The discussions which follow rest on a distinction, first expounded by Husserl, between formal logic and formal ontology. The former concerns itself with (formal) meaning-structures; the latter with formal structures amongst objects and their parts. The paper attempts to show how, when formal ontological considerations are brought into play, contemporary extensionalist theories of part and whole, and above all the mereology of Leniewski, can be generalised to embrace not only relations between concrete objects and object-pieces, but also relations between what (...) we shall call dependent parts or moments. A two-dimensional formal language is canvassed for the resultant ontological theory, a language which owes more to the tradition of Euler, Boole and Venn than to the quantifier-centred languages which have predominated amongst analytic philosophers since the time of Frege and Russell. Analytic philosophical arguments against moments, and against the entire project of a formal ontology, are considered and rejected. The paper concludes with a brief account of some applications of the theory presented. (shrink)

Biomedical research is increasingly a matter of the navigation through large computerized information resources deriving from functional genomics or from the biochemistry of disease pathways. To make such navigation possible, controlled vocabularies are needed in terms of which data from different sources can be unified. One of the most influential developments in this regard is the so-called Gene Ontology, which consists of controlled vocabularies of terms used by biologists to describe cellular constituents, biological processes and molecular functions, organized into hierarchies (...) via the relation of class subsumption. Here we seek to provide a rigorous account of the logic of classification that underlies GO and similar biomedical ontologies. Drawing on Aristotle, we develop a system of axioms and definitions for the treatment of biological classes and instances. (shrink)

The Foundational Model of Anatomy (FMA) symbolically represents the structural organization of the human body from the macromolecular to the macroscopic levels, with the goal of providing a robust and consistent scheme for classifying anatomical entities that is designed to serve as a reference ontology in biomedical informatics. Here we articulate the need for formally clarifying the is-a and part-of relations in the FMA and similar ontology and terminology systems. We diagnose certain characteristic errors in the treatment of these relations (...) and show how these errors can be avoided through adoption of the formalism we describe. We then illustrate how a consistently applied formal treatment of taxonomy and partonomy can support the alignment of ontologies. (shrink)

Quality assurance in large terminologies is a difficult issue. We present two algorithms that can help terminology developers and users to identify potential mistakes. We demon­strate the methodology by outlining the different types of mistakes that are found when the algorithms are applied to SNOMED-CT. On the basis of the results, we argue that both formal logical and linguistic tools should be used in the development and quality-assurance process of large terminologies.

We have a variety of different ways of dividing up, classifying, mapping, sorting and listing the objects in reality. The theory of granular partitions presented here seeks to provide a general and unified basis for understanding such phenomena in formal terms that is more realistic than existing alternatives. Our theory has two orthogonal parts: the first is a theory of classification; it provides an account of partitions as cells and subcells; the second is a theory of reference or intentionality; it (...) provides an account of how cells and subcells relate to objects in reality. We define a notion of well-formedness for partitions, and we give an account of what it means for a partition to project onto objects in reality. We continue by classifying partitions along three axes: (a) in terms of the degree of correspondence between partition cells and objects in reality; (b) in terms of the degree to which a partition represents the mereological structure of the domain it is projected onto; and (c) in terms of the degree of completeness with which a partition represents this domain. (shrink)