A Triptych Software Development Paradigm - Correct System Design: Recent Insights and Advances - page 35

Our (domain) observer functions are not denable by us, but are dened
by the domain. Observer functions are, however, characterisable by two kinds of
axioms. Firstly general axioms that characterise the general model of sustainable
development. One is shown above: It expresses that all resources of a specic
category must have the same set of attributes and, of course, be of that category.
We may relax the former (same set of attributes), but cannot relax the latter (be
of that category). (The symbols and can be \pronounced" `such that' and

`implies/imply', respectively.) Secondly instantiated, specic axioms: For a given,
ie. an instantiated case of sustainable development, for example the building of
a chemical plant, or fertilisation of crops, the resources, categories, attributes
and values are \xed" and a (possibly) consistent, but not necessarily complete
axiom scheme \set up": one which approximates relations that are believed to
hold between these specic resources, categories, attributes and values.

)

4.3 Indicators

An indicator is a measure of desired values of resource attributes. Sometimes an
indicator is a value with, perhaps, some fuzzy membership (or probability) func-
tion. Sometimes an indicator is a pair of values (a range) (perhaps adorned with
some sort of fuzziness). And, sometimes an indicator is a function, for example
a simple function from time to attribute values, or a more complex function, for
example a function from time and another attribute value to (perhaps fuzzy)
values.
An indicator thus expresses a desirable interval within which actual resource
attribute values are to range at given times and/or in the presence of other
(fuzzy) valued attributes, etc.

type
I
Fuzzy
value
is in Rng: R I

A ! Fuzzy

4.4 Resources, Attributes and Indicators

In development we are interested in certain resources, and for each of these, in
certain attributes, and, for each of these, in focusing on certain (intervals of)
indicators. We may speak of such a \thing" as a RAIs: A resource to attribute
indicator range \table":

type
RAIs = R

m (A m (I

I))

The above denes RAIs to be a space of maps from resources to maps from
(their) attributes to pairs of (\lo{hi") indicators.
An `abstract' example could be: