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

The Distributed Ontology Language (DOL): Use Cases, Syntax, and Extensibility

The Distributed Ontology Language (DOL) is currently being standardized within the OntoIOp (Ontology Integration and Interoperability) activity of ISO/TC 37/SC 3. It aims at providing a unified framework for (1) ontologies formalized in heterogeneous logics, (2) modular ontologies, (3) links between ontologies, and (4) annotation of ontologies. This paper presents the current state of DOL's standardization. It focuses on use cases where distributed ontologies enable interoperability and reusability. We demonstrate relevant features of the DOL syntax and semantics and explain how these integrate into existing knowledge engineering environments.Comment: Terminology and Knowledge Engineering Conference (TKE) 2012-06-20 to 2012-06-21 Madrid, Spai

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

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

"Possible Definitions of an ’A Priori’ Granule\ud in General Rough Set Theory" by A. Mani

We introduce an abstract framework for general rough set theory from a mereological perspective and consider possible concepts of ’a priori’ granules and granulation in the same. The framework is ideal for relaxing many of the\ud relatively superfluous set-theoretic axioms and for improving the semantics of many relation based, cover-based and dialectical rough set theories. This is a\ud relatively simplified presentation of a section in three different recent research papers by the present author.\u