SUO: Re: Terminology, Terminable & Interminable
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PC = Patrick Cassidy
PC: The way "relation" is defined in KIF certainly seems to
> me to be a parent class of "Class" as defined in KIF --
>
> relation -- a set of tuples
> class -- a set of tuples of length one
>
> Perhaps there is another definition of "relation" that you think
> is somehow superior, but these two definitions in KIF seem to be
> consistent with each other.
Pat,
The sources that I gave you are standard references.
They refer to standards of usage that have been standard
for as long as I personally can remember, and my reading
of the intellectual historical record tells me that they
have been standard for longer than that, some of them
from the time of Cantor, in their formalized way, and
most of them longer than that, if you look to informal
standards of usage. I do not know if these definitions
are superior -- I certainly explored all the alternatives
I could find in my time -- what I do know is that they are
the standard definitions in the communities of expertise
who first formalized these notions and who apply them to
some benefit on a daily basis as the foundations, however
mobile or shakey, of everthing else that they do.
At a bare minimum, then, I would expect that
an IEEE Standards Working Group might at least
accord them a token respect before it sets about
standarizing usage onto others.
Otherwise we are doomed to go on having these eternally recurring discussions
about elementary matters that have already been been standardized to the extent
that they can be standardized in the standards and practices of the originating
and the user communities, as they instruct their novices in the first few weeks
of their standard undergraduate curricula.
When the SUO Working Group has gotten that far,
then it will, at long last, be getting started.
Jon Awbrey
> The whole point of this is, of course, to decide which
> definition we want to use. If you propose a different
> definition, please provide specifics in your note, and
> tell us how it relates to the idea of "class" as the
> intentionally defined sets that we organize in hierarchies
> as part of our ontologies.
>
> I did check the reference you provided:
> http://mathworld.wolfram.com/
>
> . . . and looked up "class", finding the following definition:
>
> The word "class" has many specialized meanings in mathematics in which
> it refers to a group of objects with some common property (e.g.,
> characteristic class or conjugacy class.)
>
> This is consistent with the usage in KIF, but does not provide the
> kind of detail that the KIF definition does. As to relation:
>
> *****
> Relation -- from MathWorld
> Relation A relation is any subset of a Cartesian product. For
> instance, a subset of , called a "binary relation from A to B," is a
> collection of ordered pairs (a, b) with first components from A and
> second components from B, and, in particular, a subset of is called a
> "relation on A." For a binary...
>
> If unary relations are allowed (a "cartesian" product of only
> one set?) then this is also consistent with the KIF usage.
>
> But . . . These definitions are primarily dealing with highly
> specialize math topics, and say nothing about how these terms are
> used in computational ontologies. Could you provide a much more
> specific reference that deals with the specific point? If you
> prefer a set of definitions where a "relation" is a subclass of
> "class" could you give us a reference to some short discourse where
> that is mentioned explicitly, with the rationale? We are
> really short on time here, and pointing to a book or a long paper
> won't be efficient enough to allow us to resolve these issues
> quickly. Decisions on terminology should not have to take
> more than two days, it is too arbitrary for prolonged debate.
>
> Pat
>
> ======================
>
> Jon Awbrey wrote:
> > o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
> >
> > Pat,
> >
> > There are so many things wrong with
> > definitions that you suggested that
> > it's hard to know where to begin.
> >
> > Ignoring the standard distinction between
> > classes and sets for the moment, consider
> > this assertion:
> >
> > | Class is a Subclass-Of Relation?
> >
> > No, that is wrong, relations are special cases of classes (or sets).
> >
> > For a standard online resource, try:
> >
> > http://mathworld.wolfram.com/
> >
> > E.g., use the search slot on "set theory", "relation", etc.
> >
> > Jon Awbrey
> >
> > o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
> >
> > Jon Awbrey wrote:
> >
> >>o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
> >>
> >>Pat & All,
> >>
> >>For the definitions of terms like "class", "set", "function", "relation",
> >>and so on, you might consider referring to a standard text like this one:
> >>
> >>o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
> >>
> >>| John L. Kelley, 'General Topology'.
> >>| Appendix on Axiomatic Set Theory.
> >>
> >>SET. Set Theory
> >>
> >>01. http://suo.ieee.org/ontology/msg04082.html
> >>
> >>Appendix. Elementary Set Theory
> >>
> >>02. http://suo.ieee.org/ontology/msg04083.html
> >>
> >>A.1. The Classification Axiom Scheme
> >>
> >>03. http://suo.ieee.org/ontology/msg04084.html
> >>04. http://suo.ieee.org/ontology/msg04086.html
> >>05. http://suo.ieee.org/ontology/msg04088.html
> >>
> >>A.2. Elementary Algebra of Classes
> >>
> >>06. http://suo.ieee.org/ontology/msg04089.html
> >>07. http://suo.ieee.org/ontology/msg04091.html
> >>08. http://suo.ieee.org/ontology/msg04092.html
> >>09. http://suo.ieee.org/ontology/msg04093.html
> >>10. http://suo.ieee.org/ontology/msg04094.html
> >>
> >>A.3. Existence of Sets
> >>
> >>11. http://suo.ieee.org/ontology/msg04095.html
> >>12. http://suo.ieee.org/ontology/msg04096.html
> >>13. http://suo.ieee.org/ontology/msg04097.html
> >>
> >>A.4. Ordered Pairs: Relations
> >>
> >>14. http://suo.ieee.org/ontology/msg04098.html
> >>15. http://suo.ieee.org/ontology/msg04099.html
> >>
> >>A.5. Functions
> >>
> >>16. http://suo.ieee.org/ontology/msg04100.html
> >>...
> >>
> >>Links 2 through 16 of the above material are
> >>selected and transcribed into plaintext from:
> >>
> >>| John L. Kelley, 'General Topology',
> >>| Van Nostrand Reinhold, New York, NY, 1955.
> >>
> >>o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
> >>
> >>Patrick Cassidy wrote:
> >>
> >>>Terminology management:
> >>>
> >>>John F. Sowa wrote:
> >>>
> >>>>Pierre,
> >>>>
> >>>>PG>Are you pissed? I apologize.
> >>>>
> >>>>No. I'm not pissed. I'm just frustrated with the endless
> >>>>rehashing of debates about terminology.
> >>>>
> >>>
> >>> I agree that we need a standardized terminology list for
> >>>this discussion group. I seem to recall that one of us proposed
> >>>to set up such a list over a year ago, but don't recall
> >>>whether anything concrete was decided.
> >>> Can we use this thread to decide how to create a standard
> >>>terminology for this group? Does anyone have experience setting
> >>>up a WIKI? If not, I will volunteer to maintain a terminology
> >>>page on my site (simple list-nothing fancy) until someone
> >>>else sets up a better hypertext version.
> >>>
> >>> As one starting point, I would suggest a careful definition of
> >>>the terms "class" and "relation" and "predicate" (which
> >>>may require definition of "term" and "sentence").
> >>>
> >>> For "class" and "relation" I would prefer the usage that is
> >>>given for KIF classes. It may not be the same as VNBG classes,
> >>>but I think it is the most common use of the term - no?
> >>>The definitions from the KIF site are attached below. Any
> >>>dissenters? (silly question?) If the majority prefer this
> >>>definition, and there is a minority that prefer a different
> >>>usage, I would suggest creating a different term for the
> >>>alternative usage.
> >>>
> >>> Pat
> >>>
> >>>--
> >>>=============================================
> >>>Patrick Cassidy
> >>>
> >>>MICRA, Inc. || (908) 561-3416
> >>>735 Belvidere Ave. || (908) 668-5252 (if no answer)
> >>>Plainfield, NJ 07062-2054 || (908) 668-5904 (fax)
> >>>
> >>>internet: cassidy@micra.com
> >>>=============================================
> >>>from:
> >>>http://www-ksl.stanford.edu/knowledge-sharing/ontologies/html/frame-ontology/CLASS.html
> >>>
> >>>CLASS
> >>>Documentation:
> >>>A class can be thought of as a collection of individuals. Formally, a
> >>>class is a unary relation, a set of tuples (lists) of length one. Each
> >>>tuple contains an object which is said to be an instance of the class.
> >>>An individual, or object, is any identifiable entity in the universe
> >>>of discourse (anything that can be denoted by a object constant in
> >>>KIF), including classes themselves.
> >>>
> >>>The notion of CLASS is introduced in addition to the relation
> >>>vocabulary because of the importance of classes and types in knowledge
> >>>representation practice. The notion of class and relation are merged
> >>>to unify relational and object-centered representational conventions.
> >>>Classes serve the role of `sorts' and `types'.
> >>>
> >>>There is no first-order distinction between classes and unary
> >>>relations. One is free to define a second-order predicate that makes
> >>>the distinction. For example, (predicate C) could mean that the unary
> >>>relation C should be thought of more as a property than as a
> >>>collection of individuals over which one might quantify some
> >>>statement. Logically, all such predicates would still be instances of
> >>>the metaclass CLASS.
> >>>
> >>>The fact that an object i is an instance of class C is denoted by the
> >>>sentence (C i). One may also use the equivalent form (INSTANCE-OF i
> >>>C). This is not equivalent to (MEMBER i C).
> >>>An instance of a class is not a set-theoretic member of the class;
> >>>rather, the tuple containing the instance is a element of the set of
> >>>tuples which is a relation.
> >>>
> >>>The definition of a class is a predicate over a single free variable,
> >>>such that the predicate holds for instances of the class. In other
> >>>words, classes are defined intentionally. Two separately-defined
> >>>classes may have the same extension (in this case they are = to each
> >>>other). It is possible to define a class by enumerating its instances,
> >>>using KIF's set operations. For example, (define-class primary-color
> >>>(?color)
> >>>(member ?color (set red green blue)))
> >>>Subclass-Of: Relation
> >>>
> >>>========================
> >>>RELATION
> >>>
> >>>Documentation:
> >>>A relation is a set of tuples that represents a relationship among
> >>>objects in the universe of discourse. Each tuple is a finite, ordered
> >>>sequence (i.e., list) of objects. A relation is also an object itself,
> >>>namely, the set of tuples. Tuples are also entities in the universe of
> >>>discourse, and can be represented as individual objects, but they are
> >>>not equal to their symbol-level representation as lists.
> >>>
> >>>By convention, relations are defined intensionally by specifying
> >>>constraints that must hold among objects in each tuple. That is, a
> >>>relation is defined by a predicate which holds for sequences of
> >>>arguments that are in the relation.
> >>>
> >>>Relations are denoted by relation constants in KIF. A fact that a
> >>>particular tuple is a member of a relation is denoted by
> >>>(<relation-name> arg_1 arg_2 .. arg_n), where the arg_i are the
> >>>objects in the tuple. In the case of binary relations, the fact can be
> >>>read as `arg_1 is <relation-name> arg_2' or `a <relation-name> of
> >>>arg_1 is arg_2.' The relation constant is a term as well, which
> >>>denotes the set of tuples.
> >>>Subclass-Of: Set
> >>
> >>o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
> >
> > o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
> >
>
> --
> =============================================
> Patrick Cassidy
>
> MICRA, Inc. || (908) 561-3416
> 735 Belvidere Ave. || (908) 668-5252 (if no answer)
> Plainfield, NJ 07062-2054 || (908) 668-5904 (fax)
>
> internet: cassidy@micra.com
> =============================================
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