• Corpus ID: 14963629

Reasoning about Categories in Conceptual Spaces

@inproceedings{Grdenfors2001ReasoningAC,
  title={Reasoning about Categories in Conceptual Spaces},
  author={Peter G{\"a}rdenfors and Mary-Anne Williams},
  booktitle={IJCAI},
  year={2001}
}
Understanding the process of categorization is a primary research goal in artificial intelligence. The conceptual space framework provides a flexible approach to modeling context-sensitive categorization via a geometrical representation designed for modeling and managing concepts. In this paper we show how algorithms developed in computational geometry, and the Region Connection Calculus can be used to model important aspects of categorization in conceptual spaces. In particular, we demonstrate… 
cs.nyu.edu
104 Citations
Highly Influential Citations
9
Background Citations
43
Methods Citations
9

104 Citations

Citation Type

Citation Type

A Metric Conceptual Space Algebra
TLDR
This paper presents a metric conceptual space algebra that is designed to facilitate the creation of conceptual space knowledge bases and inferencing systems and demonstrates the applicability of the algebra to spatial information systems with a proof-of-concept application.
Qualitative Reasoning about Incomplete Categorization Rules Based on Interpolation and Extrapolation in Conceptual Spaces
TLDR
This paper relies on Gardenfors conceptual spaces, which allow us to express semantic relationships with a geometric flavor, and takes the inherently qualitative notion of betweenness as primitive, and shows how it naturally leads to patterns of interpolative reasoning.
Data-driven Conceptual Spaces: Creating Semantic Representations For Linguistic Descriptions Of Numerical Data
TLDR
A principled approach to automatically construct a conceptual space from a set of known observations wherein the quality dimensions and domains are not known a priori, while preserving the semantic interpretation that is needed to infer linguistic descriptions for interaction with humans.
Reasoning about Betweenness and RCC8 Constraints in Qualitative Conceptual Spaces
TLDR
This work considers the problem of deciding whether an RCC8 network extended with constraints about betweenness can be realized using bounded and convex regions in a high-dimensional Euclidean space and introduces an important fragment for which deciding realizability is NP-complete.
Representing Properties in Conceptual Spaces towards Effective Learning within Intelligent Agents
  • Ickjai Lee
  • Mathematics, Computer Science
    International Conference on Computational Intelligence for Modelling, Control and Automation and International Conference on Intelligent Agents, Web Technologies and Internet Commerce (CIMCA-IAWTIC'06)
  • 2005
TLDR
This paper uses the Voronoi diagram and its dual Delaunay triangulation to define indeterminate property boundaries with lower and upper bounds and compares and contrast this approach with some other polygonization methods.
Conceptual Ternary Diagrams for Shape Perception: A Preliminary Step
This work-in-progress provides a preliminary cognitive investigation of how the external visualization of the Ternary diagram (TD) might be used as an underlying model for exploring the…
A Categorical Semantics of Fuzzy Concepts in Conceptual Spaces
  • S. Tull
  • Computer Science, Mathematics
    ArXiv
  • 2021
TLDR
The category of log-concave probabilistic channels between convex spaces is defined, which allows one to model fuzzy reasoning with noisy inputs, and provides a novel example of a Markov category.
Lexical inference as a spatial reasoning problem
TLDR
This paper argues that most of the lexical relations that the authors need for plausible reasoning can be identified with qualitative spatial relations in semantic spaces, i.e. highdimensional Euclidean spaces in which words are represented as geometric objects.
An Empirical Study of Knowledge Representation and Learning within Conceptual Spaces for Intelligent Agents
  • Ickjai Lee, B. Portier
  • Computer Science
    6th IEEE/ACIS International Conference on Computer and Information Science (ICIS 2007)
  • 2007
TLDR
Experimental results demonstrates conceptual spaces are superior to mere multidimensional feature spaces in concept learning and confirm the virtue of conceptual spaces.
Spatial Semantics in Difference Spaces
TLDR
This work describes the following semantic frameworks: category-based ontologies, conceptual spaces, affordance based models, image schemata, and multi representation, explaining how each can be projected to a model based on differences.
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 21 REFERENCES
Qualitative Spatial Representation and Reasoning with the Region Connection Calculus
TLDR
This paper surveys the work of the qualitative spatial reasoning group at the University of Leeds and motivates the use of regions as the primary spatial entity and shows how a rich language can be built up from surprisingly few primitives.
Logical representations for automated reasoning about spatial relationships
TLDR
It is proved that entailment, which is valid according to the standard semantics for these logics, is also valid with respect to the spatial interpretation and well-known mechanisms for propositional reasoning can be applied to spatial reasoning.
On the Complexity of Qualitative Spatial Reasoning: A Maximal Tractable Fragment of the Region Connection Calculus
TLDR
It is proved that reasoning is NP-complete in general and identified a maximal tractable subset of the relations in RCC-8 that contains all base relations and shows that for this subset path-consistency is sufficient for deciding consistency.
Representing Spatial Vagueness: A Mereological Approach
TLDR
An axiomatisation of a relation of `crisping' (reducing imprecision or vagueness) between pairs of`vague' spatial regions: those with indeterminate boundaries is developed.
Categories and Concepts: Theoretical Views and Inductive Data Analysis
General introduction - purpose, underlying ideas and scope of the book, Iven Van Mechelen and Ryszard S. Michalski. Part 1 Theoretical views: psychological models of concepts - introduction, James…
Voronoi diagrams—a survey of a fundamental geometric data structure
Computational geometry is concerned with the design and analysis of algorithms for geometrical problems. In addition, other more practically oriented, areas of computer science— such as computer…
Computational Properties of Qualitative Spatial Reasoning: First Results
  • B. Nebel
  • Mathematics, Computer Science
    KI
  • 1995
TLDR
This paper focuses on the so-called RCC approach and uses Bennett's encoding of spatial reasoning in intuitionistic logic in order to show that consistency checking for the topological base relations can be done efficiently and proves path-consistency is sufficient for deciding global consistency.
Conceptual Spaces — The Geometry of Thought
nightmare—small changes in the intended semantics of predicates or procedures cause large and usually catastrophic changes in performance. There have been, I think, two responses to this. One is owed…
An architecture for autonomous agents exploiting conceptual representations
An architecture for autonomous agents is proposed that integrates the functional and the behavioral approaches to robotics. The integration is based on the introduction of a conceptual level, linking…
On the complexity ofd- dimensional Voronoi diagrams
Abstract : For n points p1,..., pn of Euclidean d-space E superscript d, the associated Voronoi diagram V(p1,...,pn) is a sequence (P1,...,Pn) of convex polyhedra covering E superscript d, where pi…
...
1
2
3
...