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> One thing is bugging me: I'll illustrate by means of an example:
> We would be inferring that the set fluxes consists of only the elements
> {f1,f2,f3} from the three statements: "f1 in fluxes", "f2 in fluxes", "f3 in
> fluxes".
> But if fluxes={f1,f2,f3,f4,f5}, that would still be consistent with the
> above three "in"/"is an element of" statements.

You could be saying two different kinds of things: either
"there exists some x such that x is in fluxes and x = f1"
or "for all x in fluxes, x = f1 or x = f2 or ... or x = f5".
Both of these are declarative in form, but the first one allows
one to add more fluxes simply.

With regards to the problem of whether a given object is in a set,
I would suggest that we firstly note that simulating all of
predicate calculus runs into computability problems.
One way to simplify things for ourselves is to assume that all
positive relations must be entailed by the model plus whatever
our base axioms are in order to be true (so, we are really looking
at derivability, rather than truth). So, if the model (including imports
and so forth) does not entail that q is in fluxes, then q is not in fluxes.
An alternative but equivalent way to view this is that we
choose to deal with the smallest positive model such that all of the
assertions that we make are true.

As long as we have a finite domain of quantification we do not
have any problems with determining entailment; we can avoid diagonalisation
and halting problems both. If we had to quantify unrestrictedly
over numbers this breaks down, but I do not see biological
models using this kind of functionality.

Taking both of these simplifications, we should be able to use
predicate calculus constructs in the same way we have been using
other equations in models, without sacrificing the declarative nature
of the language.

Regards,
Justin.

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• [cellml-discussion] Using proposed CellML 1.2 features to create more re-usable metabolic models, Randall Britten, 02/01/2008
  • [cellml-discussion] Using proposed CellML 1.2 features to create more re-usable metabolic models, Justin Marsh, 02/04/2008

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