Re: We have to wean people away from the knee-jerk reaction that
complexity is determined by the language. They have to learn that
complexity is determined by what you do with a statement, not by the
statement itself and certainly not by the language used to state it. (01)
This is then a different view of complexity than one would typically
consider in, for example, an architectural language (that may also be an
ontology) or an execution language. For this domain user complexity (of
usage) is very related to the number of statements it takes to express a
concept. A language that can express a concept in one statement is less
complex to use than one that expresses the same concept in 10
statements. However the first may be a more complex language since it
has more concepts. What the first language is providing is a
first-class representation of a concept that is likely to be a pattern
in the second language. In formal terms they are equally expressive but
in user terms one is more complex and less expressive. (02)
I would also argue that since the language requiring the pattern has not
encoded knowledge of the pattern it has lost important information as to
the intent of the more compact statement (and reversing the pattern may
not be possible). So while formal semantics may be preserved user intent
is lost. This user intent is part of the ontology of the users domain. (03)
Perhaps we could find a way to capture both these formal and
user-centric dimensions? (04)
-----Original Message-----
From: ontology-summit-bounces@xxxxxxxxxxxxxxxx
[mailto:ontology-summit-bounces@xxxxxxxxxxxxxxxx] On Behalf Of John F.
Sowa
Sent: Sunday, January 28, 2007 5:01 PM
To: Ontology Summit 2007 Forum
Subject: Re: [ontology-summit] dimensions/aspects of ontology types? (05)
Leo, (06)
Descriptive complexity is addressing a different topic, which involves
finding a description (i.e., a statement) that expresses a given
property S. As Immerman says, (07)
> ... a more natural question might be, what is the complexity > of
expressing the property S (08)
That question might be "more natural" for the problem that Immerman is
addressing: How does one express a given property? (09)
But if we are given an ontology, we already have the statements, and the
relevant question is how much time it takes to process those statements
for various purposes. That is the old-fashioned version of
computational complexity, not descriptive complexity. (010)
In any case, it doesn't matter which version of complexity is being
considered. The points I made are equally applicable to both: (011)
1. Expressivity of a statement or a theory is independent of
the language in which it is stated. Translation from one
language to another can never change the expressivity. (012)
2. Computational complexity is not determined by a statement,
but by the algorithms that process the statement. (013)
We have to wean people away from the knee-jerk reaction that complexity
is determined by the language. They have to learn that complexity is
determined by what you do with a statement, not by the statement itself
and certainly not by the language used to state it. (014)
Fundamental principle: Limiting the expressive power of a language can
never reduce the time required to solve any problem.
It merely restricts the kinds of problems that can be stated. (015)
John (016)
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