According to the prevalent ‘sum view’ of stuffs, each portion of stuff is a mereological sum of its subportions. The purpose of this paper is to re-examine the sum view in the light of a modal temporal mereology which distinguishes between different varieties of summation relations. While admitting David Barnett’s recent counter-example to the sum view (Barnett, Philos Rev 113:89–100, 2004), we show that there is nonetheless an important sense in which all portions of stuff are sums of their subportions. (...) We use our summation relations to develop, as an alternative to the sum view, an analysis of stuffs that distinguishes between the ways in which different sorts of stuffs are sums of their subportions. (shrink)
We propose an ontological theory that is powerful enough to describe both complex spatio-temporal processes and the enduring entities that participate therein. For this purpose we introduce the notion a directly depicting ontology. Directly depicting ontologies are based on relatively simple languages and fall into two major categories: ontologies of type SPAN and ontologies of type SNAP. These represent two complementary perspectives on reality and employ distinct though compatible systems of categories. A SNAP (snapshot) ontology comprehends enduring entities such as (...) organisms, geographic features, or qualities as they exist at some given moment of time. A SPAN ontology comprehends perduring entities such as processes and their parts and aggregates as they unfold themselves through some temporal interval. We give an axiomatic account of the theory of directly depicting ontologies and of the core parts of the metaontological fragment within which they are embedded. (shrink)
This paper provides an axiomatic formalization of a theory of foundational relations between three categories of entities: individuals, universals, and collections. We deal with a variety of relations between entities in these categories, including the is-a relation among universals and the part-of relation among individuals as well as cross-category relations such as instance-of, member-of, and partition-of. We show that an adequate understanding of the formal properties of such relations – in particular their behavior with respect to time – is critical (...) for formal ontology. We provide examples to support this thesis from the domain of biomedicine. (shrink)
Description Logics  are nowadays widely accepted as formalisms for implementing rigorous domain ontologies, and have been used in biomedicine in projects such as GONG  and SNOMED-CT . A key feature of such ontologies is that the associated reasoning facilities allow us to discover inconsistencies and other problems in an automatic fashion. This is important since ontologies of complex domains such as medicine are large and complex and have been built by many people over long periods of time.
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)
We propose an ontological theory that is powerful enough to describe both complex spatio-temporal processes (occurrents) and the enduring entities (continuants) that participate therein. The theory is divided into two major categories of sub-theories: (sub-) theories of type SPAN and (sub-)theories of type SNAP. These theories represent two complementary perspectives on reality and result in distinct though compatible systems of categories. In SNAP we have enduring entities such as substances, qualities, roles, functions; in SPAN we have perduring entities such as (...) processes and their parts and aggregates. We argue that both kinds of ontological theory are required in order to give a non-reductionism account of complex domains of reality. (shrink)
In this paper we propose a formal theory of partitions (ways of dividing up or sorting or mapping reality) and we show how the theory can be applied in the geospatial domain. We characterize partitions at two levels: as systems of cells (theory A), and in terms of their projective relation to reality (theory B). We lay down conditions of well-formedness for partitions and we define what it means for partitions to project truly onto reality. We continue by classifying well-formed (...) partitions along three axes: (a) degree of correspondence between partition cells and objects in reality; (b) degree to which a partition represents the mereological structure of the domain it is projected onto; and (c) degree of completeness and exhaustiveness with which a partition represents reality. This classification is used to characterize three types of partitions that play an important role in spatial information science: cadastral partitions, categorical coverages, and the partitions involved in folk categorizations of the geospatial domain. (shrink)