Parts, places, and perspectives : a theory of spatial relations based an mereotopology and convexity

This thesis suggests to carry on the philosophical work begun in Casati's and Varzi's seminal book Parts and Places, by extending their general reflections on the basic formal structure of spatial representation beyond mereotopology and absolute location to the question of perspectives and perspective-dependent spatial relations. We show how, on the basis of a conceptual analysis of such notions as perspective and direction, a mereotopological theory with convexity can express perspectival spatial relations in a strictly qualitative framework. We start by introducing a particular mereotopological theory, AKGEMT, and argue that it constitutes an adequate core for a theory of spatial relations. Two features of AKGEMT are of particular importance: AKGEMT is an extensional mereotopology, implying that sameness of proper parts is a sufficient and necessary condition for identity, and it allows for (lower- dimensional) boundary elements in its domain of quantification. We then discuss an extension of AKGEMT, AKGEMTS, which results from the addition of a binary segment operator whose interpretation is that of a straight line segment between mereotopological points. Based on existing axiom systems in standard point-set topology, we propose an axiomatic characterisation of the segment operator and show that it is strong enough to sustain complex properties of a convexity predicate and a convex hull operator. We compare our segment-based characterisation of the convex hull to Cohn et al.'s axioms for the convex hull operator, arguing that our notion of convexity is significantly stronger. The discussion of AKGEMTS defines the background theory of spatial representation on which the developments in the second part of this thesis are built. The second part deals with perspectival spatial relations in two-dimensional space, i.e., such relations as those expressed by 'in front of, 'behind', 'to the left/right of, etc., and develops a qualitative formalism for perspectival relations within the framework of AKGEMTS. Two main claims are defended in part 2: That perspectival relations in two-dimensional space are four- place relations of the kind R(x, y, z, w), to be read as x is i?-related to y as z looks at w; and that these four-place structures can be satisfactorily expressed within the qualitative theory AKGEMTS. To defend these two claims, we start by arguing for a unified account of perspectival relations, thus rejecting the traditional distinction between 'relative' and 'intrinsic' perspectival relations. We present a formal theory of perspectival relations in the framework of AKGEMTS, deploying the idea that perspectival relations in two-dimensional space are four-place relations, having a locational and a perspectival part and show how this four-place structure leads to a unified framework of perspectival relations. Finally, we present a philosophical motivation to the idea that perspectival relations are four-place, cashing out the thesis that perspectives are vectorial properties and argue that vectorial properties are relations between spatial entities. Using Fine's notion of "qua objects" for an analysis of points of view, we show at last how our four-place approach to perspectival relations compares to more traditional understandings.

Unification of multi-species vertebrate anatomy ontologies for comparative biology in Uberon.

BACKGROUND: Elucidating disease and developmental dysfunction requires understanding variation in phenotype. Single-species model organism anatomy ontologies (ssAOs) have been established to represent this variation. Multi-species anatomy ontologies (msAOs; vertebrate skeletal, vertebrate homologous, teleost, amphibian AOs) have been developed to represent 'natural' phenotypic variation across species. Our aim has been to integrate ssAOs and msAOs for various purposes, including establishing links between phenotypic variation and candidate genes. RESULTS: Previously, msAOs contained a mixture of unique and overlapping content. This hampered integration and coordination due to the need to maintain cross-references or inter-ontology equivalence axioms to the ssAOs, or to perform large-scale obsolescence and modular import. Here we present the unification of anatomy ontologies into Uberon, a single ontology resource that enables interoperability among disparate data and research groups. As a consequence, independent development of TAO, VSAO, AAO, and vHOG has been discontinued. CONCLUSIONS: The newly broadened Uberon ontology is a unified cross-taxon resource for metazoans (animals) that has been substantially expanded to include a broad diversity of vertebrate anatomical structures, permitting reasoning across anatomical variation in extinct and extant taxa. Uberon is a core resource that supports single- and cross-species queries for candidate genes using annotations for phenotypes from the systematics, biodiversity, medical, and model organism communities, while also providing entities for logical definitions in the Cell and Gene Ontologies. THE ONTOLOGY RELEASE FILES ASSOCIATED WITH THE ONTOLOGY MERGE DESCRIBED IN THIS MANUSCRIPT ARE AVAILABLE AT: http://purl.obolibrary.org/obo/uberon/releases/2013-02-21/ CURRENT ONTOLOGY RELEASE FILES ARE AVAILABLE ALWAYS AVAILABLE AT: http://purl.obolibrary.org/obo/uberon/releases/