This paper presents an axiomatic formalization of a theory of top-level relations between three categories of entities: individuals, universals, and collections. We deal with a variety of relations between entities in these categories, including the sub-universal relation among universals and the parthood relation among individuals, as well as cross-categorial relations such as instantiation and membership. We show that an adequate understanding of the formal properties of such relations – in particular their behavior with respect to time – is critical for (...) geographic information processing. The axiomatic theory is developed using Isabelle, a computational system for implementing logical formalisms. All proofs are computer verified and the computational representation of the theory is available online. (shrink)

Since 2002 we have been testing and refining a methodology for ontology development that is now being used by multiple groups of researchers in different life science domains. Gary Merrill, in a recent paper in this journal, describes some of the reasons why this methodology has been found attractive by researchers in the biological and biomedical sciences. At the same time he assails the methodology on philosophical grounds, focusing specifically on our recommendation that ontologies developed for scientific purposes should be (...) constructed in such a way that their terms are seen as referring to what we call universals or types in reality. As we show, Merrill’s critique is of little relevance to the success of our realist project, since it not only reveals no actual errors in our work but also criticizes views on universals that we do not in fact hold. However, it nonetheless provides us with a valuable opportunity to clarify the realist methodology, and to show how some of its principles are being applied, especially within the framework of the OBO (Open Biomedical Ontologies) Foundry initiative. (shrink)

Genera, typically hand-in-hand with their branching species, are essential elements of vocabulary-based information constructs, in particular scientific taxonomies. Should they also feature in formal ontologies, the highest of such constructs? I argue in this article that the answer is “Yes” and that the question posed in its title also has a Yes-answer: The way medieval ontologists sliced up the world into genera does matter to formal ontology. More specifically, the way Dietrich of Freiberg, a Latin scholastic, conceived and applied strictly (...) generic criteria to slice up the world into its entities can provide some guidelines to the field of formal ontology with respect to not only its contents, but also its scope. In particular, Dietrich's information criterion plays here a central role. (shrink)

Festschrift in Honor of Barry Smith on the occasion of his 65th Birthday. Published as issue 4:4 of the journal Cosmos + Taxis: Studies in Emergent Order and Organization. Includes contributions by Wolfgang Grassl, Nicola Guarino, John T. Kearns, Rudolf Lüthe, Luc Schneider, Peter Simons, Wojciech Żełaniec, and Jan Woleński.

In a series of papers over a period of several years Barry Smith andWerner Ceusters have offered a number of cogent criticisms of historical approaches to creating, maintaining, and applying biomedical terminologies and ontologies. And they have urged the adoption of what they refer to as a “realism-based” approach. Indeed, at times they insist that the realism-based approach not only offers clear advantages and a well-founded methodological basis for ontology development and evaluation, but that such a realist perspective is in (...) fact necessary for understanding and using terminologies and ontologies in science. -/- This paper explores a number of questions surrounding such claims, provides a careful characterization of the type of realism recommended by Smith and Ceusters, and evaluates the role that realism plays in the critiques and recommendations that they offer. The conclusion reached is that while Smith’s and Ceusters’ criticisms of prior practice in the treatment of ontologies and terminologies in medical informatics are often both perceptive and well founded, and while at least some of their own proposals demonstrate obvious merit and promise, none of this either follows from or requires the brand of realism that they propose. (shrink)

The Ontological Square is a categorial scheme that combines two metaphysical distinctions: that between types (or universals ) and tokens (or particulars ) on the one hand, and that between characters (or features ) and their substrates (or bearers ) on the other hand. The resulting four-fold classification of things comprises particular substrates, called substances , universal substrates, called kinds , particular characters, called modes or moments , and universal characters, called attributes . Things are joined together in facts by (...) primitive ontological ties or nexus . This article describes a logic that is meant to capture the basic intuitions behind the Ontological Square. Given a minimal correspondence between atomic logical form and ontological structure, the commitment to nexus as a distinct ontological category entails a rehabilitation of copulae as ties of predication. Thus, the Logic of the Ontological Square is a copula calculus rather than a predicate calculus; its soundness and completeness can be established with respect to a model akin to a so-called first-order semantics for standard second-order logic. (shrink)