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Thank you, Paola
Indeed, relationship, its nature and
forms, has poor understanding, notwithstanding that it is the principle of
order making the whole physical universe go: space-time, forces,
matter-energy relationships, fundamental interactions, physical laws, all
are natural kinds of relationships.
To establish the
proper ontological status, the relationship's nature, meanings,
structure and principles have been analyzed in the Chapters (See PDF
Doc.):
Chapter V. What Orders Reality; Chapter VI. What
Organizes the World: N-ary Relationships; Chapter VII. What Determines Reality:
Causality.
PS: And sorry for its high price, have nothing to
do with this, ...and nothing get from this.
----- Original Message -----
Sent: Thursday, February 12, 2009 4:03
PM
Subject: Re: [ontolog-forum]
Relationship: n-ary vs binary
Azamat
I remember reading with great interest that part of
your book
which really opened up my mind to understanding
relationships
what was it? chapter X?
I hope it resonates sooner
rather than later
PDM
On Thu, Feb 12, 2009 at 8:54 PM, Azamat <abdoul@xxxxxxxxxxxxxx>
wrote:
On Thursday, February 12, 2009 3:56 AM, Ravi
wrote:
But for practical
applications we need to know how to test whether a given relation (say a few
triples described by same relation type) are conforming to Cartesian product
of a set?
As a product of three sets, X, Y, and Z, a
general Cartesian product is reduced to an ordered triple of class
variables: X x Y x Z . The _expression_ on a Cartesian grid is defined
as the construct consisting of all ordered triples <x, y, z>, where
the members are the elements, individual variables, of the respective
sets. Your experimental results or observations of some tripley related
things could be depicted on 3D graphs or charts, on which, for instance,
weeks (Time, X) will be connected with Dow-Jones (Index Number,
Y) and interest rates (Economic fundamentals, Z); or commodity
production figures with prices and calendar years, etc.
Since the relations can be of many sorts,
causal, temporal, spatial, quantitative, qualitative, formal, logical, to
establish a specific type one looks at the nature of relatives, or
components, origin and direction of dependency, correlation (statistics), as
well as their formal properties.
RS: Are sets the same as subject
and object pair, tied by the relation?
If i got the question right, yes and no. As
such, everything is connected with anything. For the sake of analysis, it is
commonly identified two types of relationships: simple, pure or
homogeneous, and complex, heterogeneous.
The first type is composed of the same
kinds of things as the relatives:
1. substances related with substances,
individuals with individuals, objects with objects, as space
relations;
2. states with states; qualities (quantities)
with qualities (quantities);
3. changes with
changes, processes with processes, actions with actions, events with events,
as causality and time relations;
4. relationships with relationships, as
analogy and proportion.
The second type deals with different levels of
relatives:
1. whole/part, with many different
sorts;
2. universal/particular, as generalization or
instantiation;
3. class/member, as membership or
subsumption
Kant viewed relation as one of the canonic
classes of things, ranking it as: i. the substance-property
relation (subject-predicate) logic; ii. causality-dependence; iii.
reciprocal relation (community, reciprocality, a relation of mutual
dependence, action, or influence).
Summing up:
Relationship is an ultimate criterion of any
reference ontology candidate; for RELATIONSHIP IS A MUST IN STANDARD ONTOLOGY.
Many thanks for the discerning
reading.
Azamat Abdoullaev
-----
Original Message -----
Sent:
Thursday, February 12, 2009 3:56 AM
Subject:
Re: [ontolog-forum] Relationship: n-ary vs binary
Azamat
Great clarity and
definition of relation – I
guess what you describe ought to also factor in predicate analysis.
But for practical
applications we need to know how to test whether a given relation (say a
few triples described by same relation type) are conforming to Cartesian
product of a set? Are sets the same as subject and object pair, tied by
the relation?
Relation is a canonic class of any ontology. It is
characterized by substantial properties and formal attributes. Of the
material properties, there are their reality, nature and type and
direction of dependency. Of the second, there are transitivity, symmetry,
reflexivity, and n-ary, or cardinality, terms, or tuples, of domains,
elements, components, or arguments).
The
typical mathematical reading of relation is an extensive set of
ordered elements (as ordered pairs, Kuratowski, Wiener, Skolem;
well-ordering axiom).
There
are two formal definitions of relationship deserving attention, http://en.wikipedia.org/wiki/Relation_(mathematics):
i. [A
relation R over the sets X1, …, Xk is a subset of their
Cartesian product, written R ⊆ X1 × … × Xk.].
ii.
[A relation R over the
sets X1, …,
Xk is a
(k+1)-tuple R = (X1, …, Xk, G(L)), where G(L) is a subset of the Cartesian
product X1 × … ×
Xk. G(L) is called the graph of L.]
So,
one can say "an n-ary relation is an ordered class of n-tuples, or it is
an ordered class of (n+1) tuple". Three things are of importance here:
1.
the components of relations are of the same kind and sorts, objects,
persons, qualities, quantities, times;
2.
ordering of relations, their direction, a triadic 'giving', tetradic
'paying' or triadic 'betweenness';
3.
the key sense of relationship is represented by the graph, indicating its
nature and kind: if it's causal relation, temporal relation, spatial
relation, semantic relation, logical relation, etc.
Think
of the complex case of social networks, where social relationships
described in terms of nodes (agents) and ties (relationships), of
different sorts and kinds, like as emotional, friendly, economical,
political, or commercial links and connections.
Any
general ontology missing the class of relation as the fundamental category
of reality is internally defective. For example, there is a comprehensive
scheme of categories of reality proposed by Chisholm, who divided Entia
into Contingent things (States (Events) and Individuals (Boundaries
and Substances) and Necessary things (States and Nonstates (Attributes and
Substances). Since the class of relationship is deprecated, the
scheme is missing the adhesive of all things, Relationship, as well
as Time and Space.
Azamat Abdoullaev
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