Torsten Hahmann

Modular first-order ontologies via repositories

From its inception, the focus of ontological engineering has been to support the reusability and shareability of ontologies, as well as interoperability of ontology-based software systems. Among the approaches employed to address these challenges have been ontology repositories and the modularization of ontologies. In this paper we combine these approaches and use the relationships between first-order ontologies within a repository (such as non-conservative extension and relative interpretation) to characterize the criteria for modularity. In particular, we introduce the notion of core hierarchies, which are sets of theories with the same non-logical lexicons and which are all non-conservative extensions of a unique root theory. The technique of relative interpretation leads to the notion of reducibility of a theory to a set of theories in different core hierarchies. We show how these relationships support a semi-automated procedure that decomposes an ontology into irreducible modules. We also propose a semi-automated procedure that can use the relationships between modules to characterize which modules can be shared and reused among different ontologies.

On the Skeleton of Stonian p-Ortholattices

Boolean Contact Algebras (BCA) establish the algebraic counterpart of the mereotopolopy induced by the Region Connection Calculus (RCC). Similarly, Stonian p-ortholattices serve as a lattice theoretic version of the ontology RT *** of Asher and Vieu. In this paper we study the relationship between BCAs and Stonian p-ortholattices. We show that the skeleton of every Stonian p-ortholattice is a BCA, and, conversely, that every BCA is isomorphic to the skeleton of a Stonian p-ortholattice. Furthermore, we prove the equivalence between algebraic conditions on Stonian p-ortholattices and the axioms C5, C6, and C7 for BCAs.

Internet of Things: Toward Smart Networked Systems and Societies

Mark Underwood a, Michael Gruninger b, Leo Obrst c,∗, Ken Baclawski d, Mike Bennett e, Gary Berg-Cross f, Torsten Hahmann g and Ram Sriram h a Krypton Brothers, Port Washington, NY, USA b University of Toronto, Toronto, Canada c The MITRE Corporation, McLean, VA, USA d Northeastern University, Boston, MA, USA e Hypercube Ltd, London, UK f Knowledge Strategies, Washington, DC, USA g University of Maine, Orono, ME, USA h National Institute of Standards and Technology (NIST), Gaithersburg, MD, USA

On the algebra of regular sets

AbstractThe mereotopology RT  − has in Stonian p-ortholattices its algebraic counterpart. We study representability of these lattices and show that not all Stonian p-ortholattices can be represented by the set of regular sets of a topological space. We identify five conditions that hold in algebras of regular sets and which can be used to eliminate non-representable Stonian p-ortholattices. This shows not only that the original completeness theorem for RT  − is incorrect, but is also an important step towards an algebraic representation (up to isomorphism) of the regular sets of topological spaces.

Complementation in Representable Theories of Region-Based Space

Through contact algebras we study theories of mereotopology in a uniform way that clearly separates mereological from topological concepts. We identify and axiomatize an important subclass of closure mereotopologies (CMT) called unique closure mereotopologies (UCMT) whose models always have orthocomplemented contact algebras (OCA) an algebraic counterpart. The notion of MT-representability, a weak form of spatial representability but stronger than topological representability, suffices to prove that spatially representable complete OCAs are pseudocomplemented and satisfy the Stone identity. Within the resulting class of contact algebras the strength of the algebraic complementation delineates two classes of mereotopology according to the key ontological choice between mereological and topological closure operations. All closure operations are defined mereologically iff the corresponding contact algebras are uniquely complemented while topological closure operations highly restrict the contact relation but allow not uniquely complemented and non-distributive contact algebras. Each class contains a single ontologically coherent theory that admits discrete models.

An Ontological Analysis of Water Features

GIScience 2016 Short Paper Proceedings AN ONTOLOGICAL ANALYSIS OF WATER FEATURES Boyan Brodaric 1 , Torsten Hahmann 2 , Michael Gruninger 3 Geological Survey of Canada, Ottawa, Canada K1A0E9 Email: boyan.brodaric@canada.ca School of Computing and Information Science, University of Maine, Orono, ME 04469, USA Email: torsten.hahmann@maine.edu University of Toronto, Toronto, Canada M5S3GB Email: gruninger@mie.utoronto.ca Abstract Water features are understood and represented heterogeneously in a wide variety of settings, including in data standards, polices and regulations, and amongst different cultures and languages. Ontologies aim to reduce this heterogeneity by representing commonalities across such settings. In this paper we build upon existing work in hydro ontologies and philosophical ontology to enhance the conceptualization and representation of water features. This results in a new taxonomy for water features, which helps identify and organize their essential parts. The results are represented as a first-order logic extension of the DOLCE ontology as well as an independent ontology fragment, and these are intended to serve as a reference ontology for the hydro domain as well as an aid to data interoperability. 1. Introduction Water features are entities that are essentially composed of water and variably other things. Prototypical examples include lakes, rivers, puddles, and clouds, but can also include aquifers. They play a key role in many human activities, such as those related to health, climate and weather, agriculture, energy, recreation, and transportation. Research and operations in these domains are heavily dependent on digital representations of water features, but the inherent conceptualizations can vary widely. Examples of heterogeneity abound, and can be found when comparing international water data standards (Boisvert & Brodaric 2012; Dornblut & Atkinson 2013; INSPIRE 2013; 2014), national catalogs of hydrographic features (Duce & Janowicz 2010), ontological considerations (Galton & Mizoguchi 2009; Santos et al. 2005; Sinha et al. 2014; Wellen & Sieber 2013), and database structures (Maidment, 2002; Strassberg, et al., 2011). This is problematic as it inhibits some uses, especially their integration, which is typically an important precursor to regional scientific analysis such as water availability, or complex societal decision-making such as water allotment. At the heart of the problem is a disparity about the fundamental nature of a water feature, as different aspects are variously emphasized in distinct conceptualizations. These aspects include most notably the water body, its water matter, its container or void (the space it occupies), or even an immaterial spiritual entity (Mark et al. 2007; Wellen & Sieber 2013). The emphases exist perhaps to enable diverse uses, for example, reasoning about the presence of a water body facilitates navigation of rivers that might have wet or dry segments; reasoning about the constitution and flow of water matter informs contamination scenarios, as does reasoning about the permeability of the container; and reasoning about the container’s void informs storage and overflow scenarios. Yet, it is still somewhat surprising that an entity of such significance is so widely construed and often vaguely defined. In this paper we undertake an ontological analysis of water features and develop a new conceptualization and representation that encompass the key aspects. This is achieved by extending and uniting two significant approaches to physical ontology, namely Hayes’ ontology of liquids (1978) and Fine’s theory of parts (1999). The results contribute to the design of the HyFO reference