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Re: [ontolog-forum] Relationship: n-ary vs binary

To: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "Azamat" <abdoul@xxxxxxxxxxxxxx>
Date: Fri, 13 Feb 2009 16:20:16 +0200
Message-id: <005501c98de6$323999c0$a104810a@homepc>



I think you are very good as the devil's advocate, and highly appreciate you provocations and stimulations. To better your critical skills, let me share some observations:

1. Avoid quibbling-niggling, pettifogging over small things;

2. View ideas in the whole context;

3. Review your understanding of nonsense.


To understand the last observation, you need a liberal intelligence. Everything in the world has some sense and meaning, including nonsense, http://en.wikipedia.org/wiki/Nonsense. In literature, there is a whole booming style, literary nonsense http://en.wikipedia.org/wiki/Literary_nonsense, using all sorts of techniques and devices to create nonsensical effects, like L. Carroll.

There is nonsense (stupid, bad) and nonsense (intelligent, good). The samples of the latter are when the parts make sense, while the whole is senseless, or vice versa. The case of the former, when you know nothing about some domain of knowledge, say, real ontology, then all its things will sound nonsensical; they are not intelligible and understandable since transcend somebody's narrow mind, his cognition, beliefs and perception.


If some big ideas, as reality and its aspect, relation, beyond you kin and understanding, this will make nonsense for you, for your particular mind, however well-seasoned. I state as below: [relations are classified with respects of their nature, mode of existence, the numbers of the relatives as well as formal properties as transitivity, symmetry, reflexivity.]  If you are missing the clear meaning, then it is nonsense for you mind, nothing can be done here.

Now, I state [a relation can exist apart from the terms it relates], for 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.] Again, you can't get the meaning of it, another nonsense for your specialized mind. For it may still believes the relation is an entity without a reality, that the relation exists when the terms it connects exist. 

Another source of nonsense to be mentioned is #2, when one is missing to see ideas, concepts, statements in the whole context. This is a lore: "Many relations relate things of different kinds." Answering to the discreet questions of Ravi S, i specified:

[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.]


Azamat Abdoullaev


PS: I noticed that your personal relationship with "relation" is rather casual, http://www.w3.org/TR/2006/NOTE-swbp-n-aryRelations-20060412/, showing shallow understanding of its exclusive status. Here i hold with Gian Zarri, "very poor content", http://markmail.org/message/tk6ftny72wpfzgvg.  It is always better to ask questions, if you don't know something well, thus heading off badly nonsensical judgments.


----- Original Message -----
From: Pat Hayes
Sent: Friday, February 13, 2009 8:28 AM
Subject: Re: [ontolog-forum] Relationship: n-ary vs binary

On Feb 11, 2009, at 10:55 AM, Azamat wrote:

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).

None of the above makes sense. 

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 thegraph of L.]
So, one can say "an n-ary relation is an ordered class of n-tuples

Exactly. This is the standard mathematical "extensional" notion of relation, and is used in logical ("Tarskian") semantics. However, it is in many ways more natural to distinguish the relation itself from its extension (set of tuples), as apparently different relations can have the same extension 'by accident'. Of course, those who adopt an extensionalist discipline as a matter of principle would disagree with this. 

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;

Nonsense. Many relations relate things of different kinds. In fact, these are the most important relations in most ontologies. 

2. ordering of relations, their direction, a triadic 'giving', tetradic 'paying' or triadic 'betweenness';

What ordering are you referring to? The tuples are ordered by definition (that is what 'tuple' means). Other than that - essentially the ordering of the relational arguments - relations have no intrinsic order. 

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.

Wrong. This is not represented by the graph. In general, there is no way to tell, given the graph of relation (which just means, given the extension of the relation) what "kind" of relation it is. For example, any causal relation can also be interpreted as a (weaker) temporal relation, since there is a temporal relation with exactly the same graph (because causes never follow their consequences.)

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. 

Indeed, that is a rich collection of examples: but it is misleading to think that all relations are similar to social relationships between people. 

Any general ontology missing the class of relation as the fundamental category of reality is internally defective.

Well, the point can be argued. Certainly, one must use relations when describing reality. But a nominalist might balk at admitting that these relations exist in the same sense that physical things exist. 

Pat H

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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