Measuring Relations Between Concepts In Conceptual Spaces

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 regions in this space. Our recent mathematical formalization of this framework is capable of representing correlations between different domains in a geometric way. In this paper, we extend our formalization by providing quantitative mathematical definitions for the notions of concept size, subsethood, implication, similarity, and betweenness. This considerably increases the representational power of our formalization by introducing measurable ways of describing relations between concepts.Comment: Accepted at SGAI 2017 (http://www.bcs-sgai.org/ai2017/). The final publication is available at Springer via https://doi.org/10.1007/978-3-319-71078-5_7. arXiv admin note: substantial text overlap with arXiv:1707.05165, arXiv:1706.0636

A Categorical Semantics of Fuzzy Concepts in Conceptual Spaces

We define a symmetric monoidal category modelling fuzzy concepts and fuzzy conceptual reasoning within G\"ardenfors' framework of conceptual (convex) spaces. We propose log-concave functions as models of fuzzy concepts, showing that these are the most general choice satisfying a criterion due to G\"ardenfors and which are well-behaved compositionally. We then generalise these to define the category of log-concave probabilistic channels between convex spaces, which allows one to model fuzzy reasoning with noisy inputs, and provides a novel example of a Markov category.Comment: In Proceedings ACT 2021, arXiv:2211.0110

Experience-Oriented Conceptual Space for Designing the System with Software

The design of any system with software is a behavioral process that encompasses a certain area of the physical space on the definite interval of time. The space of designing is useful for expressing in forms of the corresponding models. The paper presents a reflection of an operational space onto a conceptual space CS(t) that is experience-oriented. It can be achieved via question-answer interactions of designers with an accessible experience and it, in its turn, will facilitate increasing the success of designing

Formalized Conceptual Spaces with a Geometric Representation of Correlations

The highly influential framework of conceptual spaces provides a geometric way of representing knowledge. Instances are represented by points in a similarity 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 various operations for our formalization, both for creating new concepts from old ones and for measuring relations between concepts. We present an illustrative toy-example and sketch a research project on concept formation that is based on both our formalization and its implementation.Comment: Published in the edited volume "Conceptual Spaces: Elaborations and Applications". arXiv admin note: text overlap with arXiv:1706.06366, arXiv:1707.02292, arXiv:1707.0516

Similarity space theories and the problem of concept acquisition.

232 p.Uno de los principales problemas a los que se enfrenta el empirismo es el de explicar cómo se adquieren los elementos más básicos de los conceptos, sin recurrir para ello a elementos innatos preexistentes. El propósito de esta tesis es mostrar que los mejores argumentos nativistas en contra de la posibilidad de aprender conceptos (primitivos) dependen de la asunción de que los constituyentes de los conceptos deben estar disponibles de antemano, como entrada de los procesos de adquisición. No obstante, mostraré que nada obliga a aceptar esa asunción (de precedencia). De hecho, presentaré un modelo en donde los elementos constitutivos de un concepto resultan del mismo proceso de aprendizaje en virtud del cual ese concepto se adquiere. Mi propuesta está basada en una teoría de espacios de similaridad articulada mediante prototipos. Además pruebo: (A) que dos nociones distintas de concepto deben distinguirse en este tipo de aproximación, a saber, conceptos como almacenamiento y conceptos como instanciación; y (B) que una propuesta como ésta reúne virtudes tanto del ámbito invariantista como del contextualista. Argumento también que, si los conceptos son dependientes del contexto ¿según sostiene el contextualismo¿, entonces los conceptos instanciados carecen de persistencia mínima y, por ello, no pueden ser una representación de sus categorías asociadas

Metafictional anaphora:A comparison of different accounts

I argue that pronominal anaphora across mixed parafictional/ metafictional discourse (e.g. In The Lord of the Rings, Frodoi goes through an immense mental struggle. Hei is an intriguing fictional character! ) poses a problem for a workspace account. I evaluate different possible solutions based on a descriptivist approach, Zalta's logic of abstract objects and Recanati's dot-object theory