A case against convexity in conceptual spaces

Hernández-Conde, José V.

doi:10.1007/s11229-016-1123-z

Cited by 13 publications

(4 citation statements)

References 20 publications

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“…Since the beginning of Gärdenfors theory one of the most controversial constraint in his definition concerns convexity of the conceptual fields. One side of this dispute, with Gärdenfors at the helm, proclaimed that if two objects O 1 , O 2 belong to the same concept C then all objects located between them (in the geometric sense) should also have the same properties and therefore be inside C. The others like (Bechberger & Kühnberger, 2017;Hernández-Conde, 2017) reject this claim. Here we present solution that fit somewhere in between.…”

Section: General Overview Of the Papermentioning

confidence: 99%

Type-2 Fuzzy Sets and Newton’s Fuzzy Potential in an Algorithm of Classification Objects of a Conceptual Space

Jagiełło

Lisowski

Urban

2022

J of Log Lang and Inf

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This paper deals with Gärdenfors’ theory of conceptual spaces. Let $${\mathcal {S}}$$ S be a conceptual space consisting of 2-type fuzzy sets equipped with several kinds of metrics. Let a finite set of prototypes $$\tilde{P}_1,\ldots ,\tilde{P}_n\in \mathcal {S}$$ P ~ 1 , … , P ~ n ∈ S be given. Our main result is the construction of a classification algorithm. That is, given an element $${\tilde{A}}\in \mathcal {S},$$ A ~ ∈ S , our algorithm classifies it into the conceptual field determined by one of the given prototypes $$\tilde{P}_i.$$ P ~ i . The construction of our algorithm uses some physical analogies and the Newton potential plays a significant role here. Importantly, the resulting conceptual fields are not convex in the Euclidean sense, which we believe is a reasonable departure from the assumptions of Gardenfors’ original definition of the conceptual space. A partitioning algorithm of the space $$\mathcal {S}$$ S is also considered in the paper. In the application section, we test our classification algorithm on real data and obtain very satisfactory results. Moreover, the example we consider is another argument against requiring convexity of conceptual fields.

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Section: General Overview Of the Papermentioning

confidence: 99%

Type-2 Fuzzy Sets and Newton’s Fuzzy Potential in an Algorithm of Classification Objects of a Conceptual Space

Jagiełło

Lisowski

Urban

2022

J of Log Lang and Inf

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“…Based on the principle of cognitive economy, Gärdenfors argues that both properties and concepts should be represented as convex sets. However, this convexity assumption has recently been criticized [19] and we demonstrated in [7] that one cannot geometrically encode correlations between domains when using convex sets: The left part of Figure 1 shows two domains, age and height, and the concepts of child and adult. The solid ellipses illustrate the intuitive way of defining these concepts.…”

Section: Properties and Conceptsmentioning

confidence: 99%

A Comprehensive Implementation of Conceptual Spaces

Bechberger¹,

Kühnberger²

2017

Preprint

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The highly influential framework of conceptual spaces provides a geometric way of representing knowledge. Instances are represented by points and concepts are represented by regions in a (potentially) high-dimensional space. Based on our recent formalization, we present a comprehensive implementation of the conceptual spaces framework that is not only capable of representing concepts with inter-domain correlations, but that also offers a variety of operations on these concepts.

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“…The TTCS system takes in input a pair t, ctx t where t is a term and ctx t is the context in which t occurs, 4 and produces as output a set of attribute-value pairs:…”

Section: Ttcs: Terms To Conceptual Spacesmentioning

confidence: 99%

“…The paper is structured as follows: we first survey related literature, elaborate on the existing approaches and about the differences with the current proposal (Section 2); we then illustrate in full detail the strategy implemented by the TTCS system and report 1 Recently the convexity constraint of conceptual spaces has been argued as a plausible but not necessary condition for the characterisation of concepts within this framework in the case, for example, of the adoption of non-euclidean metrics (see [4]). In our case-study we considered such constraint as proposed in the original theory since we didn't consider non-euclidean metrics.…”

Section: Introductionmentioning

confidence: 99%

A Resource-Driven Approach for Anchoring Linguistic Resources to Conceptual Spaces

Lieto

Mensa

Radicioni

2016

AI*IA 2016 Advances in Artificial Intelligence

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Abstract. In this paper we introduce the TTCS system, so named after Terms To Conceptual Spaces, that exploits a resource-driven approach relying on BabelNet, NASARI and ConceptNet. TTCS takes in input a term and its context of usage and produces as output a specific type of vector-based semantic representation, where conceptual information is encoded through the Conceptual Spaces (a geometric framework for common-sense knowledge representation and reasoning). The system has been evaluated in a twofold experimentation. In the first case we assessed the quality of the extracted common-sense conceptual information with respect to human judgments with an online questionnaire. In the second one we compared the performances of a conceptual categorization system that was run twice, once fed with extracted annotations and once with hand-crafted annotations. In both cases the results are encouraging and provide precious insights to make substantial improvements.

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A case against convexity in conceptual spaces

Cited by 13 publications

References 20 publications

Type-2 Fuzzy Sets and Newton’s Fuzzy Potential in an Algorithm of Classification Objects of a Conceptual Space

Type-2 Fuzzy Sets and Newton’s Fuzzy Potential in an Algorithm of Classification Objects of a Conceptual Space

A Comprehensive Implementation of Conceptual Spaces

A Resource-Driven Approach for Anchoring Linguistic Resources to Conceptual Spaces

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