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Re: [ontolog-forum] Ontology and methodology

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
Date: Tue, 20 Mar 2007 12:16:36 -0500
Message-id: <460016F4.9050202@xxxxxxxxxxx>
Dear Matthew, Pat, Chris, Ingvar, Florian, and Erick,    (01)

MW> Pat took the words out of my mouth.    (02)

PH> We are quantifying over 4-d entities, ie 'slices' of
 > a 'history-worm' ... which I will write by pairing a name
 > with a time-interval, eg [PatH, 1997-2007]. Person, to wit
 > [PatH, (lifetimeOf PatH)]. It is not a Person. So
 > forall x Employee(x) implies Person(x)
 > is false: in fact, this is a counterexample.
 > So Employee is not < Person.    (03)

OK.  I accept the point that the definition of
"Employee < Person" is equivalent to    (04)

    forall x Employee(x) implies Person(x)    (05)

in a 3D ontology, but it creates problems in 4D.    (06)

However, in ordinary English, which is soaked through and
through with 3D-ism, it is natural to say that every employee
is a person.  Since one of my primary goals is to support a
smooth mapping between language and logic, I put a very high
priority on being able to express logic in a natural form.    (07)

In order to provide a mapping between a 3D or 4D perspective,
there are two possible ways of defining "<" in a 4D ontology:    (08)

  1. X<Y implies that every spatiotemporal extent in which
     predicate X is true is contained in the spatiotemporal
     extent in which Y is true.    (09)

  2. The formula above can be retained by adding a restriction
     to the quantifier by defining "Employee < Person" as    (010)

     (forall ((x HistoryWorm))
             (if (Employee x) (Person x))    (011)

CP> As I have researched it, the situation was that bishops
 > have always kept their property intact - not the person
 > occupying the position.    (012)

I have no quarrel with that point.  I also accept the fact
that a clerk who receives a payment in a store is obliged
to put it into the company's coffers, not his or her purse.    (013)

But as I'm typing this email note, I also have a cup of coffee
on the desk.  As I alternate between the roles of Typist and
CoffeeDrinker, I take care not to pour coffee into the keyboard
or poke my fingers into hot coffee.  But I don't become two
different individuals as I switch between those roles.    (014)

The same kind of alternation of activity occurs when clerks and
bishops perform actions for their organizations or for themselves.
Most people can "walk and chew gum at the same time" without
becoming schizophrenic.    (015)

IJ> No famous philosophical ontologist who posits physical (material)
 > things in space and time has argued that everything that exists
 > in space and time is physical (material); for instance, many claim
 > that property instances *inhere in* physical things, but this does
 > not mean that these spatiotemporal instances *are* physical entities.    (016)

The terms "physical" and "abstract" have become loaded with too many
connotations to permit us to reach a consensus on suitable definitions.
Pat Hayes suggested the distinction between categories that are
localizable in space-time or independent of any localization in space
or time.  Those entities that are localizable have a high overlap
with physical entities, and those that are not localizable have
a high overlap with at least the structures of pure mathematics.    (017)

I believe we would make more progress by adopting this distinction
as fundamental, and relegate the discussion of how it relates to
the physical/abstract distinction to the pre-dinner cocktail hour.    (018)

FP> Yet I am struggling, finding it difficult to work with roles
 > while not letting them take over the whole ontology. How to
 > "balance" the usage of roles in ontology engineering?    (019)

Peirce had a solution.  His three "metalevel" categories are
Firstness, Secondness, and Thirdness.  This is a metalevel
distinction because it is not a single trichotomy at a fixed
level of the ontology, but a principle that can be applied
repetitively at *every* level (including recursively).    (020)

I don't want to get into the details, but a simplified
summary of that principle creates the following triad:    (021)

  1. Inherent.  A category defined by a predicate P(x), where
     the definition of P depends only on the structure or
     properties of x, independent of anything other than x.    (022)

  2. Relative.  A category defined by a predicate R(x,y), where
     the entity x is characterized by its relationship R to
     something y that is external to x.    (023)

  3. Mediating.  A category defined by a predicate M(x,y,z),
     where the entity x is characterized by the way it mediates
     the relationship(s) between y and z.    (024)

Examples of the first are characteristics such as size, mass,
shape, color, etc.  Obviously, color is not observable without
shining a light on the object, but the properties of an object
that determine what light it reflects are present whether or
not a light is shining on it.    (025)

Examples of the second are Employee, Mother, CoffeeDrinker, etc.
Anything that is classified by a dyadic relation R, such as
Employee, also has prerequisites that are defined by a monadic
predicate such as isHuman.  Those monadic predicates justify
a claim such as Employee<Human, but the dyadic relation R is
what distinguishes anything of category Employee from human
beings classified by other relations.    (026)

Examples of the third include Causality, Intention, Possession,
Goal, Purpose, Motivation, Enthusiasm, Tendency, Habit, Sign,
Law, Default, Business, Organization, Government, and Life.    (027)

FP> In natural language, it would be the normal way to refer
 > to the human, the employee and the father with, say, "Tom".
 > The same NAME refers to different entities. Here is, in
 > my understanding, where semantic heterogeneity is introduced.    (028)

The question whether a name like "Tom" is heterogeneous is theory
dependent.  In Peirce's theory, proper names are grouped with
indexicals such as "this" or "that".  (Peirce, by the way, coined
the word "indexical".)  A name is a vocal way of pointing.  The
thing it points to can be classified in multiple ways -- first,
by its inherent qualities; second, by its relationships; or third,
by its mediating effects.    (029)

I believe that Peirce's approach cuts through the mush and murk
in a more precise and systematic way than anything else I have
ever seen.    (030)

EA> We are building an application ontology for the cell...    (031)

Anything related to life involves Thirdness, e.g., function,
purpose, etc.  One of Peirce's prerequisites for life is the
ability to respond to signs.  By this criterion, a bacterium
is alive, but a virus is not since a virus cannot respond to
signs.  In fact, a virus is itself a sign -- and a living
cell responds to such signs by creating replicas.    (032)

John    (033)

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