Term "Configuration"
Massimo Dentico
m.dentico@virgilio.it
Sat Apr 12 13:08:02 2003
Some reference material, questions and comments only to start the
discussion. Probably other will follow.
First some basic terminology about predicative languages, excerpted from
an italian book on logic [1], translated and sligthly adapted (I try
always to be pedagogical for myself and other less math-oriented people
on this list; my apology to other with a strong mathematical background
for which this is trivial).
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The /words/ of a language are finite sequences, obtained concatenating
symbols and sequences of symbols. The concatenation operation will be
indicated simply by juxtaposition of symbols from left to right as in
Indo-European languages.
/Well-formed/ words, called /expressions/, are words in 2 category:
- /terms/, corresponding to names;
- /formulae/, corresponding to phrases.
The set of /terms/ is the smallest set of words with the following
closure properties:
- each words constituted by a single variable is a /term/,
- each words constituted by a single constant is a /term/,
- if F is a functional symbol with n arguments and t1,...,tn are terms,
even Ft1...tn is a term, of which t1,...,tn are immediate /subterms/.
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Now it is clear that the definition of /term/ is mostly syntactic.
So on Wed, 9 Apr 2003 16:37:46 -0700 (PDT), when you (Brian T Rice
<water@tunes.org>) wrote:
> It occurs to me that the same configuration concept could be used for
> both purposes. We could cover the collection-like or -based
> requirements with such concepts, and this seems to blend well with the
> idea of terms.
are you alluding to possible interpretations (semantics) of the /term/
concept? I think to be so.
This remind me about two possible kind of collection (set) definitions
(to simplify the exposition here I'm ignoring some details when I equate
collections and sets, such as order, multiple instances, etc.):
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- /Intension/: a definition of a Set by mentioning a defining property.
[2]
- /Extension/: the definition of a Set by enumerating its members. An
extensional definition can always be reduced to an Intentional one.
[3]
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Your examples are apparently of the second kind here:
> Indeed, terms are often thought of as collections: Lisp uses lists,
> people here have mentioned "tuples" (with whatever meaning they
> intended), and Slate uses objects with attributes, some of which are
> different kinds of collections (mostly Sequences).
but I'm quite sure that the first is implicit in your discourse (for
example: in Prolog a variable plays often the role of a set via
backtracking and unification).
> This sounds great, but the idea needs to reach some definite
> formality; something we can see implementing. We can talk about a set
> of objects: a minimum amount of collection information to say that
> some objects are part of a configuration, just that "they belong".
> With higher-orderness, we can use this idea to say that attributes
> also "belong", although this kind of reflection required for just an
> argument list is a lot of overhead at runtime which just should exist.
> So there should be optimized versions (subtypes) of this
> implementation, specialized for specific cases.
This is not clear to me: collection-oriented languages use intensional
(operators and functions) and extensional (some syntax for literals and
enumeration) terms in expressions even if there are some more
declarative and other more operational. Note that even in this case you
can often establish, under some constraints, some equivalence; for
example between relational algebra, which is, in a sense, more
operational, and the relational calculus of domains or tuples, which are
more declarative.
Expressions are always relationships/constraints between objects and
calling some of these expressions "configurations" seems arbitrary.
Nothing wrong with this, but what are precisely the distinguishing
features of these configurations wrt other expressions?
REFERENCES
[1] Gabriele Lolli, "Introduzione alla logica formale" [Introduction to
formal logic], 1991, Il Mulino, Bologna.
[2] and [3] below are from Eric W. Weisstein, "Concise Encyclopedia of
Mathematics CD-ROM", CD-ROM edition 1.0, May 20, 1999
[2] http://mathworld.pdox.net/math/i/i161.htm
[3] http://mathworld.pdox.net/math/e/e422.htm
Regards.
--
Massimo Dentico