Cory, (01)
I'd like to respond to both of your last two messages in the
same note. In your comment about ODM, you said (02)
> I am not sure I understand your characterization of ODM as
> lost in syntax, ODM is defined in terms of the meta model
> behind the syntax, not the syntax. Now, such meta models can
> be more syntactically focused or more conceptually focused
> and I would agree that the ODM meta models represent more of
> an "abstract syntax" than "concepts", but you could take any
> one of those models and express them in any form of syntax... (03)
This gets into the question of what is semantics. The definition
of semantics that is used in logic is very straightforward: (04)
Two statements s1 and s2 have the same semantics if and only if
s1 and s2 always have exactly the same truth value (T or F) in
the same circumstances or state of affairs. (05)
To relate this to data models, I'd like to use the example of the
relational data model (as implemented in SQL databases) vs. the
network data model (as defined by the old Codasyl DBTG). (06)
Since both data models are capable of representing exactly the
same information -- any fact represented in one can be translated
to a fact in the other which is true or false in exactly the same
circumstances or state of affairs -- the difference between them
would be considered a syntactic, not a semantic difference. (07)
Those syntactic differences may have a major influence on the
readability, usability, and even the efficiency of a particular
implementation or application. But since they do not affect
the truth value of what is stored in the database, they are
considered syntactic, rather than semantic. (08)
> That ODM captures these composite concepts (including the meta
> modal for and mapping to CL!) seems like a good thing, the
> concepts exist in that domain and are part of the conceptual
> framework of those languages. (09)
I would certainly agree that definitional methods for defining
higher-level concepts (or types) in terms of lower-level ones
are very important. However, if your definition simply says
that some simple expression X is a synonym for some complex
expression Y that has many more symbols, that is still considered
a purely syntactic transformation -- because every statement in
which X occurs can be replaced by Y without changing the truth
value. (010)
> What I don't want to do is lose potentially useful concepts
> just because they can be "reduced" into something else. (011)
The ability to define X in terms of Y is important, and some
languages give you more definitional capability than others.
CL is a very general language that enables all the options in
the source languages to be preserved. So CL would also let
you define X in terms of Y. But that is still a syntactic
transformation, not a semantic one. (012)
> But I don't see it playing the same role as ODM or even an
> ODM like thing that was more normalized over concepts. (013)
I didn't say that ODM isn't be useful for many purposes. But
I would claim that any definition possible in ODM could be
translated to an equivalent definition in CL. Furthermore,
that translation would highlight exactly where the semantic
differences might be. (014)
> I am a fan of the lattice, not sure it is the subject of this
> thread, but a fan anyway.
>
> What I am wondering about is the most effective organization
> of the lattice...
>
> that a node in the lattice should contain all of the facts
> that have identical context (apply to the same kinds of
> situations... (015)
I'm not sure what you mean by "context". If you mean that a
theory should state the details about when it should be applicable,
I would answer that it could contain axioms that state such
details. (016)
If you give a formal definition of what context means, then it
would be possible to have very general (context independent)
theories high up in the lattice, and more specialized (context
dependent) versions further down in the lattice. (017)
> Does this fit with your lattice? Or, do you have an organizing
> principle for the lattice? (018)
I would say that it does fit in with the lattice. But I would add
that there are many different organizing principles or design
principles that could be supported with exactly the same lattice. (019)
For example, there are many theories about program development,
each of which recommends different design patterns or structures
for software development. But if different principles result
in programs that have exactly the same outputs for exactly the
same inputs, then those programs would considered semantically
equivalent, even though the notation and organizing principles
might be radically different. (020)
I am certainly in favor of good data models, design patterns,
or organizing principles. But the question of whether those
principles have a syntactic or semantic effect would depend on
the basic question: (021)
Do two different statements s1 and s2 have exactly the same
truth values in every circumstance or state of affairs? (022)
If yes, the difference between them is syntactic. If no, the
difference is semantic. (023)
John (024)
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