Relating Domain Concepts Intensionally by Ordering Connections - Formal Methods and Hybrid Real-Time Systems - page 203

Definition 8 (Object Aspect). By an object aspect (x:X), we understand a
proper part of an object existing in a possible world causally reachable from the
actual world 6 .

With object aspects we abstract from the actual elaboration of artefacts; elab-
orations which change the artefacts physically but not change the identity of
the artefacts. In the area of building construction, object aspects are the var-
ious parts of the building to be build and they are referred to in construction
specifications, budgets, project plans, and other documents. In the area of the
service and consulting sector, object aspects are the services to be provided and
these are likewise referred to in specifications, budgets, project plans, and other
documents.
Resource types (rn:Rn) denote the kinds of resources that are consumed by
operations in a construction works. In the area of building construction, resources
are building components like pre-cast concrete walls, materials like sand, etc.
They are also machines and personnel. In the area of the service and consulting
sector, resources are usually personnel, but can also be machines. Resources are
counted in quantities (q:Q) which may be considered discrete or continuous.
Resources constitute the entire input to works and are thus the subject for
expense calculation and estimation.
A mapping from resource types to natural numbers defines the quantities of
resources for each resource type. We define the operations meet and join for
combining such mappings. The operation meet gives the map where all resource
type are in both argument maps, and the quantities are the smallest from the
argument maps. The operation join gives the map where each resource type is
in either argument map, and the quantities for common resource types is the
sum.
We shall say that a map (rm:(Rn m Nat)) is a sub-map of another map if

and only if all resource types of the former map is present in the other map and
quantities are either equal of less than in the other map.
We assume that resources consumed by operations concerning one object as-
pect are distinct from those consumed by operations concerning other object
aspects. That is, the cost of reusing a tool is distributed on the works in which it
is used. The types and quantities of resources may be the same but the physical
resources are not 7 .

5.2 Formalization

type
On,
X,
Rn,
Q =

{|

q:Real • q > 0.0

|}

6 Note, that this definition does not commit ontologically to a concept for every object
aspect there may be.
7 Note, that we abstract from the physical resources in this paper.