ontolog-forum
[Top] [All Lists]

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

To: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Edward Barkmeyer <ebarkmeyer@xxxxxxxxxxxx>
Date: Sat, 17 Oct 2015 04:10:13 +0000
Message-id: <CO2PR11MB0005BABBEBD09979645C58F5BC3C0@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx>
Oops!  Apologies to Leo and Pat for the confusion.  In what I sent below, the 
references to "Pat" should have been to "Leo".    (01)

I also omitted an extension to the class kind of role.  A class/role like 
teacher or software engineer does not actually require the existential.  A 
thing can be a member of the class/role by having the required qualifications 
and thus the capability of playing the underlying relational role, even if the 
thing does not currently play the role and perhaps never has.  Keri Anderson 
Healy's example is worth noting:  "An umbrella can be a weapon."    (02)

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".  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).  And similarly, it does not have a 
computational representation as a single column table or an o-o 'class'.  One 
might say the same is true of 'employee', but in a universe that consists 
solely of persons who have some relationship to a specific organization, 
'employee' and 'customer' can be predicates (and classes).   (And that takes us 
back to another theme in this thread -- the 'scope' of a computational 
ontology, the deliberate limitation on the universe of discourse.)    (03)

-Ed    (04)

-----Original Message-----
From: Edward Barkmeyer 
Sent: Friday, October 16, 2015 6:25 PM
To: ontolog-forum@xxxxxxxxxxxxxxxx
Subject: RE: [ontolog-forum] A Question About Mathematical Logic    (05)

John,    (06)

You have hit upon an issue that has troubled a lot of 'conceptual model' and 
'ontology' developers for many years.  I would describe that issue as the 
ambiguity of the term 'role'.  Pat's examples: employee, buyer, seller are 
instances of what one might call a 'relational role' (there is probably a more 
formal philosophical term).  That is, such terms only make sense *relative* to 
some specific situation or thing.  One cannot be "a buyer"; one can only be "a 
buyer of" something.    (07)

Student, OTOH, can be a relational role -- one can be a "student of" a given 
professor, or a "student at" a given school; but student can also be a 
(temporal) class.  The class is derived from the relational role by existential 
quantification of the related object.  Student = a human who is enrolled as a 
"student at" *some* school.  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.)      (08)

I have also sometimes found it important semantically to distinguish between a 
'participation role' and a relational role.  One can be 'the buyer in' a 
specific purchase transaction, which is a relationship to the event/situation, 
as distinct from 'the buyer of' the item that is purchased in that transaction. 
 The relationship between the person and the purchased item is derived from the 
participation relationship.  The concept of 'role' in process modeling is 
always a participation.    (09)

There is yet another kind of role which we might dub 'reified role', but most 
organizations would call a 'position', such as Dean of the Engineering School.  
Such a role exists as a thing in the UoD, even when no thing plays the role.    (010)

Put another way, the different notions of 'role' can be modeled in OWL as a 
Property, a Property slot, a Class, or an Individual, according to what one 
intends by the term 'role' and how one expects to use it in making inferences.    (011)

I do expect that an expert in one of the cognitive science disciplines can tell 
us that 'role' is carefully defined in that discipline and should be used only 
with that intent.  (In particular, I'm pretty sure Pat used the term carefully, 
with the accepted meaning in some discipline.)  But the literature of the 
information sciences is littered with uses of 'role' that appeal to the 
intuition of the reader to determine what is meant.  Even worse, some of the 
literature "defines" the term in such a way that it is not clear which of the 
above is intended.    (012)

-Ed    (013)


-----Original Message-----
From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx 
[mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of John F Sowa
Sent: Friday, October 16, 2015 4:31 PM
To: ontolog-forum@xxxxxxxxxxxxxxxx
Subject: Re: [ontolog-forum] A Question About Mathematical Logic    (014)

On 10/16/2015 1:44 PM, Obrst, Leo J. wrote:
> Example: Student. Employee. Buyer. Seller. And so on.
> These are roles, and can be characterized in a role hierarchy, if one 
> wishes.    (015)

I agree that it's important to distinguish roles.  In my CS book (1984), I 
distinguished them as role type (e.g., Student) vs.
natural type (e.g., Human).  Nouns that represent role types have more typical 
or expected relationships than those that represent natural types.  But natural 
types also have expected relationships (e.g., Human vs Elephant vs Rose vs 
Cabbage).    (016)

> But e.g., Student is not a subclass of Person (or, more clearly Human).    (017)

That is a prime example of a typical confusion.  The phrase 'more clearly' is a 
clue that it's not clear.    (018)

A class is normally defined as a set that is characterized by some criterion 
that may be stated by a monadic predicate.  The students in a school form a set 
that may be represented by a monadic predicate.    (019)

Q: Why would anyone claim that 'Student' is not worthy of being a class?    (020)

A: Some philosopher said so.    (021)

Q: Does that distinction make a difference in how the term is
    represented in ordinary language?    (022)

A: Role types and natural types are both represented as nouns.
    But a noun that represents a role may occur in some phrases
    that are not expected for a natural type:  e.g., "a student
    of physics", "a teacher of physics", but it's unusual to say
    "a man of physics".  In any case, 'unusual' means "unexpected,
    but not impossible".    (023)

Q: Does it make a difference in how the term is represented in logic?    (024)

A: Not in predicate calculus.  But some people choose different
    ways of making that distinction in some versions of logic.    (025)

Q: Does it make a difference in a theorem prover?    (026)

A: No.  If you represent all the required, expected, and unusual
    relationships, you get the same implications.    (027)

Q: So why does anyone make that distinction?    (028)

A: Because some philosopher said so.    (029)

Q: Do all philosophers agree on that point?    (030)

A: No.  Some say it's a pseudo-problem.  Others say there's
    a continuum with many borderline cases.    (031)

Summary:  I have a high regard for good philosophy.  But I have little patience 
with those who make a fetish of distinctions that don't make a difference in 
computing the implications.  I have even less patience when those distinctions 
create incompatibilities between systems that happen to make different choices.    (032)

John    (033)

_________________________________________________________________
Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/
Config Subscr: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/
Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx
Shared Files: http://ontolog.cim3.net/file/ Community Wiki: 
http://ontolog.cim3.net/wiki/ To join: 
http://ontolog.cim3.net/cgi-bin/wiki.pl?WikiHomePage#nid1J    (034)


_________________________________________________________________
Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/  
Config Subscr: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/  
Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx
Shared Files: http://ontolog.cim3.net/file/
Community Wiki: http://ontolog.cim3.net/wiki/ 
To join: http://ontolog.cim3.net/cgi-bin/wiki.pl?WikiHomePage#nid1J    (035)

<Prev in Thread] Current Thread [Next in Thread>