Two ontology-driven formalisations of functions and their comparison

Abstract

In this paper, we give formalisations of two engineering concepts of technical function and present in more general terms the project of supporting functional description translation by ontological analysis. The formalisations are given within the foundational dolce ontology and the concepts formalised are as follows: (1) the function as defined in the Functional Representation approach by Chandrasekaran and Josephson and (2) the function as defined in the Functional Basis approach by Stone and Wood. These two concepts represent two main ways of understanding functions in engineering: the first by means of the behaviour of artefacts, and the second by means of operations on flows as performed by artefacts. We analyse the similarities and differences between these concepts by means of the formalisations and show how the formalisations support the automated translation between functional descriptions based on these two concepts. In addition, we compare our strategy of formalising different engineering concepts of function within one foundational ontology with other strategies in the ontology-driven formalisation, such as defining a single formalised concept of function, either for replacing existing engineering concepts, or for use as a reference by which such existing concepts can be related. We compare these strategies and sketch the merits and shortcomings of our strategy.

Keywords:

• function
• formal ontology
• dolce
• functional description translation
• formalisation strategy

Acknowledgements

This work has been developed while taking part in the Marie Curie ‘EuJoint’ project (IRSES 247503). Research by Pieter Vermaas for this paper is supported by the Netherlands Organisation of Scientific Research (NWO).

Notes

Both formalisations are presented here at a level of detail sufficient to our current goals of comparison and translation. For the unabridged versions the reader is referred to Borgo et al. (2009a, 2009c, 2010a, 2010b).

See Masolo et al. (2002).

Some parts of this paper originate from Borgo et al. (2009b).

Although foundational ontologies are meant to be stable systems, they are sometimes subject to changes. Typically this happens when the ontology is extended to include new concepts and relations and/or to include improvements in the formalisation. More rarely a foundational ontology undergoes fairly relevant structural changes, e.g. to simplify the use (and understanding) of the system or to embrace a more expressive structure. In these latter cases one might need to revise application systems that rely on the ontology. This however does not affect the overall ontological analysis inspired by the ontology, which is why ontological analyses, like the contribution we make in this paper, remain valid over time. We provide references to the ontologies’ webpages so the reader will find the most current versions. Interestingly, a similar observation applies to the Functional Representation and Functional Basis approaches: these approaches can result in a variety of theories (differing in, say, the taxonomy of function, the taxonomy of flows, the relationships among flows, etc.) but since we mainly focus on their basic perspectives, our work remains of value even when switching from one version of these theories to another. Admittedly, some adaptation in our formal system might be needed, yet the overall system will remain in place.

In Carrara et al. (2011) we have argued against the adequacy of Arp and Smith's definition of function to capture some basic features of engineering functions. In fact, it excludes certain entities from the domain of functions although they are usually included in engineering models, and it includes certain objects as functions although they are rarely, if ever, included in engineering models. We return to this criticism in Section 3.1 after having introduced the distinction between device-centric and environment-centric functions in the Functional Representation system.

The term ‘middle-out method’ is used in the sense described in Uschold and Gruninger (1996).

For instance, three meanings are selected in Vermaas (2009, 2010) as archetypical to engineering. Two of these archetypical meanings correspond to the meanings considered in this paper.

BHP stands for Brake Horse Power and it is described as the amount of real horsepower going to the pump.

We discussed partial objectivity and partial subjectivity in Borgo et al. (2009a). This distinction is one that Chandrasekaran and Josephson made themselves. In particular, for the subjective aspect, they want to emphasise that a state variable of an artefact represents some feature or aspect of this artefact that might be relevant from a specific point of view.

Consider, again, Arp and Smith's definition of function. It seems that they would not acknowledge any of the environment-centric functions in the Functional Representation system, due to the fact that these functions exist not only because of the physical make-up of their bearers, but also, and mainly, because of the existence and make-up of other entities, which compose the environment concerned. So, their definition excludes certain entities from the domain of functions although they are usually included in engineering models.

The notion of material is construed here rather broadly as it comprises also such objects as screws, air, human beings, and their parts, e.g. human hands.

fb is the result of a reconciliation of two previous taxonomies: the NIST taxonomy (Szykman et al. 2000), and the older versions of fb developed in, for example (McAdams et al. 2000).

In dolce they are called physical qualities and are denoted by means of the PQ predicate.

The use of variables for our fr ontology is explained in Table A2 in the appendix.

Indeed, we begin by looking at capacitor instances (tokens) and do not address the behaviour of a type of capacitors.

In our formalisation of fb functions, we speak about devices rather than about artefacts. Stone and Wood themselves use the concepts of artefact, device and product side-by-side, without indicating whether there are differences between these concepts.

The use of variables for our fb ontology is explained in Table A4 in the appendix.

The classification of human force as physical quality might be challenged in dolce since human force, to be understood, requires to take time into consideration. In dolce this fact leads to think that human force should be seen as a quality of perdurants. However, in fb the term human force seems to be used quite broadly embracing several views. We do not discuss these aspects in detail and, for the sake of the argument, take the simplest view here. This observation applies to other entries in this table like relative rotation and torque.

Since we compare in this section two different formal theories, we abstain here from the previously used variables and adopt the ‘neutral’ set of variables: x, y, z, etc. for the sake of comparison.

Formally speaking, they are pairs of behaviours.

Strictly speaking, they are subtypes of QT because they are types of physical qualities themselves.