The domain: Incremental design

The domain is that of conceptual design models and the operations which build up and elaborate on such models. The models we callartefact modelsas they are abstract descriptions of things to be man–made. The notion of artefact model is inspired by the notion ofartefaction which is defined in [79]. The operations on artefact models are design moves. By a design move, we understand the cognitive or physical action of changing and elaborating a design representation.

The notion ofmove in context of design originates in [149] and the notion has been picked up in various work [164, 139, 79, 62].

We follow [64, 67, 75, 167, 62] and understand design as an incremental process in which objects are introduced, properties are ascribed to objects, and objects are related.

It is convenient to define each design move as a move in the smallest sense.

That is, to minimize the change of effect a design move has on the present design. Thereby, we are able to restrict to a minimum of fundamental generator functions for representing design moves. We thus, see all design moves as small steps.

6.1.2 Design lattices

As in Chapter 5, we consider the design moves of: conceiving an object, as-cribing a property to an object, and adding a relation between two objects, to a model. Furthermore, we have the lattice operationmeet which combines artefact models, and the lattice operationjoin which gives the artefact models having the intersection set of objects, properties, and relations.

In this paper we shall follow the principles of algebraic specification in RAISE [134, 135]. This means that each design move (modelled as a generator func-tion) takes (among other parameters) a previous artefact model which is then modified. This principle is applied besides for the two lattice operations which apply on pairs of artefact models.

In addition to the design moves defined in Chapter 5, we introduce the design move of decomposition. This design move serves another cognitive purpose.

Decomposition introduces a special relation holding between objects and sub–

objects. However, the relation is not represented by edges in the design lattice as expected using mereological thinking. It is part of the artefact model itself.

The difference is that the part–whole relation ontologically is a more diffuse re-lation than a rere-lation between an object and its properties, or binary (possibly topological) relations between objects. In Chapter 8 it is argued that the dis-tinction between parts and whole often may be a matter of convention³. Often decomposition is used simply in order to be able to refer to an object as a whole and its parts. Other times decomposition is used as part–whole knowledge may come after the conception of the object being decomposed.

Many paths and many lattices can lead to the same design. Knowledge of an artefact may be conceived and added to the model in different orders. Also, similar designs may be achieved by taking either a bottom up or top–down approach. Figure 6.1 shows a bottom up approach in which three objects are added in parallel paths⁴. The objects are independently specialised by adding properties, and are finally put together to form an entrance section for a house.

Figure 6.2 shows a top–down approach which leads to a similar design⁵. In this approach a single object is introduced, specialised, and then decomposed into three sub–objects forming a similar entrance section.

3Socially or based on the present use of language.

4We use dashed lines in lack of better graphical ways of depicting object without properties (and thus also without specific dimension and size.)

5We use dashed boxes with round edges in order not to confuse lines representing part–

whole relations and arrows representing design moves.

6.2 Artefact models 153

add object add object

add object

add dimension properties

add dimension properties

add dimension properties

add form properties

add form properties lattice meet

lattice meet

Figure 6.1: Bottom–up design lattice.

6.2 Artefact models

In the following, we present an algebraic specification of artefact models (θ:Θ) containing: objects (x:X), properties (p:P) of objects, and relations (r:R) be-tween objects. A property is considered a pair of which the first component is called the attribute⁶ (a:AP) and the latter is a set of values⁷ (vs:VP-infset).

A set of values may be infinite in order to express properties like weighing at least 200 pounds. An attribute uniquely identifies a set of values for a given object. An example of an attribute iscolour. The corresponding set of property values could be{blue, grey, green}. A set with more than one element means that the object can be realised in more than one way; namely one for each of the property values.

If an object has properties with attributesa1, . . . , amand corresponding values {v11, . . . , v1n1}, . . . ,{vm1, . . . , v1nm}, the number of possible realisations isn1×

. . .×nm.

The empty set of values corresponds to absurdum: no possible realisation ex-ists. Absurdum can be used to designate an error which may occur because of

6or property attribute.

7called property values.

add object

add dimension properties

decompose (incl. certain property ascriptions)

add topology relations (A and B)

add topology relations (B and C)

lattice meet A

B B

C

Figure 6.2: Top–down design lattice.

conflicting models on which lattice meet is applied. A similar account is given for relations. A relation between two objects is a pair of two component. The first is the attribute⁸ (a:AR) and the second is a set of values⁹ (vs:VR-infset).

An example of an attribute of a relation is horizontal–distance for which the corresponding relation values could be{20m,30m,60m}. Another example of an attribute isplacement with the values {on_top, next_to}. As it appears, many relations concern topology.

8or relation attribute.

9called relation values.

6.2 Artefact models 155