Learning and Reasoning with Conceptual Space
Representations
Zied Bouraoui
Centre de Recherche en Informatique de Lens (CRIL)-CNRS UMR 8188, Artois University, France



Conceptual spaces were proposed by Gärdenfors as an intermediate representation level between symbolic
and connectionist representations [1]. They are geometric representations of knowledge, in which the
objects from some domain of interest (e.g. movies) are represented as points in a metric space, and
concepts (e.g. comedy) or properties (e.g. scary) are modelled as (possibly vague) convex regions. As
such, they are similar in spirit to vector space representations that have been proposed and largely used
in NLP and machine learning, but there are also notable differences. Conceptual spaces support the view
that symbolic knowledge can be expressed as qualitative constraints on some underlying geometric
model. While the theory of conceptual spaces offers an elegant solution to combine symbolic and vector
representations, in practice, it is often difficult to learn region-based representations of concepts from
data. In this talk, we will discuss learning and reasoning with conceptual spaces. I will present some
methods for learning suitable entity embedding (e.g. [2]), and region-based representations of concepts
(e.g. [3, 4]). I will show how meaningful (interpretable) dimensions can be discovered and organised
into domains from a given vector representation in an unsupervised fashion (e.g. [5, 6, 7]). Finally, I will
present some examples of reasoning with conceptual spaces (e.g. [8, 9]).


References
[1] P. Gärdenfors, Conceptual spaces: The geometry of thought, MIT press, 2000.
[2] S. Jameel, Z. Bouraoui, S. Schockaert, Member: Max-margin based embeddings for entity retrieval,
    in: N. Kando, T. Sakai, H. Joho, H. Li, A. P. de Vries, R. W. White (Eds.), Proceedings of the 40th
    International ACM SIGIR Conference on Research and Development in Information Retrieval,
    Shinjuku, Tokyo, Japan, August 7-11, 2017, ACM, 2017, pp. 783–792. URL: https://doi.org/10.1145/
    3077136.3080803. doi:10.1145/3077136.3080803.
[3] Z. Bouraoui, S. Schockaert, Learning conceptual space representations of interrelated concepts,
    in: J. Lang (Ed.), Proceedings of the Twenty-Seventh International Joint Conference on Artificial
    Intelligence, IJCAI 2018, July 13-19, 2018, Stockholm, Sweden, ijcai.org, 2018, pp. 1760–1766. URL:
    https://doi.org/10.24963/ijcai.2018/243. doi:10.24963/ijcai.2018/243.
[4] Z. Bouraoui, J. Camacho-Collados, L. E. Anke, S. Schockaert, Modelling semantic categories using
    conceptual neighborhood, in: The Thirty-Fourth AAAI Conference on Artificial Intelligence, AAAI
    2020, The Thirty-Second Innovative Applications of Artificial Intelligence Conference, IAAI 2020,
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    York, NY, USA, February 7-12, 2020, AAAI Press, 2020, pp. 7448–7455. URL: https://ojs.aaai.org/index.
    php/AAAI/article/view/6241.
[5] R. Alshaikh, Z. Bouraoui, S. S. Jeawak, S. Schockaert, A mixture-of-experts model for learning multi-
    facet entity embeddings, in: D. Scott, N. Bel, C. Zong (Eds.), Proceedings of the 28th International

STRL’22: First International Workshop on Spatio-Temporal Reasoning and Learning, July 24, 2022, Vienna, Austria
$ zied.bouraoui@cril.fr (Z. Bouraoui)
                                    © 2022 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
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    Conference on Computational Linguistics, COLING 2020, Barcelona, Spain (Online), December
    8-13, 2020, International Committee on Computational Linguistics, 2020, pp. 5124–5135. URL: https:
    //doi.org/10.18653/v1/2020.coling-main.449. doi:10.18653/v1/2020.coling-main.449.
[6] R. Alshaikh, Z. Bouraoui, S. Schockaert, Learning conceptual spaces with disentangled facets,
    in: M. Bansal, A. Villavicencio (Eds.), Proceedings of the 23rd Conference on Computational
    Natural Language Learning, CoNLL 2019, Hong Kong, China, November 3-4, 2019, Associa-
    tion for Computational Linguistics, 2019, pp. 131–139. URL: https://doi.org/10.18653/v1/K19-1013.
    doi:10.18653/v1/K19-1013.
[7] R. Alshaikh, Z. Bouraoui, S. Schockaert, Hierarchical linear disentanglement of data-driven concep-
    tual spaces, in: C. Bessiere (Ed.), Proceedings of the Twenty-Ninth International Joint Conference
    on Artificial Intelligence, IJCAI 2020, ijcai.org, 2020, pp. 3573–3579. URL: https://doi.org/10.24963/
    ijcai.2020/494. doi:10.24963/ijcai.2020/494.
[8] Z. Bouraoui, S. Jameel, S. Schockaert, Inductive reasoning about ontologies using conceptual spaces,
    in: S. Singh, S. Markovitch (Eds.), Proceedings of the Thirty-First AAAI Conference on Artificial
    Intelligence, February 4-9, 2017, San Francisco, California, USA, AAAI Press, 2017, pp. 4364–4370.
    URL: http://aaai.org/ocs/index.php/AAAI/AAAI17/paper/view/14916.
[9] Z. Bouraoui, S. Konieczny, T. M. N. Schwind, I. Varzinczak, Region-based merging of open-domain
    terminological knowledge, in: Proceedings of the 19th International Conference on Principles of
    Knowledge Representation and Reasoning, KR 2022, 2022.