Re: SUO: Re: More Terminology
Jon,
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.
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
=============================================