We present a preliminary high-level formal theory, grounded on knowledge representation techniques and foundational ontologies, for the uniform and integrated representation of the di erent kinds of (qualitative and quantitative) knowledge involved in the designing process. We discuss the conceptual nature of engineering design by individuating and analyzing the involved notions. These notions are then formally characterized by extending the DOLCE foundational ontology. Our ultimate purpose is twofold: (i) to contribute to foundational issues of design; and (ii) to support the development of advanced modelling systems for (qualitative and quantitative) representation of design knowledge.
After the requirement list has been completed, experts start specifying the
design solution by means of various technical speci cations. Examples include:
{ Functional model: the main functionality of the product under design is
represented and decomposed into sub-functionalities (e.g. [
These are however only a few cases; at the current state of the art there is no
complete, nor standardised list of models used in engineering design [
The importance of technical speci cations is due to the fact that they
determine the nal properties that particular objects have to satisfy to be considered
as products of a certain type. If a particular object satis es the properties
speci ed by its corresponding model, it is said to conform to the model [
This brief introduction suggests that the main core of designing is the
development of (design) concepts, rather than their codi ed description, as suggested
by Figure 1. It also shows that various quantitative but also qualitative
knowledge aspects have to be considered. For instance, the functional aspects|a sort
of teleological information about the product|have often a qualitative nature.
Furthermore, at the early phases of the development of a product, the
requirements and the characteristics of the product, including the geometrical ones,
are not precise. The designer still has a quite general idea of the de nitive form
of the product and vague tolerances are accepted. The need to enrich
quantitative product models with qualitative speci cations about the design intents
has been advocated for more than 20 years now [
The ultimate purpose of this work is twofold: (i) to contribute to foundational issues of engineering design; and (ii) to support the development of advanced modelling systems for design knowledge. However, in order to achieve these goals, it is needed beforehand a clear understanding of what a product model is and how it relates to its corresponding physical products. We thus present in this paper an high level approach, based on foundational ontologies and knowledge representation techniques, concerned with the individuation and analysis of the general notions needed for an integrated model of design. Our proposal o ers just a conceptual base that needs to be specialized and instantiated to be useful for the practical purposes of knowledge representation in design.
The paper is structured as follows: in Section 2 we introduce the proposed formal model and we discuss some shortcomings and problematic issues related to design knowledge representation. In section 3 we brie y compare our approach with similar research initiatives. 2
We sketch a general and high-level theory that is capable of representing in a uniform and integrated way both the qualitative and the quantitative aspects of design. Manufacturing aspects are excluded from this analysis, even though our model is compatible with a future extension that addresses these aspects. Firstorder logic (FOL) is employed as representational language. This has clearly some impacts on the technics, in particular rei cation technics, used to overcome some limitations in the expressive power. 2.1
We want to distinguish the design of a product from both its speci cations, such as a Computer-Aided Design (CAD) le or a printed drawing on a piece of paper, and from the set of objects that are possibly produced. For this purpose, it is worth presenting our point by means of the semiotic triangle developed in semantics. For instance, the word `red' in its predicative sense is related to the concept of being red (the intension) and to the class to things that are red (the extension). In the case of a design, we distinguish three aspects of it (cf. Figure 2): its speci cations as the physical supports of the design, the product type as its intension, and the class of physical products, or simply products, as the extension of the product type. For example, John's car (particular physical product) satis es the technical speci cation of Ferrari Testa Rossa 512 TR (product type).
Firstly, the product type is distinguished from the speci cation, as the same product type may be represented by di erent supports, e.g., a CAD model and a pencil-made sketch. The speci cation is useful to represent and communicate aspects of the product type, but the design cannot be reduced to it.
Secondly, the product type is not identi able with the class of products that can be realized by means of the design. This view copes with the fact that the product type specification
product design may be about not yet realized products. If the design reduces to a class of products, then, before their realizations, one could only talk about the design in terms of future or possible objects. Although this view may be formalized by means of modal logic, we believe that it does not capture the nature of design. In principle, a design may exist even if the objects that are its realizations are never produced. This does not mean that a design may be about impossible objects: the point is that a design still exists, we can understand it, and practitioners can interact about it, even in the case that no concrete product is ever going to be realized. By focusing on the product type, we indeed construe the design as a type rather than a set of tokens (physical objects). Accordingly, we shall treat the product type as a concept in the sense made precise by the axioms we shall introduce in the next sections. From this perspective, our interpretation of the designing process departs from the one depicted in Figure 1. The outcome of the process there is understood as the \description of the technical product (TP(s))" plus \full information for possible manufacture" of a class of objects. By contrast, even though we recognize the importance of the speci cation (cf. Figure 2), we stress here the conceptual nature of the design. In the following sections, we do not discuss speci cation languages for engineering purposes, nor we will approach the analysis of manufacturing. We will rather formalize the conceptual nature of a design.
For this purpose, we rely on the dolce ontology [
To address these crucial aspects in FOL, we reify concepts into the domain of quanti cation, i.e., we introduce a new kind of entities: cn(x) stands for \x is a concept " (or more generally a property). In this way, we can predicate on concepts, but we loose the possibility of representing classi cation via predication. It is then necessary to introduce a new primitive to relate the concepts to the entities they classify, a sort of (possibly intensional) `instance-of' relation, that here we call classi cation: CF(x; y; t) stands for \the concept x classi es the entity y as it is at time t". From a design perspective CF(x; y; t) can be interpreted in a more restricted way as \the product y, as it is at time t, conforms to (the speci cation of) the product type x", or, more lengthily, \at time t, the physical product y has all the properties required to satisfy (the speci cation of) the product type x". The classi cation relation is temporally quali ed: the entity y may change through time, thus the classi cation under a certain concept is, in general, contingent. For instance, a product y that at time t conforms with the (speci cations of the) type x, could not conform anymore with x at time t0 because of the loss of some properties necessary to be classi ed under x. That means that t does not individuate the time at which the classi cation is done but the time at which y is considered (measured, perceived, etc.). Consequently, the classi cation at time t does not necessarily implies the existence at t of the concept, see (a1) where EX(y; t) stands for \the entity y exists at time t". However, concepts are in time (a2), they can be created or destroyed (for instance, when no speci cation, including mental ones, exists any longer). Concepts created at a given time t can then classify, according to past information, entities that do not exist anymore at t.2
A similar modelling approach, even though (change through) time is not considered, is employed in the Industry Foundation Classes3 (IFC)|a data modelling standard supported by most of the major CAD vendors|in which classication is called IfcRelDefinesByType. This relationship is used to represent the fact that the instances of a IfcTypeProduct (a product type) satisfy the properties de ned by a IfcProduct (a physical product).
Standard extensional relations between concepts can be introduced relying on CF, e.g., the extensional subsumption relation (d1). However, concepts have an intensional nature, they are not reducible to their extensions, di erent concepts may classify the same entities: the extensional subsumption is not antisymmetric, i.e., x y ^ y x ! x = y does not hold in our theory. a1 CF(x; y; t) ! cn(x) ^ EX(y; t) a2 cn(x) ! 9t(EX(x; t)) d1 x y , 8zt(CF(x; z; t) ! CF(y; z; t)) 2.2
For the sake of example, assume that in our domain all the round entities are
also red and vice versa. In our framework, this does not imply the identity of
the concepts (properties) being red and being round. The distinction between the
extensional and the intensional level of design is also used in design models and
2 For our goal, the time at which the classi cation is done is not relevant. However it
is easy to add a second temporal argument to CF to account for that.
3 http://www.buildingsmart-tech.org/ifc/IFC2x4/rc4/html/
data modelling standards. In the IFC, for example, IfcTypeProduct is
understood as the information common to all instances of IfcProduct. Borgo and
colleagues [
After Carnap, the intensionality of properties is traditionally approached in logic from a modal perspective: the co-extensionality of being red and being round is contingent, it holds in the actual world but there are other possible worlds where being red and being round have di erent extensions. In our theory, the reference to possible worlds is not necessary although, indeed, one can still have an informal modal understanding of intensionality. Here, the intension is captured in a di erent way that is especially e ective for products types.
The idea is that concepts cannot be characterized \in isolation", they always
refer to other concepts. For instance, product types are usually characterized in
terms of simpler concepts that are typically shared by the designers involved in
a given phase, the common background of designers. This idea is quite similar
to the one followed in [
Objects can be compared and characterized in terms of a variety of aspects such as weight, shape, size, color, function, etc. Such aspects are represented via (quality) spaces composed by basic properties (called regions in dolcecore).4 For instance, the color space contains several basic properties, e.g., being red, being orange, being scarlet, etc. Basic properties in the same space can be organized in taxonomies or in more sophisticated ways: from ordering (weight, size) to complex topological or geometrical relations (color splinter).
We assume a nite number N of spaces spi that partition the basic properties
bcn (a3){(a5).5 The idea is that basic properties|that still have an intensional
nature|are used, but not created, during the design process, i.e., they
represent the conceptual knowledge in the background, the conceptual knowledge
that allows the product type to be characterized throughout the design phases.6
Consequently, the intensional subsumption relation v, assumed to be a classical
extensional mereology closed under sum [
As we saw, the product types are complex concepts ccn (a8) characterized in
terms of basic properties. We need then to link complex concepts to their basic
properties: CH(x; y) stands for \the complex concept x is characterized by the
basic property y" (a9). For example, Ferrari Testarossa 512 TR (product type)
is characterised by the basic properties being red, being 1500kg heavy, among
others. Complex concepts are characterized at least by two, but usually several,
basic properties, i.e., they have a multi-dimensional nature (a10).9 This is similar
to composition of spaces in more complex ones, at least if the geometry of the
complex space can be de ned in terms of the geometries of its components.
a3 bcn(x) ! cn(x)
a4 bcn(x) $ Wi2f1;:::;Ng spi(x)
a5 Vi6=j2f1;:::;Ng(spi(x) ! :spj (x))
a6 x v y ! Vi2f1;:::;Ng(spi(x) $ spi(y))
a7 x v y ! x y
a8 ccn(x) ! cn(x) ^ :bcn(x)
a9 CH(x; y) ! ccn(x) ^ bcn(y)
a10 ccn(x) ! 9yz(CH(x; y) ^ CH(x; z) ^ Wi2f1;:::;Ng(spi(y) ^ :spi(z)))
a11 ccn(x) ! (CF(x; y; t) $ 8z(CH(x; z) ! CF(z; y; t)))
7 This option has already been considered in [
Firstly, we need to guarantee that the classi cation under a complex concept x reduces to the classi cation under all the basic properties that characterize x (a11), i.e., the extension of x is the intersection of the extensions of all the basic properties that characterize x. This seems to authorize to interpret CH as a sort of intensional subsumption. However, the antisymmetry of v would imply the identity of complex concepts with the same characterizing basic properties. This is acceptable only if we assume that the characterization of complex concepts is always complete. For the moment, we prefer a weaker approach that allows also for partial characterizations of concepts, i.e., two di erent concepts can have the same partial characterization. Note that these partial characterizations are particularly interesting for hiding very speci c or practical properties.
Secondly, while it seems quite reasonable to have a static view on the background knowledge, the product type under design could be intended as an evolving concept. This can be modeled by adding a temporal parameter to both CH and CF, i.e., what characterizes a concept can vary through time, thus the classication depends also on the time at which the concept is considered: CF(x; t; y; t0) stands for \the complex concept x, as it is at t, classi es the object y, as it is at t0" (a12). The double temporal quali cation allows to reclassify an object as it is at t0 across the evolution through time of a given concept.10 (a11) needs then to be substituted by (a13) where we assume the basic properties to be static. Consequently, the extensional subsumption relations between complex concepts may be temporally quali ed as in (d2). The identity of concepts can be intended in terms of the `trajectory' across time of its characterizing properties, i.e., (CH(x; z; t) $ CH(x0; z; t)) ! x = x0, but weaker options that consider the designers and/or the design process can be considered. For this reason, we do not commit to this identity criterion. a12 CF(x; t; y; t0) ! ccn(x) ^ EX(x; t) ^ EX(y; t0) a13 ccn(x) ! (CF(x; t; y; t0) $ 8z(CH(x; z; t) ! CF(z; y; t0))) d2 x t1 t2 y , ccn(x) ^ ccn(y) ^ 8zt(CF(x; t1; z; t) ! CF(y; t2; z; t))
At this point we can also address the notion of requirement that is usually
de ned as the \[p]roperty that is required to be ful lled during the origination
phase of the object to satisfy the [customer] requirements" [1, p.317]. Customer
requirements can then be seen as the (maybe rough) idea of product that the
customers, as opposed to designers, have. Note that also the requirements, i.e.,
the customer concept, can evolve in time during the design process, maybe
because of market change, or maybe because of the interaction with engineers
that discovered some unrealizable constraints. We have then two complex
concepts characterized in terms of intensions (their characterizing basic properties)
and extensions (the objects that they classify). This allows for both an
inten10 Firstly, note that t is not the time at which the classi cation is done, it just `freezes'
the concept (while t0 freezes the object). Secondly, to avoid evolving concepts, one
could follow [
As an illustrative example, let us consider a customer asking for a product to prepare Italian co ee. In addition to the function, her requirements regard the height (between 16cm and 20cm) and the material (aluminium) of the product. Assuming to dispose of the function, height, and material spaces, the required product type can be represented by a complex concept rpt that, at the starting time t0 is characterized by three basic properties: CH(rpt; prep it coffee; t0), CH(rpt; 16-20cm; t0), CH(rpt; alu; t0). Assume that 16-20cm is a non-atomic basic property while alu an atomic one, even though, because properties apply to the whole product, this does not necessarily imply the product to be exclusively made of aluminium. More controversial is the case of prep it coffee because it is unclear, for instance, whether the kind of energy used to prepare the co ee is part of the function or pertains a separate space. For our illustrative purposes we assume the rst hypothesis and that there are at least two (intensional) subfunctions (v) of prep it coffee, namely prep it coffee methane and prep it coffee elect. The designers start to consider the requirements (speci ed by the customer in some way) by assuming a designed product type dpt (a complex concept) such that CH(dpt; prep it coffee elect; t0), CH(dpt; 1620cm; t0), CH(dpt; steel; t0). This choice is partially based on the expertise of the company in developing products for induction hobs. Note that the designers know that (at t0) dpt does not match rpt because steel is not a subconcept of alu. Therefore they interact with the customer to explain the strategical importance of having a product to prepare italian co ee to work with induction hobs, and this constraints the material to steel. The customer agrees on that but change the size-constraints, in this case she wants a very small, less than 12cm high, product. The designers agree on that and at time t1 the requirements are matched: CH(rpt; prep it coffee; t1), CH(rpt; 12cm; t1), CH(rpt; steel; t1) and CH(dpt; prep it coffee elect; t1), CH(rpt; 10-11cm; t1), CH(rpt; steel; t1).11 11 Here we are totally liberal with respect to how concepts can change through time.
However, constraints on the way concepts \move" inside the spaces can be added. 2.3
Dependencies between spaces One interesting aspect of spaces is that it is
quite easy to add dependence links between basic properties, i.e., to shape the
composed space. This is the case of the color splinter: not all the combinations of
hue, saturation, and brightness correspond to a color, a given hue constraints the
possible values of brightness and saturation. In this case the consistency of the
di erent characteristics of a model can be guaranteed from the beginning. The
proposed framework can be extended to take into account these dependencies.
From the designing perspective, this is interesting because it makes possible to
represent the dependencies between di erent designing phases and design
specications by means of the dependencies between the spaces that are used at these
phases. For instance, functional modeling is particularly relevant during the rst
stages of the design process, where more emphasis is given on what the product
is designed to do, rather than on how this purpose will be achieved. Vice versa,
at the design embodiment stage, designers focus more on the physical properties
of the product, i.e., on how the functionality is realized. Dependencies between
functional and physical properties can help the designer in (i) understanding
how a required function constrains the product's physical layout|a top-down
perspective: from the abstract functional view to the concrete physical one; (ii)
verifying whether the chosen physical layout can, at least in principle, ful ll
the required functionality (a bottom-up perspective); (iii) making explicit
possible accidental functions, as opposed to proper functions, that could result from
(improper) usages of the product. For instance, a screwdriver has the proper
function of, it has been designed for, driving screws, while it has the
accidental function of opening cans. According to de Vries [
However, as already said some properties like colors or shapes can be designed
(actually, structural information seems fundamental to design new shapes). In these
cases, it is not clear to us if the designed properties are reducible to original ways
of putting together more basic properties or if an extension of a space is needed. It
would be interesting to analyze creativity in terms of spaces.
[
Without structure-spaces, to minimally represent structural constraints, we extend our framework with a temporally quali ed classical extensional mereology de ned on objects: P(x; y; t) stands for \the object x is part of the object y at time t". Consider the previous example of the Italian co ee and assume that at time t2 the designers subdivide the main functionality prepare Italian co ee in sub-functionalities to boil water, to store powdered co ee, to lter co ee by boiled water, to store brewed co ee and to serve co ee. Amongst the various solutions for the embodiment of these functionalities, they decide to develop a moka pot product type (moka) with, among the others, three components (that are themselves product types): boiler pot (pot), co ee container (container), and lter (filter) that are characterized (in terms of CH) by the rst three functions discussed above (plus additional heigh and material properties). In the proposed theory, this structural constraint is represented by (f1), but because a structure space does not exist, it is not possible to understand if this constraint matches the original one about the function of the whole object. f 1 CF(moka; t2; x; t) ! 9yzw(CF(pot; t2; y; t) ^ CF(container; t2; z; t) ^
CF(filter; t2; w; t) ^ P(y; x; t) ^ P(z; x; t) ^ P(w; x; t)) 3
We presented a high-level modelling approach based on conceptual spaces and ontology engineering methods for the formal representation and integration of (qualitative and quantitative) aspects of design. Foundational issues related to engineering design and the integration of di erent aspects of design knowledge have been discussed in various research areas, from knowledge representation approaches, to theories of design and philosophy of technology.
The conceptual view proposed in this paper is mostly based on the
engineering literature. According to Pahl and colleagues, the goal of designing is \the
mental creation of a new product" [3, p.1]. Along the same lines, Lindemann [
In the philosophical analysis of engineering design proposed by Vermaas and colleagues [23], designing tasks are mainly aimed at providing a description for a technical product: \[...] the core of technical designing lies in nding a description DS of an artefact with a physical structure S that is able to e ectively and e ciently ful l a certain function F " [23, p.28] (emphasis ours). In this perspective, DS is a document speci ed in a modelling language suited for engineering purposes. The authors thus focus on speci cation as the core dimension of design, while we have rather focused on its conceptual nature. The two approaches, however, are not contrasting but rather orthogonal, since concepts have to be speci ed for representational and communication purposes.
Knowledge representation has been primarily focused on the physical makeup of products, while little (if any) attention has been given to design models. For instance, the Core Product Model (CPM) [24] associates the class artifact to (requirement) specification, meaning that the former has to satisfy the latter's properties. However, neither the di erence between requirements properties and design speci cations properties is discussed, nor it is clear whether specification refers to an encoded description, or its content.
In ontology engineering, the Information Artifact Ontology (IAO) [25] has been explicitly developed to represent information entities, that is, the content of encoded descriptions. The IAO thus shares in some degree the same purpose of the work hereby presented. There are however some relevant distinctions to be noted: (i) the IAO directly links a representation to the physical object that it is about. In our approach, concepts mediate this relationship (cf. Figure 2), since they cannot be reduced to their extensions, as argued in Section 2.1. (ii) information content entity (concept in our terminology) is only weakly characterised as an entity that existentially depends on some representation and is about something else. In our theory, there is no such a dependence, since a product type is not necessarily speci ed in a physical medium. Additionally, we have provided a more detailed characterisation of concepts by taking into account the theories of quality spaces in dolce-core.
Acknowledgements: This work was partially funded by the VISCOSO project nanced by the Autonomous Province of Trento through the \Team 2011" funding programme, and the FourByThree project funded by the European Horizon 2020 program (grant agreement 637095). 19. P. Simons, Parts: a Study in Ontology. Oxford: Clarendon Press, 1987. 20. S. Rama Fiorini and M. Abel, \Part-whole relations as products of metric spaces," in Tools with Arti cial Intelligence (ICTAI), 2013 IEEE 25th International Conference on, pp. 55{62, 2013. 21. S. Rama Fiorini, P. Gardenfors, and M. Abel, \Representing part-whole relations in conceptual spaces," Cognitive Processing, vol. 15, no. 2, pp. 127{142, 2014. 22. P.Kroes, Technical Artefacts: Creations of Mind and Matter. A Philosophy of Engineering Design. Springer, 2012. 23. P. Vermaas, P.Kroes, I. de Poel, and M.Franseen, A Philosophy of Technology. From Technical Artefacts to Sociotechnical Systems. Morgan and Claypool Publishers, 2011. 24. S. Fenves., S. Foufou, C. Bock, and R.D. Sriram, \CPM: a core model for product data," Journal of Computing and Information Science in Engineering, vol. 8, 2008. 25. B. Smith and W. Ceusters, \Aboutness: Towards foundations for the information artifact ontology," in Proceedings of the Sixth International Conference on Biomedical Ontology (ICBO), 2015.