A diagrammatic representation for entities and mereotopological relations in ontologies

In the graphical representation of ontologies, it is customary to use graph theory as the representational background. We claim here that the standard graph-based approach has a number of limitations. We focus here on a problem in the graph-based representation of ontologies in complex domains such as biomedical, engineering and manufacturing: lack of mereotopological representation. Based on such limitation, we proposed a diagrammatic way to represent an entity’s structure and various forms of mereotopological relationships between the entities

Mereotopological Connection

The paper outlines a model-theoretic framework for investigating and comparing a variety of mereotopological theories. In the first part we consider different ways of characterizing a mereotopology with respect to (i) the intended interpretation of the connection primitive, and (ii) the composition of the admissible domains of quantification (e.g., whether or not they include boundary elements). The second part extends this study by considering two further dimensions along which different patterns of topological connection can be classified—the strength of the connection and its multiplicity

Interpreting mereotopological connection

This paper examines ten possible topological interpretations of connection and for each interpretation, identifies sufficient conditions under which a significant class of topological spaces provides models of General Extensional Mereotopology with Closure Conditions (GEMTC) in which some key mereotopological ideas align with their topological analogues. In particular, there is an interpretation under which the non-empty sets of any symmetric topology are a model of GEMTC with alignment between the mereotopological and topological definitions of (self-)connection, open and closed entities, interior, exterior, closure, and boundary

The Category of Mereotopology and Its Ontological Consequences

We introduce the category of mereotopology Mtop as an alternative category to that of topology Top, stating ontological consequences throughout. We consider entities such as boundaries utilizing Brentano’s thesis and holes utilizing homotopy theory with a rigorous proof of Hausdorff Spaces satisfying [GEM]TC axioms. Lastly, we mention further areas of study in this category

Topological Foundations of Cognitive Science

A collection of papers presented at the First International Summer Institute in Cognitive Science, University at Buffalo, July 1994, including the following papers: ** Topological Foundations of Cognitive Science, Barry Smith ** The Bounds of Axiomatisation, Graham White ** Rethinking Boundaries, Wojciech Zelaniec ** Sheaf Mereology and Space Cognition, Jean Petitot ** A Mereotopological Definition of 'Point', Carola Eschenbach ** Discreteness, Finiteness, and the Structure of Topological Spaces, Christopher Habel ** Mass Reference and the Geometry of Solids, Almerindo E. Ojeda ** Defining a 'Doughnut' Made Difficult, N .M. Gotts ** A Theory of Spatial Regions with Indeterminate Boundaries, A.G. Cohn and N.M. Gotts ** Mereotopological Construction of Time from Events, Fabio Pianesi and Achille C. Varzi ** Computational Mereology: A Study of Part-of Relations for Multi-media Indexing, Wlodek Zadrozny and Michelle Ki

Modelling mammographic microcalcification clusters using persistent mereotopology

AbstractIn mammographic imaging, the presence of microcalcifications, small deposits of calcium in the breast, is a primary indicator of breast cancer. However, not all microcalcifications are malignant and their distribution within the breast can be used to indicate whether clusters of microcalcifications are benign or malignant. Computer-aided diagnosis (CAD) systems can be employed to help classify such microcalcification clusters. In this paper a novel method for classifying microcalcification clusters is presented by representing discrete mereotopological relations between the individual microcalcifications over a range of scales in the form of a mereotopological barcode. This barcode based representation is able to model complex relations between multiple regions and the results on mammographic microcalcification data shows the effectiveness of this approach. Classification accuracies of 95% and 80% are achieved on the MIAS and DDSM datasets, respectively. These results are comparable to existing state-of-the art methods. This work also demonstrates that mereotopological barcodes could be used to help trained clinicians in their diagnosis by providing a clinical interpretation of barcodes that represent both benign and malignant cases

Mereotopological Patterns for Ontology Evolution and Debugging

In this paper the foundational principles and the application of a mereotopological theory, the Region Connection Calculus, for controlling the revision of formal ontologies by means of visual arrangements is presented. The visual representation of logical relationships between concepts of an ontology is defined, and it is computed by means of an automated theorem prover. The user can recognize mereotopological patterns in the visual representation, particularly those representing anomalies in the ontology. An intelligent tool called Paella is designed and implemented for this task. Also, the extension to this formalism for managing uncertainty in concept reasoning is described

The Logic of Discrete Qualitative Relations

We consider a modal logic based on mathematical morphology which allows the expression of mereotopological relations between subgraphs. A specific form of topological closure between graphs is expressible in this logic, both as a combination of the negation ¬ and its dual , and as modality, using the stable relation Q, which describes the incidence structure of the graph. This allows to define qualitative spatial relations between discrete regions, and to compare them with earlier works in mereotopology, both in the discrete and in the continuous space