Dear Matthew, (01)
> The truth is that there are multiple ways in which roles can be
> represented...
>
> The most common mistake I see in models of roles is roles being treated
> as subtypes of the role-player. As long as you have not fallen into that
> trap, the chances are that what you have done is “not wrong”. (02)
I agree that treating any type as a subtype of a physical instance
is the worst mistake. (03)
But you can always take any way of characterizing an instance and
add further constraints that characterize it in more detail in any
way that you please. (04)
One reason why there is so much confusion in the field of ontology
is the enormous amount of terminology and notation that has been
generated in several millennia of innovation, analysis, and debate. (05)
For a summary and analysis of that debate, see the slides of the
tutorial I presented at the Semantic Technology Conference in June: (06)
http://www.jfsowa.com/talks/kdptut.pdf
Knowledge Design Patterns (07)
Aristotle defined the basic patterns for logic and ontology that we
are still following today. For a brief summary, see slides 11 to 18. (08)
In particular, note the distinction between substance and accident shown
in slides 12 to 15. Slide 15 specifies George Washington's "Substance"
as "a man". The other 9 categories specify accidents that were true
at a particular time and place: 19 October 1781, Yorktown, Virginia. (09)
Many people, notably Willard Van Orman Quine, have criticized that
distinction. In effect, they are going back to Plato's ontology
(Slide 12), which treats every individual as a "receptacle" for
a "bundle of properties". As Peirce, Whitehead, and others observed,
the debates between Plato and Aristotle have never been settled. (010)
Then look at the slides about logic (40 to 68). Start with slides
41 to 45, which show that you can represent all of first-order logic
with combinations of four basic notions: relations, conjunction,
negation, and existence. (011)
All the debates about ontology can be reduced to three questions: (012)
1. What relations and kinds of relations do you choose? (013)
2. How do you combine them with logical operators that can be defined
in terms of negation, conjunction, and existence? (014)
3. How do you map those combinations to anything and everything you
want to say in any language, natural or artificial. (015)
For a summary of the debates and innovations since Aristotle, see
slides 69 to 107. The last section (slides 108 to 129) summarizes
some of my recommendations about future directions. (016)
John (017)
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