A Formal Specifiction for Conceptualizationsin Computer Aided

Visual Design Processes

Ewa Grabska

Faculty of Physics, Astronomy and Applied Computer Science, Jagiellonian University, 11 Łojasiewicza, Krakow, Poland

Keywords: Visual Design, Design Knowledge, Conceptualization, Ontological Commitment, Logical Language,

Ontology.

Abstract: The paper is the next attempt to formalize an ontology-based knowledge framework helpful for CAD pro-

cess. Our previous research has showed the need for a more expressive specification in order to capture the

intended models corresponding to a certain design conceptualization. This paper presents a more general

approach to ontological framework which will be illustrated with examples of designing floor-layouts. This

formal framework can be useful for many different applications, for instance to biological systems, cultural

heritage and economical aspects.

1 INTRODUCTION

This paper is an attempt to analyse conceptual de-

sign phase in Computer Aided Design (CAD) sys-

tem in the framework of computational ontology

Ontologies in computer science started to be-

come a relevant notion in the 1990’s. At that time

ontologies were related to work in knowledge acqui-

sition. From computer science point of view the

basic definition of an ontology is as follows: “An

ontology is an explicit specification of a conceptual-

ization”. In other words the ontology analyses rele-

vant entities and organizes them into concepts and

relations (Guarino et al., 2009).

Conceptualization is one of the most challenging

aspects of designing because it forces designers to

considers many disparate factors. There exists the

need to keep in mind objects, concepts, and other

entities that are assumed to exist in the considered

design domain of discourse, and the relationships

that hold among them. It is perhaps for this reason

drawing is such a popular tool of initial stages of

designer’s conceptualization. Drawings, being ex-

ternalization of designer’s conceptualization, are

seen as thinking aids (Suwa and Tversky, 1997). It

seems helpful if there exists a commitment between

the drawing and the level of certainty in the design-

er’s mind at the time. A CAD system communicates

with the designer via drawings displayed on the

monitor screen.

Nowadays, construction projects are commonly

represented in the Building Information Modelling

(BIM) to store all project 3D elements in a central

data-base and generate 2D drawings and 3D render-

ings (Eastman et al., 2008). However, during the

conceptual design phase most of these tools do not

use data structures to reflect the design knowledge

extracted from design drawings on the monitor

screen, although this knowledge provides a starting

point for design refinement (Lawson, 2001). The

importance of visualization in design was discussed

in (Visser, 2006), while visual conventions allowing

for man-machine interaction were described in

(Booch, et al. 2005). It turns out that referring to

ontological terminology the communication between

the designer and the computer can be improved

(Yurchyshyna and Zarli, 2009).

Besides CAD there exist many different applica-

tions based on ontologies. They are related for in-

stance to biological systems, cultural heritage and

economical aspects. This paper presents common

rational grounds for existence of different applica-

tions in the similar ontological framework. The

formal framework based on ontological terminology

will be illustrated with examples of designing floor-

layouts.

2 CONCEPTUALIZATIONS AND

OBSERVABLE WORLD STATES

A conceptualization is an abstract and simplified

Grabska, E..

A Formal Speciﬁction for Conceptualizationsin Computer Aided Visual Design Processes.

In Proceedings of the 7th International Joint Conference on Knowledge Discovery, Knowledge Engineering and Knowledge Management (IC3K 2015) - Volume 2: KEOD, pages 395-401

ISBN: 978-989-758-158-8

395

view of the world created in a domain of discourse

that is a subset of some cognitive domain. In this

paper design aided by computer is our cognitive

domain, while designing floor-layout makes the

domain of discourse. Formally, we start with the

definition of conceptualization stated by Genesereth

and Nilsson (Genesereth and Nilsson, 1987).

Definition 2.1

A conceptualization is a tuple (D, R), where



D is a set called the universe of discourse, and



R is a set of relations on D.

Each element of R is an extensional relation, reflect-

ing a specific world state involving the elements of

D, such as one depicted in Fig. 1. In design aided by

computer we need to explicitly specify conceptual-

ization, while conceptualizations are typically im-

plicit in the mind of designer. In CAD system con-

ceptual process in designer’s mind is supported by a

cognitive tool, such as computer screen. There exists

many specialized editors for drawing floor layouts

on the monitor screen, where for instance a floor

layout is composed of polygons representing func-

tional areas or rooms (Grabska, 2011).

Example 2.1

Let assume that the designer visualizes an initial

drawing shown in Figure 1. We can extract the fol-

lowing knowledge that specifies the universe of

discourse and relations:

D = {room, wall, door} .

R = {bedroom, living-room, hall, adjacent- to,

accessible- to}.

A generalization/specialization hierarchy, i.e., a

taxonomy forms the backbone of an ontology. Then

room, bedroom, living room, hall might be relevant

concepts, where the first is a super-concepts of the

latter three. On the other side, we have a content

hierarchy a room consists of walls, a door is con-

tained in a wall. Relations of R can be defined be-

tween rooms:

adjacent-to = { (living room, bedroom), …}, acces-

sible-to = {…,(living room, bedroom)}.

The designer on the base of the conceptualization

can generate an observable world state. However,

this does not meet designer’s needs because it de-

pends too much on a specific state of the world. In

each step of design process the designer can change

number of elements of the domain of discourse D

and/or relations of R on D because both the require-

ments and the design become more refined as the

project proceeds.

Figure 1: The drawing reflecting a specific world state for

the conceptualization (D,R).

Example 2.2

Let assume that the designer on the base of the con-

ceptualization in Fig. 1 decides to divide the bed-

room into two rooms: bathroom and smaller bed-

room. Although only one room is added we obtain

the second conceptualization (see: Fig. 2),

Figure 2: Another world state for the concep-tualization

(D’,R’).

where D’ = D and R’ = R



{bathroom}



adja-

cent-to’



accessible-to’, where adjacent-to’ =

adjacent –to



{bathroom, (bedroom, bathroom),

(bathroom, hall), (bathroom, living room)}, and

accessible-to’ = accessible-to  {bedroom, bath-

room}.

A conceptualization should not change when the

world changes. We need to focus on the meaning of

the underlying concepts, which are independent of a

single world state: the meaning of accessible to is

related to two rooms in the floor-layout. Understand-

KEOD 2015 - 7th International Conference on Knowledge Engineering and Ontology Development

396

ing such meaning implies having a rule to decide,

observing different patterns, whether or not there

exists a relation accessibility between two rooms.

Between rooms in an accessibility relation there

exists a door opening which can be with or without a

door. They are hundreds of different types of door.

Moreover, instead a door a curtain can be hung in

the door opening. In most cases this is impossible to

list all elements of the relation, which are independ-

ent of a single world state.

The meaning of “accessibility” can be defined as

a function that, for each global context involving all

our universe, gives us the list of pairs of accessible

rooms. The revers of this function grounds the

meaning of a concept in a specific world state. Link-

ing this with conceptualization we define a function

from a set of possible world states into extensional

relations. To formalize this function, we first have to

clarify what a world and a world state is. In the

stage of conceptual process aided by computer when

the conceptualisation is formed in the mind of de-

signer he/she try to externalize own concepts using

drawings. In other words initial solutions in the form

drawings being observable states of affairs constitute

states of designer’s world. In this paper to represent

the world state, the concept of visual site will be

used (Shimojima, 1996). A visual site is a drawing

along with a surface on which it is drawn. In general

different surfaces can be used for drawing, e.g., a

sheet of paper or a monitor screen. Two different

drawings on the same surface determine two differ-

ent visual sites. In visual design aided by computer,

monitor screen is a basic visual site on which be-

sides drawing some information from computer

system can be generated (Grabska, 2014).

Each designer generates his/her own world. Ob-

servable states of the world should be defined with

the reference to the notion of a design space S, i.e., a

piece of reality we want to model. In our case the

design space will be all configurations of rooms with

its components such as walls, doors, etc., which can

be treated as admissible floor-layouts.

Definition 2.2

A world is an ordered set of world states, corre-

sponding to the evolution of the design space in

time.

Definition 2.3

Let S be a design space, D an arbitrary set of distin-

guished elements of S, and W the set of possible

states for S. The tuple (D, W) is called a domain

space for S.

A conceptual relation



of arity n



1 defined for a

domain space (D, W) is a function



:W →

)

from the set W into the family of all subsets of the set

of n-ary relations on D.

A conceptual relation is a function from a set of

possible world states into extensional relations. This

function allows one to extend the notion of concep-

tualization for all observable world states (Guarino

et al., 2009).

Definition 2.4

A conceptualization for W is a triple

C =

(D, W, R ),

where



D is a domain of discourse,



W is a set of world states, and



= {



}



is a family of all conceptual rela-

tions 

on the domain space (D, W)

3 MODELS IN ONTOLOGY

In practical applications we use a language to de-

scribe the elements of a conceptualization. For in-

stance, accessible to is a predicate symbol which

expresses the fact that bathroom is accessible to

bedroom. The symbol represents a certain conceptu-

al relation. Our language denoted by L should com-

mit to a conceptualization. Let assume that L is a

first-order logical language with its vocabulary as

the set {bathroom, bedroom, living room, hall, ac-

cessible-to, adjacent-to}. We shall not consider

function symbols here.

The basic problem is to interpret each symbol

according to the conceptualization we commit to. It

turns out that the vocabulary can be interpreted in

many different ways even if the cognitive domain

and its subset – the domain of discourse were fixed.

A conceptualization is specified in two ways: exten-

sionally and intensionally. An extensional specifica-

tion of the conceptualization requires listing the

extensions of every conceptual relation for all possi-

ble worlds. However, it is impossible if the universe

of discourse D or the set W of possible states of

world are infinite. A conceptualization is often spec-

ified by means of examples related to selected world

states. A more effective way to specify a conceptual-

izations is to fix a language and to constrain its in-

terpretation in an intensional way, by means of axi-

oms called meaning postulates. For our example, we

can write simple axioms stating that accessible-to is

symmetric, irreflexive, and transitive, while adja-

cent-to is symmetric, irreflexive and intransitive.

A Formal Speciﬁction for Conceptualizationsin Computer Aided Visual Design Processes

397

According to (Guarino et al., 2009) the notion of

ontology can be tentatively defined in the following

way: An ontology is a set of axioms, i.e., a logical

theory designed in order to capture the intended

models corresponding to a certain conceptualization

and to exclude the unintended ones.

In other words we have to deal with an approxi-

mate specification of a conceptualization: the better

intended models will be captured and non-intended

models will be excluded.

Now when we have an intuitive grasp of ontolog-

ical commitment and ontology, let us embed them in

a more formal framework. We start with the defini-

tion of model.

Definition 3.1

Let L be a first order logical language with vocabu-

lary V and (D,R) be a conceptualization. A model

for L is a triple M = ( D,R, I ), where I: V





is an interpretation function that maps each symbol

of V to either an element of D or a relation belong-

ing to R.

Let us consider the model shown in Fig. 1. We can

assign suitable rooms depicted in the Fig. 1 to sym-

bols bathroom, bedroom, living room, and hall. The

two symbol relations accessible-to and adjacent-to

are defined by listing all suitable pairs of rooms.

Two rooms are adjacent if they have at least one

common wall, while room1 is accessible to room2 if

there exists a common wall with door. Wall and

door are represented by a segment and door icon,

respectively.

Definition 3.2

Let L be a first-order logical language with vocabu-

lary V and C = (D,W,R) be a conceptualization for

W. An ontological commitment for L is a tuple K =

(C, I ) where





that maps each vocabulary symbol of

V to either D or a conceptual relation belonging to

the set R

The notion of ontological commitment is an exten-

sion of the standard notion of model to intensional

meaning. Now we can define a notion of intended

models corresponding to a certain conceptualization.

As it has been considered capturing these models is

the biggest challenge in ontology.

Definition 3.3

Let C = (D,W,R) be a conceptualization for W, L be

a first-order logical language with vocabulary V

and ontological commitment K = (C, I).

A model M = (D, R, I) is called an intended model

of L according to K iff

1. For all constant symbols c



V we have I(c)= I

(c),

2. There exists a world w



W such that, for each

predicate symbol v



V there exists an inten-

sional relation





such that I(v) =



and I(v)



(w).

For intended model the mapping of constant sym-

bols to elements of universe of discourse is the same

for I and I

and there must exists a world such that

every predicate symbol is mapped into an intension-

al relation whose value, for that world, coincides

with the extensional interpretation of this symbol.

The set I

(L) of all models of L that are compatible

with K is called the set of intended models of L ac-

cording to K.

Finally, the next tentative definitions of ontology

is proposed (Guarino et al., 2009):

Definition 3.4

Let C be a conceptualization for W, and L a logical

language with vocabulary V and ontological com-

mitment K. An ontology O

for C with vocabulary V

and ontological commitment K is a logical theory

consisting of a set of formulas of L, designed so that

the set of its models approximate as well as possible

the set of intended of L according to K.

Example 3.1

We build an ontology O for floor-layout design,

which consists of a set of logical formulae. Floor-

layout domain is specified with increasing precision.

 Taxonomic Information:

= { living room(x)  room(x), bedroom(x) 

room(x), …}

 Domains and Ranges of Relations:

= O

 {accessible-to(x,y) 

room(x)room(y),…}

 Symmetry:

= O

 {accessible-to(x,y)  accessible-

to(y,x), …}

4 ONTOLOGIES IN CAD SYSTEMS

When considering ontologies in computer science

the conceptualization should be expressed in a for-

mal machine readable format. In design aided by

knowledge based computer system we need to make

knowledge representation extracted from conceptu-

KEOD 2015 - 7th International Conference on Knowledge Engineering and Ontology Development

398

Figure 3: A B-graph representing the world state in Fig. 1.

alization: accessible electronically; structured and

understandable by computers, interoperable, and

transparent. Graphs can be combined with the most

popular logic-based knowledge representation tech-

nique, where knowledge is represented explicitly by

symbolic terms and reasoning is the manipulation of

these terms. Graph data structures are used to reflect

the design knowledge extracted from design draw-

ings on the monitor screen. This knowledge provides

a starting point for design refinement.

There exist many types of graphs useful for spec-

ification and modelling of design knowledge during

conceptualization in CAD processes. In this paper

we use a specific graphs called B-graphs whose

nodes represent objects of the domain of discourse.

Their nodes contain bonds which are also nodes

representing arguments of relations. Relations are

defined between bonds (Grabska 1994). Two kinds

of bonds are distinguished: engaged and free bonds

which correspond to arguments of existing and po-

tential relations, respectively. B-graphs are content-

hierarchical. Hierarchy also allows for sub-bonds

(for example, a room consists of walls and one of

them has a door – this door is contained in the room,

but also is subordinate to the wall).

The Fig. 3 presents the B-graph corresponding to

the drawing considered in Example 2.1. Three nodes

represent three rooms. The number of walls of room

determines the number of bonds representing them.

If the wall has a door then the bond representing the

door is contained in the wall bond. An edge between

the door bonds represents the accessibility relation,

while between the wall bonds – adjacency one. The

walls of each room shown in Fig. 1 can be ordered

clock-wise starting from the top left –most one. The

distinct of bonds is essential in definitions of opera-

tions on graphs that reflect modifications of design

phases (compare: Fig. 3 with Fig. 4).

The B-graphs shown in Fig. 3 and Fig. 4 can be

treated as internal representations for the drawings

created on the monitor by the designer and shown in

Fig. 1 and Fig. 2. These drawings reflect the results

of some phases of designer’s conceptualization

while B-graphs corresponding to them determine

A Formal Speciﬁction for Conceptualizationsin Computer Aided Visual Design Processes

399

Figure 4: The B-graph for the drawing in Fig. 2.

Figure 5: The relationships between designer’s conceptualization, the formal conceptualization for worlds, the logical lan-

guage used to describe ontology, the IT specialist, and ontological intended models.

KEOD 2015 - 7th International Conference on Knowledge Engineering and Ontology Development

400

elements of the graph based data structure. B-graphs

are specified by the IT specialist.

The presented approach allows to define formal-

ly correspondence between drawings and B-graphs

in the framework of ontology. The B-graph in Fig.3

reflects a world state shown in Fig. 1. The visual site

with drawing presented in Fig.1 and the B-graph in

Fig. 3 belong to the set of intended models of L

according to the same ontological commitment K.

The summary of our consideration is shown in

Fig 5.

5 CONCLUSIONS

Within architectural design, key aspects of the antic-

ipated function of buildings are determined by their

structural form, i.e., their shape, layout, or connec-

tivity. The formal modelling of structural form for

CAD systems remains elusive. The structural form

emerges during the conceptual design phase.

This paper has presented the practical concerns

surrounding the formal interpretations of the struc-

tural form with respect to its applicability in CAD

systems in the ontological framework. The basic

notions of ontology: conceptualizations, models,

ontological commitments, and intended models have

been defined in a formal way.

One of the challenges of CAD systems is to au-

tomatically transform design drawings on the moni-

tor screen into appropriate graph based date struc-

tures. The framework of ontology proposed in this

paper allows to define the correspondence between

the drawings and their graphs in a formal way. This

formal approach to the definition of ontology facili-

tates the development of reasoning modules of CAD

system which are based on graph data structure.

Thanks to this, dialogue between the designer and

computer can be improved.

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