In this paper, we describe the conceptual elusiveness of the notion of function as used in engineering practice. We argue that it should be accepted as an ambiguous notion, and then review philosophical argumentations in which engineering functions occur in order to identify the consequences of this ambiguity. Function is a key notion in engineering, yet is used by engineers systematically in a variety of meanings. First, we demonstrate that this ambiguous use is rational for engineers by considering the role (...) of functions in design methods and by analysing the ambiguity in terms of Kuhn’s notion of methodological incommensurability. Second, we discuss ontological and mereological analyses of engineering functions and describe a proof that subfunctions cannot formally be taken as parts of the functions they decompose. Engineering functions figure sometimes in philosophical work and are then typically taken as having an unambiguous, well-defined meaning. Finally, we therefore revisit work in philosophy of technology on the dual nature of technical artefacts, in philosophy of science on functional and mechanistic explanations, and in philosophy of biology on biological functions, and explore the consequences of the fact that engineering function is an ambiguous notion. It is argued that one of these consequences may be that also the notion of biological function has an ambiguous meaning. (shrink)

This article introduces finitist set theory (FST) and shows how it can be applied in modeling finite nested structures. Mereology is a straightforward foundation for transitive chains of part-whole relations between individuals but is incapable of modeling antitransitive chains. Traditional set theories are capable of modeling transitive and antitransitive chains of relations, but due to their function as foundations of mathematics they come with features that make them unnecessarily difficult in modeling finite structures. FST has been designed to function as (...) a practical tool in modeling transitive and antitransitive chains of relations without suffering from difficulties of traditional set theories, and a major portion of the functionality of discrete mereology can be incorporated in FST. This makes FST a viable collection theory in ontological modeling. (shrink)

This paper addresses questions of universality related to ontological engineering, namely aims at substantiating (negative) answers to the following three basic questions: (i) Is there a ‘universal ontology’?, (ii) Is there a ‘universal formal ontology language’?, and (iii) Is there a universally applicable ‘mode of reasoning’ for formal ontologies? To support our answers in a principled way, we present a general framework for the design of formal ontologies resting on two main principles: firstly, we endorse Rudolf Carnap’s principle of logical (...) tolerance by giving central stage to the concept of logical heterogeneity, i.e. the use of a plurality of logical languages within one ontology design. Secondly, to structure and combine heterogeneous ontologies in a semantically well-founded way, we base our work on abstract model theory in the form of institutional semantics, as forcefully put forward by Joseph Goguen and Rod Burstall. In particular, we employ the structuring mechanisms of the heterogeneous algebraic specification language HetCasl for defining a general concept of heterogeneous, distributed, highly modular and structured ontologies, called hyperontologies. Moreover, we distinguish, on a structural and semantic level, several different kinds of combining and aligning heterogeneous ontologies, namely integration, connection, and refinement. We show how the notion of heterogeneous refinement can be used to provide both a general notion of sub-ontology as well as a notion of heterogeneous equivalence of ontologies, and finally sketch how different modes of reasoning over ontologies are related to these different structuring aspects. (shrink)

Expressions designating collectives, such as “the committee” or “the ships in the port”, may be interpreted de re or de dicto, depending on context, according as they pick out collectives defined by their members or collectives defined by some criterion for membership. We call these E-collectives and I-collectives respectively, and in this paper we explore in depth the relationship between these two categories. In particular, we identify important respects in which they differ, regarding the nature of the dependence of the (...) collective on its members, the nature of the parthood relation in which the members stand to the whole, and, from an application perspective, the different methods used for identifying the two forms of collective from large spatio-temporal data-sets. (shrink)

In the domain of ontology design as well as in Knowledge Representation, modeling universals is a challenging problem.Most approaches that have addressed this problem rely on Description Logics (DLs) but many difficulties remain, due to under-constrained representation which reduces the inferences that can be drawn and further causes problems in expressiveness. In mathematical logic and program checking, type theories have proved to be appealing but, so far they have not been applied in the formalization of ontologies. To bridge this gap, (...) we present in this paper a theory for representing ontologies in a dependently typed framework which relies on strong formal foundations including both a constructive logic and a functional type system. The language of this theory defines in a precise way what ontological primitives such as classes, relations, properties, etc., and thereof roles, are. The first part of the paper details how these primitives are defined and used within the theory. In a second part, we focus on the formalization of the role primitive. A review of significant role properties leads to the specification of a role profile and most of the remaining work details through numerous examples, how the proposed theory is able to fully satisfy this profile. It is demonstrated that dependent types can model several non-trivial aspects of roles including a formal solution for generalization hierarchies, identity criteria for roles and other contributions. A discussion is given on how the theory is able to cope with many of the constraints inherent in a good role representation. (shrink)

Unlike identification with keys and reference schemes in ER and ORM, UML uses internal, system-generated, identifiers, with a little-known underspecified option for user-defined identifiers. To increase the ontological foundations of UML, we propose two language enhancements for UML, being formally defined simple and compound identifiers and the notion of defined class, which also have a corresponding extension of UML’s metamodel.

A recurring problem in conceptual modelling and ontology development is the representation of part-whole relations, with a requirement to be able to distinguish between essential and mandatory parts. To solve this problem, we formally characterize the semantics of these shareability notions by resorting to the temporal conceptual model E RVT and its formalization in the description logic DLRUS.

Natural systems are categorized according to their structural and dynamical similarities. A two-dimensional schema is proposed as a kind of "periodic table" of natural systems. Six of eight levels in this schema serve as sources of analogies, two levels are the targets of analogical reasoning. The source domains are the atomic, molecular, macromolecular, micro-organismic, organismic and socio-cultural systems and processes. One of the target domains discussed in the article is the level of subatomic particles. The other target domain, not discussed (...) in the article, could be the level of future supra-national systems. Three types of processes are identified occurring in natural systems: conservation, modification and transformation. Modifications allow a reversible adaptation of a system to environmental influences by changing its internal state. The entirety of all internal states defines the "state space" of the system. Similarities of state spaces between systems of six levels are investigated. A dual-space picture of natural systems can be defined on six levels, the source domains of analogical reasoning. On the subatomic level, space-time is identified as part of the state space of subatomic particles. However, space-time needs a completion by an additional state space in order to obtain a dual-space picture also for subatomic particles. A "basic space" is proposed, so that subatomic particles exist simultaneously in space-time and in basic space. The basic space is assumed to be a circular space, where masses and charges circulate force-free and generate the spin and the magnetic moment of particles. A presumption about the existence of hypothetical matter not detectable in space-time is derived. Such primitive forms of matter could exist in basic space only and represent the dark matter. (shrink)