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Re: [ontolog-forum] A Question About Mathematical Logic

To: ontolog-forum@xxxxxxxxxxxxxxxx
From: John F Sowa <sowa@xxxxxxxxxxx>
Date: Sun, 18 Oct 2015 16:59:35 -0400
Message-id: <56240837.2070308@xxxxxxxxxxx>
Ed and Leo,    (01)

I don't think we disagree on what should be represented.
What I've been trying to say is that (a) the traditional
philosophical terminology is too complicated, and (b) it's
too limited and imprecise to express what needs to be said.    (02)

EJB
> I would take issue with John's last assertion, to wit, that
> the distinction between a 'role' and a 'class' "doesn't make
> a difference in computing the implications".    (03)

As I said in my first note, I distinguished role types from natural
types in my ontology.  And I agree that there are many different
kinds of roles.  *All* distinctions that make a difference in
computing any implications must be represented.  But where and how?    (04)

EJB
> I think it rather depends on which version of 'role' is being used.
> It is most certainly the case that a (relational) role like 'owner'
> does not correspond logically to a simple predicate, but rather
> to a logical function (or at least a relation).    (05)

I agree.  The question is what kind of metalevel terminology
should we use in (a) stating guidelines about writing ontology
and (b) teaching students how to use those guidelines.    (06)

Leo
> One problem is if a given term widely used in some field is not
> really a (rigid) category per se, but instead has other meta-
> properties associated with it (along the lines of e.g., OntoClean).    (07)

To solve it, you need to distinguish the physical world from the
languages (natural or artificial) for talking about it.  Ontoclean
has some useful guidelines, but it doesn't clearly distinguish the
subject matter (the world) from the terminology that is used to
describe the world.    (08)

The term 'rigid category' mixes the language term 'category' with
a term 'rigid' that applies to something in the world.  You need
to decouple those terms.    (09)

Leo
> Student is not a subclass of Person (or, more clearly Human).    (010)

That is a confusing guideline. Every student is a human. Therefore
the set of all students is always a subset of the set of all humans
(even though both sets are constantly changing).  Any definitions
you adopt will determine that (Ax)(student(x) -> human(x)).    (011)

By rigid, I assume that you're putting time limits on the use
of one predicate or another.  As your examples and Ed's show,
both the world and the language(s) used to talk about it vary
in ways that a single word like 'rigid' can't accommodate:    (012)

Leo
> Or phased sortals such as Teenager, Caterpillar, etc.
> Artifacts introduce additional issues...    (013)

Yes.  There's no end to the issues, and the terminology
(e.g., 'sortals') keeps proliferating.  I pity both the
teachers and the students of that terminology.    (014)

EJB
> Museums, for example, often treat students and 'seniors' (another
> temporal category) as special classes of human when charging entry
> fees. (Then again, one might treat 'student' as a specialization
> of the relational role 'visitor' in that case, and it might be
> argued that every use of the supposed class 'student' is actually
> a specialization of some other relational role.)    (015)

Yes.  And the world keeps getting more complicated. (Or rather,
science is beginning to recognize and represent with more complex
aspects.)  For example, sex used to be a feature that remained
unchanged from birth to death.  But it is now nonrigid.  Biologists
are also finding animals that can change sex naturally and can
reproduce in either or both modes.    (016)

There is much more to say.  As a short summary, I would say
that (a) the traditional philosophical terminology is both
too complex and too limited to deal with the full range of
issues; (b) a better organization is to distinguish the
physical world from the semiotic systems (languages, logics,
and other kinds of signs); and (c) clearly distinguish the
mappings that relate a and b.    (017)

I am also highly skeptical about attempts to construct
a "commonsense ontology".  That term is highly dependent
on time, place, language, culture, level of education,
and domain of application.  Instead, I suggest that we just
adopt Schema.org as a de facto set of terms that need to be
supported, at least approximately, by any useful ontology.    (018)

John    (019)

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