about a thing or concept that serve to convey the intent to the
human reader without necessarily being definitive. (I don't see a problem with
that definition, but if you think you can formalize it, don't let me stop you.) (06)
In a UML model, all concepts are necessarily primitive -- the language does not
have a form of formal definition. All it ever has is English language
"comments", which may be taken as "descriptions". In OCL, there is an explicit
definition construct, but UML models that carry such definitions are
extraordinarily rare. The primary use of OCL is to express only the
constraints that are important to understanding (and thus properly
implementing) the model. (07)
In an OWL ontology, some concepts will necessarily be primitive. Many others
need not be, but in many OWL models, actually defining a class by a class
expression or characterizing it axiomatically, seems to be a rather
hit-and-miss practice. There are, however, many OWL models of good quality
that are careful to define formally every concept other than the ones they
intentionally take to be 'primitive'. Consider the BFO and its descendants, or
OWL Time. (08)
The KIF world was much like the OWL world in that regard. The earlier
adherents understood the value of producing axiomatic definitions where
"possible" (i.e., without creating a requirement for unnecessary philosophy).
But that is primarily an academic pursuit. Later users, who were more
interested in practical results, saw no need to define predicates where the
expected reasoning process would not need to make inferences from the
definitions. I expect that the CLIF world (which is at best "emerging") will
be similar. (09)
-Ed (010)
> -----Original Message-----
> From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx [mailto:ontolog-forum-
> bounces@xxxxxxxxxxxxxxxx] On Behalf Of John F Sowa
> Sent: Tuesday, June 24, 2014 1:38 AM
> To: ontolog-forum@xxxxxxxxxxxxxxxx
> Subject: Re: [ontolog-forum] Types of Formal (logical) Definitions in ontology
>
> Ed,
>
> The basic point I was trying to make is that metalanguage is a major source of
> confusion. Each metalevel term should be specified by a construct in some
> version of logic.
>
> JFS
> >> Any term, such as 'primitive concept' or 'description' that is not
> >> specified in terms of logic does not belong in a standard
> >> -- except as an informal (non-normative) comment.
>
> EJB
> > I reject this outright! Try defining 'time interval' or 'duration'
> > rigorously. You can axiomatize them into the ground, and still be
> > unable to tell time from length, without appealing to some other
> > undefinable term.
>
> First, by "such as" I was talking about metalevel terms. But I admit that I
> should have clarified that statement by explicitly saying "any metalevel term
> such as 'primitive concept' or 'description'".
>
> For example, people keep kicking around words like 'feature', 'property',
> 'attribute', and 'characteristic'. In FOL, all of them get translated to
> predicates. I have never met anyone who could clearly state the differences
> between them.
>
> EJB
> > AFAIK, only in mathematics can one define a body of knowledge entirely
> > in terms of axiomatic characterizations. Every natural and social
> > science starts with some concepts taken to be primitive.
>
> I agree with everything in those two sentences except the words 'concept'
> and 'primitive'. Those are pseudo-technical terms that create more
> confusion that they can possibly clarify.
>
> Observation: The so-called "symbol grounding problem" for linking symbols
> in the computer to anything in the world is just as critical for humans.
>Every
> branch of science, engineering, business, and the law has established
> practices for linking their technical terms to their subject matter.
>Specifying
> all of them would go far beyond the scope of any reasonable standards
> project.
>
> My recommendation is to say that a standard should begin with a list of
> "terms of art" that are used with the accepted definitions in the field.
>Then it
> can use formal methods to define other terms, which may be terms of art
> that are being standardized.
>
> John
>
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