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Constructing geoontologies by reification of observation data
 In ACM GIS
, 2011
"... The semantic integration of heterogeneous, spatiotemporal information is a major challenge for achieving the vision of a multithematic and multiperspective Digital Earth. The Semantic Web technology stack has been proposed to address the integration problem by knowledge representation languages and ..."
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The semantic integration of heterogeneous, spatiotemporal information is a major challenge for achieving the vision of a multithematic and multiperspective Digital Earth. The Semantic Web technology stack has been proposed to address the integration problem by knowledge representation languages and reasoning. However approaches such as the Web Ontology Languages (OWL) were developed with decidability in mind. They do not integrate well with established modeling paradigms in the geosciences that are dominated by numerical and geometric methods. Additionally, work on the Semantic Web is mostly featurecentric and a fieldbased view is difficult to integrate. A layer specifying the transition from observation data to classes and relations is missing. In this work we combine OWL with geometric and topological language constructs based on similarity spaces. Our approach provides three main benefits. First, class constructors can be built from a larger palette of mathematical operations based on vector algebra. Second, it affords the representation of prototypebased classes. Third, it facilitates the representation of classes derived from machine learning classifiers that utilize a multidimensional feature space. Instead of following a onesizefitsall approach, our work allows one to derive contextualized OWL ontologies by reification of observation data.
Mathematical models of cognitive space and time
 In Mitsu Okada and Daniel Andler, editors, Reasoning and Cognition. To appear
, 2006
"... Abstract. This paper explores reasoning about space and time, e.g., in metaphors of time as space; an important method is to find minimal assumptions needed to reach the same conclusions that humans reach. Some mathematical language, including the notion of triad, is introduced for this purpose, for ..."
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Abstract. This paper explores reasoning about space and time, e.g., in metaphors of time as space; an important method is to find minimal assumptions needed to reach the same conclusions that humans reach. Some mathematical language, including the notion of triad, is introduced for this purpose, formalizing and generalizing the cognitive semantics approaches to conceptual spaces (in the senses of both Fauconnier & Turner and of Gärdenfors), blending, and metaphor; in particular, continuous mathematics is used to model space and time. A new explanation of emergent structure in blend spaces is also discussed, and proposed as a source of creativity. Four main examples illustrate the approach, and an appendix encapsulates the most difficult mathematics. 1
Isotone Lbonds
"... Abstract. Lbonds represent relationships between formal contexts. We study properties of these intercontextual structures w.r.t. isotone conceptforming operators in fuzzy setting. We also focus on the direct product of two formal fuzzy contexts and show conditions under which a bond can be obtained ..."
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Abstract. Lbonds represent relationships between formal contexts. We study properties of these intercontextual structures w.r.t. isotone conceptforming operators in fuzzy setting. We also focus on the direct product of two formal fuzzy contexts and show conditions under which a bond can be obtained as an intent of the product. In addition, we show that the previously studied properties of their antitone counterparts can be easily derived from the present results. 1
Towards a Functional Approach to Modular Ontologies using Institutions
"... We propose a functional view of ontologies that emphasises their role in determining answers to queries, irrespective of the formalism in which they are written. A notion of framework is introduced that captures the situation of a global language into which both an ontology language and a query lang ..."
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We propose a functional view of ontologies that emphasises their role in determining answers to queries, irrespective of the formalism in which they are written. A notion of framework is introduced that captures the situation of a global language into which both an ontology language and a query language can be translated, in an abstract way. We then generalise existing notions of robustness from the literature, and relate these to interpolation properties that support modularisation of ontologies.
COINVENT: Towards a Computational Concept Invention Theory
"... We aim to develop a computationally feasible, cognitivelyinspired, formal model of concept invention, drawing on Fauconnier and Turner’s theory of conceptual blending, and grounding it on a sound mathematical theory of concepts. Conceptual blending, although successfully applied to describing comb ..."
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We aim to develop a computationally feasible, cognitivelyinspired, formal model of concept invention, drawing on Fauconnier and Turner’s theory of conceptual blending, and grounding it on a sound mathematical theory of concepts. Conceptual blending, although successfully applied to describing combinational creativity in a varied number of fields, has barely been used at all for implementing creative computational systems, mainly due to the lack of sufficiently precise mathematical characterisations thereof. The model we will define will be based on Goguen’s proposal of a Unified Concept Theory, and will draw from interdisciplinary research results from cognitive science, artificial intelligence, formal methods and computational creativity. To validate our model, we will implement a proof of concept of an autonomous computational creative system that will be evaluated in two testbed scenarios: mathematical reasoning and melodic harmonisation. We envisage that the results of this project will be significant for gaining a deeper scientific understanding of creativity, for fostering the synergy between understanding and enhancing human creativity, and for developing new technologies for autonomous creative systems.
star.edu.sg
"... Conceptual Indexing is a way to produce only one index for many multilingual documents. InterMedia conceptual indexing promotes the use of common concepts between two media in order to use a single index for several media. In this paper we explore such an advance indexing point of view. We show the ..."
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Conceptual Indexing is a way to produce only one index for many multilingual documents. InterMedia conceptual indexing promotes the use of common concepts between two media in order to use a single index for several media. In this paper we explore such an advance indexing point of view. We show the benefit of an automatic conceptual indexing for texts and its extension for text and image documents. Tests are conducted on the multilingual image and text medical document corpus of the CLEF initiative, where we obtain best results on text in 2005 and 2006, and show promising results on images, and best results for the combination of image and text.
Towards a Functional Approach to Modular Ontologies using Institutions
"... Abstract. We propose a functional view of ontologies that emphasises their role in determining answers to queries, irrespective of the formalism in which they are written. A notion of framework is introduced that captures the situation of a global language into which both an ontology language and a ..."
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Abstract. We propose a functional view of ontologies that emphasises their role in determining answers to queries, irrespective of the formalism in which they are written. A notion of framework is introduced that captures the situation of a global language into which both an ontology language and a query language can be translated, in an abstract way. We then generalise existing notions of robustness from the literature, and relate these to interpolation properties that support modularisation of ontologies.
Annals of Mathematics and Artificial Intelligence manuscript No. (will be inserted by the editor) Congruence
, 2008
"... relations on some hyperstructures ..."
Using analogies to find and evaluate mathematical conjectures
"... Abstract. Analogical reasoning can shed light on both of the two key processes of creativity – generation and evaluation. Hence, it is a powerful tool for creativity. We illustrate this with three historical case studies of creative mathematical conjectures which were either found or evaluated via a ..."
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Abstract. Analogical reasoning can shed light on both of the two key processes of creativity – generation and evaluation. Hence, it is a powerful tool for creativity. We illustrate this with three historical case studies of creative mathematical conjectures which were either found or evaluated via analogies. We conclude by describing our ongoing efforts to build computational realisations of these ideas. 1