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Re: [ontolog-forum] Ontology and methodology

To: "John F. Sowa" <sowa@xxxxxxxxxxx>
Cc: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Pat Hayes <phayes@xxxxxxx>
Date: Mon, 19 Mar 2007 17:11:47 -0500
Message-id: <p06230912c224b72ce93d@[]>
>Dear Matthew, David, Chris, Pat, John,
>MW> So Matthew West the employee of Shell is only the same
>  > thing as Matthew West the person if Matthew West is an
>  > employee of Shell for the whole of his life.
>Nonetheless, it is always true in both 3-D and 4-D models
>that every instant of time when MW is an employee, MW is
>also a person.  Therefore, Employee < Person.    (01)

No, that doesn't follow at all. We are quantifying over 4-d entities, 
ie 'slices' of a 'history-worm' (using a commonly used way of 
ridiculing this POV) which I will write by pairing a name with a 
time-interval, eg [PatH, 1997-2007]. That is not a person, it is a 
temporal part of a person. The actual person, Pat Hayes, is [PatH, 
(lifetimeOf PatH)], which I will not tempt fate by giving a numerical 
form for. OK, now, suppose that I was an employee of the State of 
Illinois from 1994 to 1999, at which time I left to come to Florida. 
Then [PatH, 1994-1999] is an Employee and a temporal part of a 
Person, to wit [PatH, (lifetimeOf PatH)]. It is not a Person. So    (02)

forall x Employee(x) implies Person(x)    (03)

is false: in fact, this is a counterexample. So Employee is not < Person.    (04)

>MW> The employee instance is not a person-for-the-whole-of-their-life,
>Of course.  But every employee instance is a part of the person
>instance.  That is exactly what is implied by Employee < Person.    (05)

Your earlier explanation of < didn't mention anything about parts. On 
the face of it, that seems to be about employees and people. Usually, 
an employee is an instance of a temporal part of a person, not of a 
whole person (someone born into servitude might be the only exception 
I can think of). All speaking in 4-d language here, of course.    (06)

>DD> Simply said, identifying whether something is a 'natural kind'
>  > or a role might be very hard in some cases and completely depends
>  > on the level of granularity of your ontology or the background
>  > of the modeler.
>This is one of many reasons why trying to draw a hard-and-fast
>distinction that holds for every possible case is not easy.
>Therefore, it makes more sense to put all the concept types into
>a single hierarchy and leave it underspecified, if necessary.
>CP> Your notion of employee does not distinguish between employers
>  > - and it is also temporalised - one is an employee at a time.
>No.  The statement X<Y is about *types*, not about *individuals*,
>and the *definition* of a type is independent of space and time.
>What is time dependent is whether a particular individual is
>an instance of a particular type at a given time.
>CP> It seems that implicitly mean that *at time t1*, X < Y means
>  > that every instance of X is an instance of Y. Maybe better to
>  > say that X <t1 Y means that at t1 every instance of X is
>  > an instance of Y.
>No. To say Employee<Person means that at *every* point in time
>and place, if x is an employee, then x is a person.    (07)

That is a 3-d-ish way of talking, however, in which things that 
endure through time, retaining their identity, have properties *at a 
time*. In a 4-d framework properties are all timeless, and if 
something *at a point in time* is a person, then it is a very 
unfortunate - because very short-lived - person.    (08)

Pat    (09)

PS. Just for the record, I often talk this 3-d-ish way myself. But I 
can speak 4-d when required :-)
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