A Thorough Formalization of Conceptual Spaces

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Title: A Thorough Formalization of Conceptual Spaces
Authors: Lucas, Bechberger
Kai-Uwe, K√ľhnberger
Abstract: The highly influential framework of conceptual spaces provides a geometric way of representing knowledge. Instances are represented by points in a high-dimensional space and concepts are represented by convex regions in this space. After pointing out a problem with the convexity requirement, we propose a formalization of conceptual spaces based on fuzzy star-shaped sets. Our formalization uses a parametric definition of concepts and extends the original framework by adding means to represent correlations between different domains in a geometric way. Moreover, we define computationally efficient operations on concepts (intersection, union, and projection onto a subspace) and show that these operations can support both learning and reasoning processes.
Citations: Buchtitel: "KI 2017: Advances in Artificial Intelligence: 40th Annual German Conference on AI, Dortmund, Germany, September 25--29, 2017, Proceedings"; Seiten: "58-71" Herausgeber/Verlag: "Springer International Publishing"; Jahr: "2017"; Serie: "Lecture Notes in Computer Science"; Volume = "10505"
URL: https://doi.org/10.1007/978-3-319-67190-1_5
ISBN: 978-3-319-67190-1
Subject Keywords: Conceptual Spaces; Star-Shaped Sets; Fuzzy Sets
Issue Date: 8-Feb-2018
Type of publication: Konferenzver√∂ffentlichung [ConferenceObject]
Appears in Collections:FB08 - Hochschulschriften

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