Conceptual Spaces as Philosophers’ Tools

2015

This introductory chapter provides a non-technical presentation of conceptual spaces as a representational framework for modeling different kinds of similarity relations in various cognitive domains. Moreover, we briefly summarize each chapter.

Kybernetes, 2005

Minds and Machines, 2007

Synthese Library, 2019

A recent naturalistic epistemological account suggests that there are three nested basic forms of knowledge: procedural knowledge-how, conceptual knowledge-what, and propositional knowledge-that. These three knowledgeforms are grounded in cognitive neuroscience and are mapped to procedural, semantic, and episodic long-term memory respectively. This article investigates and integrates the neuroscientifically grounded account with knowledge-accounts from cognitive ethology and cognitive psychology. It is found that procedural and semantic memory, on a neuroscientific level of analysis, matches an ethological reliabilist account. This formation also matches System 1 from dual process theory on a psychological level, whereas the addition of episodic memory, on the neuroscientific level of analysis, can account for System 2 on the psychological level. It is furthermore argued that semantic memory (conceptual knowledge-what) and the cognitive ability of categorization are linked to each other, and that they can be fruitfully modeled within a conceptual spaces framework.

Types are fundamental for conceptual domain modeling and knowledge representation in computer science. Frequently, mo- nadic types used in domain models have as their instances objects (endurants, continuants), i.e., entities persisting in time that experi- ence qualitative changes while keeping their numerical identity. In this paper, I revisit a philosophically and cognitively well-founded theory of object types and propose a system of modal logics with re- stricted quantification designed to formally characterize the distinc- tions and constraints proposed by this theory. The formal system proposed also addresses the limitations of classical (unrestricted ex- tensional) modal logics in differentiating between types that repre- sent mere properties (or attributions) ascribed to individual objects from types that carry a principle of identity for those individuals (the so-called sortal types). Finally, I also show here how this proposal can complement the theory of conceptual spaces by offering an ac- count for kind-supplied principles of cross-world identity. The ac- count addresses an important criticism posed to conceptual spaces in the literature and is in line with a number of empirical results in the literature of cognitive psychology.

How people acquire and classify knowledge, interrelate classified knowledge and apply it in solving problems remains a central question in cognition research. notes "Concept learning has been the primary focus of machine learning research" (p.2). Within the past two decades a probabilistic understanding of concepts emerged and attracted many researchers. It now appears probabilistic theories are less powerful than initially thought. Keil (1989) and Medin (1989), for example, are re-evaluating concept theories. Medin (1989) observes "the viability of probabilistic view theories...is being seriously questioned" (p. 1473) and Keil (1989) argues "concepts are not mere probabilistic distributions of features or properties or passive reflections of feature frequencies and correlations in the world " (p. 1).

It is well known that classical set theory is not expressive enough to adequately model categorization and prototype theory. Recent work on compositionality and concept determination showed that the quantitative solution initially offered by classical fuzzy logic also led to important drawbacks. Several qualitative approaches were thereafter tempted, that aimed at modelling membership through ordinal scales or lattice fuzzy sets. Most of the solutions obtained by these theoretical constructions however are of difficult use in categorization theory. We propose a simple qualitative model in which membership relative to a given concept f is represented by a function that takes its value in an abstract set A f equipped with a bounded total order. This function is recursively built through a stratification of the set of concepts at hand based on a notion of complexity. Similarly, the typicality associated with a concept f will be described using an ordering that takes into account the characteristic features of f . Once the basic notions of membership and typicality are set, the study of compound concepts is possible and leads to interesting results. In particular, we investigate the internal structure of concepts, and obtain the characterization of all smooth subconcepts of a given concept.

Journal of Philosophical Logic, 2013

The conceptual spaces approach has recently emerged as a novel account of concepts. Its guiding idea is that concepts can be represented geometrically, by means of metrical spaces. While it is generally recognized that many of our concepts are vague, the question of how to model vagueness in the conceptual spaces approach has not been addressed so far, even though the answer is far from straightforward. The present paper aims to fill this lacuna.

The dominating models of information processes have been based on symbolic representations of information and knowledge. During the last decades, a variety of non-symbolic models have been proposed as superior. The prime examples of models within the non-symbolic approach are neural networks. However, to a large extent they lack a higher-level theory of representation. In this paper, conceptual spaces are suggested as an appropriate framework for non-symbolic models. Conceptual spaces consist of a number of “quality dimensions” that often are derived from perceptual mechanisms. It will be outlined how conceptual spaces can represent various kind of information and how they can be used to describe concept learning. The connections to prototype theory will also be presented.

Cognitive semantics has been proposed by as an alternative to truth-conditional semantics that models the relationship between language and mental representations of cognitive agents. Similar motivations emerged in philosophical logic, since a number of non-classical logics have been interpreted as modelling the reasoning capability of a knowing subject. In particular, relevant logics have been discussed as logics of information in . In a recent paper, tightened the connection between the tradition of cognitive semantics and relevant logics, by providing a model of a propositional relevant logic in terms of conceptual spaces. There, the interpretation is restricted to propositions that correspond to predications of properties. This restriction is motivated by the fact that, besides a recent treatment of the part-whole relation , a precise and general method to represent n-ary relations in conceptual spaces isas we will try to better motivate in the rest of the paper-still missing. In our view, this is also linked to the fact that the aim of conceptual spaces is to rep-