Allow me to top with one sample to illustrate the nature of nD
relationships - natural fundamental forces, relation-forces. First of all,
it's what shapes the universe, gravitation, graviration force, or gravity,
but defined as the force of attraction AMONG all masses of the universe.
Remember the n-body problem in the celestial mechanics, where the simplest
three body problem makes the Earth-Moon-Sun system, still giving only
restricted (quasi-binary relations) solutions. Considering the n point
masses in n-dimensional space, instead of 3D, one could make out the full
meaning of n-relations, when the n-body problem in general relativity will
look as fun.
It's generally accepted that the binary relations are most ubiquitous. In
fact, its common only for human perception, while the nature operates by the
Some comments below. Generally, we are in the same line, but there are still
----- Original Message -----
From: "doug foxvog" <doug@xxxxxxxxxx>
To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
Sent: Tuesday, November 08, 2011 11:34 PM
Subject: Re: [ontolog-forum] N-RELATIONs: Formal Ontology, Semantic Web and
Smart Applications (01)
> On Tue, November 8, 2011 13:54, AzamatAbdoullaev said:
>> i want to emphasise a couple of key points concerning my part of message:
>> The task of ontology is to identify the nature of concepts or the real
>> semanics of terms,
> When natural language terms have multiple concepts/semantics/meanings --
> including multiple overlapping meanings -- the task of ontology is to
> tease out the semantics of the individual meanings, not to identify the
> cluster of meanings that are related to each individual term. (02)
Still, we need to define the meaning of meaning, or the significance of
signifcation: meaning = representation cum sense. Sense always involves a
set of associations, " a cluster of meanings", as you say. But the principal
meaning is invariant, constant value.
>> having the same things as the signified or as the meant,
>> say, 'lexical" meanings, references, senses.
> If you mean to distinguish the individual meanings, references and
> senses, i agree. I also note that different terms may signify
> identical meanings (even if some of their other meanings do not
> overlap. (03)
>> It's important to see how the relationships of meaning and significance
>> are interrelated.
>> For if the WORD "marriage" signifies, both
>> denotes/refers/stands for/symbolize and connotes,
> Of course, these are different properties.
>> the CONCEPT of marriage
>> means, both represents and senses/implies...
> ?? If the word has multiple meanings (etc.) that does not mean that
> a concept modeled in the ontology should have multiple meanings. That
> means the various meanings of the word which are desired to be represented
> in the ontology should each be modeled by distinct concepts. (04)
AA: How the same word can have different meanings and how the same meaning
can be expressed by words, i.e. the source of semantic ambiguity and
nonsense, request a relation ontology.
>> The class of things involved in the signification relationship
>> (symbols-things) and the meaning relationship (concept-things) is the
>> Still "marriage" is a binary relation, relating elements in pairs.
> If by "relation" you mean a situation in which several people have
> a kinship relationship, i would agree. If you mean a binary predicate,
> i disagree.
> In computational ontology, relations are a product of modeling.
> Binary predicates are easy to state and reason with, and so are
> useful for many types of reasoning. Higher arity relations are
> normally used when one can not easily make a statement using
> binary relations. Such cases include stating orderings and set
> definitions. A higher-arity relationship in which each argument
> plays a different role with respect to a specific situation can
> be better modeled by reifying the situation type and defining
> individual relations between the situation and the various role
AA: It all depends how wide you define a situation. As i mentioned on other
message, a sound working definition of n-ary relations could follow the
Morgan's extended as:
"When a number of objects, qualities, classes, or attributes...are seen
under some connexion, that connexion is called an n-ary relation." (05)
> I would define a marriage as a situation in which various people and
> other entities play various roles. A (generic) marriage is defined as
> having two spouses, and a (temporally constrained) binary relationship
> relates the two spouses. The marriage is customarily performed by a
> third person. It is normally authorized by one or more organizations
> (governments, religious groups) and has a wedding ceremony as an initial
> subevent. A dowry might be part of a marriage (and thus have a binary
> relation to the marriage). (06)
AA: We need not mix the associations (senses) with the principal meaning of
marriage, a legally related couple on a set of adult individuals. You just
try to add a sort of provenance relations. Take a ternary relation of
introducing between 3 individuals:
"x was-introduced-to y by z", where (x,y,z) is a 3-tuple of persons. A
degenerated introduction, if one introduces himself :) (07)
> Two individuals might marry each other several times (e.g., after
> divorce or annulment), so a binary relationship between the two
> people does not necessarily denote a unique marriage. A ternary
> relationship, with the third argument being the start time can
> uniquely denote a marriage. Note that multiple statements
> involving more or less precisely defined starting times can
> uniquely denote the same marriage, so no marriage has a unique
> relation that defines it.
>> What is of more interest is a triadic relations
>> as "giving" or "asking"
> or "marries" as in "Father Jon married Ellen and Joe"
> 8)# (08)
That's serious - not to mix the n-dimensional relations. You might have a
harem, still the mariage is a binary relation between two individuals. It's
only a special type of binary relation: one-to-one, or one-to-many, or
many-to-many, or many-to-one. (09)
> Why not model Giving and Asking as event types?
You can, but it becomes a sort of relational event, with all proper for
> roles: donor, recipient, transferredThing (or requester, requestee,
> eventTypeRequested) could be defined and triadic relations
> need not be defined.
>> or tetradic
>> relations as "paying" (x pays y to z for w),
> or (John married Ellen to Joe in Denver) 8)#
> If you only model marriages by relations, how would you express this? (010)
AA: its about what the semweb folks call the provenance information, while
they do the reification/nominalization of relationships for better logical
and computational manipulation. Or as with the multigraph, you could add any
association types. (011)
> A Buying event could have the roles:
> and express your 7-item statement as:
> (isa Purchase1324 Buying)
> (buyer Purchase1324 x)
> (moneyTransferred Purchase1324 y)
> (seller Purchase1324 z)
> (objectPaidFor Purchase1324 w)
>> etc.; to see how formally
>> represent such n-dimensional relationships,
> If one models situations or events, one does not need to create
> different relations of various arities to express different things
> about the same event.
AA: It depends on how complex situations or events are, and how you define
them. I head some general descriptions covering all the world. You might see
it as the general state of things, a state of affairs, the combination of
everything, objects, states, circs and relationships at the same time. (012)
>> and if reducing polyadic relations to dyadic ones is validated,
>> or what a cyclic order of relations
>> is, and so on.
> doug foxvog doug@xxxxxxxxxx http://ProgressiveAustin.org
> "I speak as an American to the leaders of my own nation. The great
> initiative in this war is ours. The initiative to stop it must be ours."
> - Dr. Martin Luther King Jr.
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