Re: Troublesome relations

Danny Ayers wrote:

> The comments in [3] don't seem unreasonable (however debatable), but
> [2] is a longish query with a terse response from Date:
> 
> [[ This approach is the old argument that all relvars should be
> binary in a different guise! Thus, a cogent counterargument is:  How
> do you deal with irreducible n-order predicates for n <> 2? ]]
> 
> Problem I'm having is coming up with practical examples of such 
> predicates, or how this might impact on RDF modelling. (I could well 
> be misinterpreting Date's statement, as Googling "all relvars should 
> be binary" doesn't exactly give evidence of an old argument, rather
> it gives [2] as the first hit and expanding to 'relation variables' 
> didn't help any).

John Sowa has discussed irreducible triads several time on the 
Conceptual Graphs list, which unfortunately seem not to have an archive, 
although some were cross-posted in the SUO list whoch does.  Here are a 
few congent quotes from his posts -

 From http://suo.ieee.org/email/msg10941.html -

[[
As another example, the attached diagram (feedback.gif) shows
a triadic relation that is very important for engineers:
the feedback loop.  The classic discovery, which occurred
in the mid 19th century, was the regulator or governor for
steam engines.  Before it was invented, steam engines were
difficult to use because some human being constantly had
to adjust the input fuel and the steam pressure in order to
keep the speed relatively constant.

A similar example is cruise contol for a car.  As feedback.gif
illustrates, may be considered a dyadic relation between
the fuel and the speed.  Without cruise control, the driver
must constantly adjust the fuel to maintain constant speed.
But cruise control is a triadic relation that constantly
monitors the speed and adjusts the amount of fuel to maintain
constant speed.  (This diagram is simplified because many
different factors affect speed, but they can be represented
by multiple dyadic relations.  Feedback involves an
irreducible triad.)

The connection between purpose or intention and triads,
which is illustrated by the feedback loop for cruise control,
also appears in other human inventions, such as thermostats,
alarm clocks, and the refill mechanism in a toilet tank.
In nature, triadic relationships most commonly appear in
living organisms, which involve feedback loops to control
every iportant aspect of life.

There are, however, some inanimate things in nature that
involve feedback, and interestingly, they are often
personified as living beings.  One example is a hurricane,
which has a complex feedback loop involving wind, water,
and speed.  That feedback loop enables the hurricane to
maintain a fairly constant speed and configuration over
a period of many days.  The resulting behavior is so
"life-like" that people give them names, such as the
current hurricane named Isabelle, which is supposed
to hit the eastern US tomorrow.

Summary:  Thirdness is a metametalevel notion, which
characterizes the metalevel axioms that define a large
number of important ontological relations.  Thirdness
is essential to all the relations involving signs and
representations of any kind, to most relations that
are characteristic of living organisms, to any human
artifacts that involve feedback loops, and to some
inanimate processes, such as hurricanes.  The connection
between Thirdness and life is so common that people
tend to personify inanimate things that involve
naturally occurring feedback loops.

Bottom line:  Thirdness is important for ontology
because an irreducible triadic relation is usually
a central or characteristic feature of whatever
entity is associated with it.
]]


 From http://grouper.ieee.org/groups/suo/email/msg12155.html -

[[
- Trichotomy:  Peirce showed that it is possible to
     transform any graph that contains a node with 4 or
     more attached arcs into a graph that contains no
     node with more than 3 attached arcs.  See the
     diagram nodes.gif for a transformation that splits
     the node X with four arcs into two nodes X1 and X2,
     which have three arcs each; similar transformations
     can be used to split nodes with any number of arcs
     to additional nodes that have no more than 3.
]]

Cheers,

Tom P
-- 
Thomas B. Passin
Explorer's Guide to the Semantic Web (Manning Books)
http://www.manning.com/catalog/view.php?book=passin

Received on Tuesday, 19 October 2004 12:43:04 UTC