A unified theory of granularity, vagueness and approximation

Abstract: We propose a view of vagueness as a semantic property of names and predicates. All entities are crisp, on this semantic view, but there are, for each vague name, multiple portions of reality that are equally good candidates for being its referent, and, for each vague predicate, multiple classes of objects that are equally good candidates for being its extension. We provide a new formulation of these ideas in terms of a theory of granular partitions. We show that this theory provides a general framework within which we can understand the relation between vague terms and concepts and the corresponding crisp portions of reality. We also sketch how it might be possible to formulate within this framework a theory of vagueness which dispenses with the notion of truth-value gaps and other artifacts of more familiar approaches. Central to our approach is the idea that judgments about reality involve in every case (1) a separation of reality into foreground and background of attention and (2) the feature of granularity. On this basis we attempt to show that even vague judgments made in naturally occurring contexts are not marked by truth-value indeterminacy. We distinguish, in addition to crisp granular partitions, also vague partitions, and reference partitions, and we explain the role of the latter in the context of judgments that involve vagueness. We conclude by showing how reference partitions provide an effective means by which judging subjects are able to temper the vagueness of their judgments by means of approximations

Directly depicting granular ontologies

Published in extended form as "Endurants and Perdurants in Directly Depicting Ontologies", We propose an ontological theory that is powerful enough to describe both complex spatio-temporal processes and the enduring entities that participate in such processes. For this purpose we distinguish between ontologies and metaontology. Ontologies are based on very simple directly depicting languages and fall into two major categories: ontologies of type SPAN and ontologies of type SNAP. These represent two complementary perspectives on reality and result in distinct though compatible systems of categories. In a SNAP (snapshot) ontology we have the enduring entities in a given domain as they exist to be inventoried at some given moment of time. In a SPAN ontology we have perduring entities such as processes and their parts and aggregates. We argue that both kinds of ontology are required, together with the meta-ontology which joins them together. On the level of meta-ontology we are able to impose constraints on ontologies of a sort which can support efficient processing of large amounts of data

A formal theory for spatial representation and reasoning in biomedical ontologies

Objective: The objective of this paper is to demonstrate how a formal spatial theory can be used as an important tool for disambiguating the spatial information embodied in biomedical ontologies and for enhancing their automatic reasoning capabilities. Method and Materials: This paper presents a formal theory of parthood and location relations among individuals, called Basic Inclusion Theory (BIT). Since biomedical ontologies are comprised of assertions about classes of individuals (rather than assertions about individuals), we define parthood and location relations among classes in the extended theory BIT+Cl (Basic Inclusion Theory for Classes). We then demonstrate the usefulness of this formal theory for making the logical structure of spatial information more precise in two ontologies concerned with human anatomy: the Foundational Model of Anatomy (FMA) and GALEN. Results: We find that in both the FMA and GALEN, class-level spatial relations with different logical properties are not always explicitly distinguished. As a result, the spatial information included in these biomedical ontologies is often ambiguous and the possibilities for implementing consistent automatic reasoning within or across ontologies are limited. Conclusion: Precise formal characterizations of all spatial relations assumed by a biomedical ontology are necessary to ensure that the information embodied in the ontology can be fully and coherently utilized in a computational environment. This paper can be seen as an important beginning step toward achieving this goal, but much more work is along these lines is required

Towards a Quantum Theory of Geographic Fields

This paper proposes a framework that that allows for the possibility that multiple classically incompatible states are expressed simultaneously at a given point of a geographic field. The admission of such superposition states provides the basis for a new understanding of indeterminacy and ontological vagueness in the geographic world

A Theory of Granular Partitions

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

Building an Inclusive Society: Post-Secondary Youth Perspectives on Immigration, Multiculturalism and Racism in Newfoundland and Labrador

Building an Inclusive Society: Post-secondary Youth Perspectives on Immigration, Multiculturalism and Racism in Newfoundland and Labrador is a project that seeks to understand youth attitudes towards immigration, multiculturalism, and politics in addition to the experiences of racism among university students within the province. In addition, this project was designed to better understand the program needs and sociological circumstances of youth in St. John’s and surrounding areas and involves surveying, and subsequently analyzing, the views of postsecondary students in Newfoundland and Labrador. It also aims to gain a better understanding of how and why such attitudes are formed in order to test existing theories established by scholars. By capturing and understanding the attitudes of students in Newfoundland and Labrador, this report will not only add to a growing body of literature, but will also complement existing community efforts to enhance the integration of newcomers. As such, this report is a step towards ensuring that newcomers not only integrate into Newfoundland and Labrador society, but feel welcomed while doing so

Biomedical ontologies: What part-of is and isn’t

AbstractMereological relations such as part-of and its inverse has-part are fundamental to the description of the structure of living organisms. Whereas classical mereology focuses on individual entities, mereological relations in biomedical ontologies are generally asserted between classes of individuals. In general, this practice leaves some basic issues unanswered: type constraints of mereological relations, e.g., concerning artifacts and biological entities, the relation between parthood and time, inferred parts and wholes as well as a delimitation of parthood against spatial inclusion. Furthermore, mereological relations can be asserted not only between physical objects but also between biological processes and medical procedures. We analyze these ambiguities and make suggestions for a standardization of mereological relations in biomedical ontologies

Endurants and Perdurants in Directly Depicting Ontologies

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

Universality of the evaporation/condensation transition

AbstractBy making use of the well-known lattice-gas interpretation, we investigated the evaporation/condensation transition through Monte Carlo simulations of the square lattice Ising model with nearest-neighbour couplings and periodic boundary conditions. The particle density can be varied by choosing different fixed magnetisations. In the analysis of our data we followed recent analytical work by Biskup et al. [Europhys. Lett. 60 (2002) 21], who also used the Ising model to study liquid-vapour systems at a fixed excess δN of particles above the ambient gas density in the limit of large system sizes. By identifying a dimensionless parameter Δ(δN), they showed that for Δ<Δc all excess is absorbed in background fluctuations (“evaporated” system), while for Δ>Δc a single large droplet of the dense phase occurs (“condensed” system). Besides the threshold value Δc also the fraction λ of excess particles forming the droplet is given explicitly.To test the applicability of these asymptotic results to practically accessible system sizes, we measured the volume of the largest minority droplet, corresponding to a fluid drop, for various L×L lattices with L=40,…,640. Using analytic values for the spontaneous magnetisation m0, the susceptibility χ and the Wulff interfacial free-energy density τW for the infinite system, we were able to determine Δc and λ numerically in very good agreement with the theoretical prediction. We also discuss the associated free-energy barrier and its implication for multimagnetical simulations, and put these findings into context with the related droplet/strip transition respectively barrier

The RNA Ontology (RNAO): An ontology for integrating RNA sequence and structure data

Biomedical Ontologies are intended to integrate diverse biomedical data to enable intelligent data-mining and facilitate translation of basic research into useful clinical knowledge. We present the first version of RNAO, an ontology for integrating RNA 3D structural, biochemical and sequence data. While each 3D data file depicts the structure of a specific molecule, such data have broader significance as representatives of classes of homologous molecules, which, while differing in sequence, generally share core structural features of functional importance. Thus, 3D structure data gain value by being linked to homologous sequences in genomic data and databases of sequence alignments. Likewise genomic data can increase in value by annotation of shared structural features, especially when these can be linked to specific functions. The RNAO is being developed in line with the developing standards of the Open Biomedical Ontologies (OBO) Consortium