This article takes a cognitive approach to natural concepts. The aim is to introduce criteria that are evaluated with respect to how they support the cognitive economy of humans when using concepts in reasoning and communicating with them. I first present the theory of conceptual spaces as a tool for expressing the criteria. Then I introduce the central idea that natural concepts correspond to _convex_ regions of a conceptual space. I argue that this criterion has far-reaching consequences as regards natural (...) concepts. Partly following earlier work, I present some other criteria that further delimit the class of natural concepts. One of these is coherence, which does not seem to have been discussed previously. Finally, I show that convexity and other criteria make it possible to ensure that people mean the same thing when they communicate using concepts. Apart from its philosophical interest, the analysis presented in the article will be relevant for tasks of conceptual engineering in artificial systems that work with concepts. (shrink)

Category-based induction is an inferential mechanism that uses knowledge of conceptual relations in order to estimate how likely is for a property to be projected from one category to another. During the last decades, psychologists have identified several features of this mechanism, and they have proposed different formal models of it. In this article; we propose a new mathematical model for category-based induction based on distances on conceptual spaces. We show how this model can predict most of the properties of (...) this kind of reasoning while providing a solid theoretical foundation for it. We also show that it subsumes some of the previous models proposed in the literature and that it generates new predictions. (shrink)

This paper extends earlier work by its authors on formal aspects of the processes of contracting a theory to eliminate a proposition and revising a theory to introduce a proposition. In the course of the earlier work, Gardenfors developed general postulates of a more or less equational nature for such processes, whilst Alchourron and Makinson studied the particular case of contraction functions that are maximal, in the sense of yielding a maximal subset of the theory (or alternatively, of one (...) of its axiomatic bases), that fails to imply the proposition being eliminated. In the present paper, the authors study a broader class, including contraction functions that may be less than maximal. Specifically, they investigate "partial meet contraction functions", which are defined to yield the intersection of some nonempty family of maximal subsets of the theory that fail to imply the proposition being eliminated. Basic properties of these functions are established: it is shown in particular that they satisfy the Gardenfors postulates, and moreover that they are sufficiently general to provide a representation theorem for those postulates. Some special classes of partial meet contraction functions, notably those that are "relational" and "transitively relational", are studied in detail, and their connections with certain "supplementary postulates" of Gardenfors investigated, with a further representation theorem established. (shrink)

A computational theory of induction must be able to identify the projectible predicates, that is to distinguish between which predicates can be used in inductive inferences and which cannot. The problems of projectibility are introduced by reviewing some of the stumbling blocks for the theory of induction that was developed by the logical empiricists. My diagnosis of these problems is that the traditional theory of induction, which started from a given (observational) language in relation to which all inductive rules are (...) formulated, does not go deep enough in representing the kind of information used in inductive inferences. As an interlude, I argue that the problem of induction, like so many other problems within AI, is a problem of knowledge representation. To the extent that AI-systems are based on linguistic representations of knowledge, these systems will face basically the same problems as did the logical empiricists over induction. In a more constructive mode, I then outline a non-linguistic knowledge representation based on conceptual spaces. The fundamental units of these spaces are "quality dimensions". In relation to such a representation it is possible to define "natural" properties which can be used for inductive projections. I argue that this approach evades most of the traditional problems. (shrink)

It is argued that it is not sufficient to consider only the sentences included in the explanans and explanandum when determining whether they constitute an explanation, but these sentences must always be evaluated relative to a knowledge situation. The central criterion on an explanation is that the explanans in a non-trivial way increases the belief value of the explanandum, where the belief value of a sentence is determined from the given knowledge situation. The outlined theory of explanations is applied to (...) some well-known examples and is also compared to other theories of explanation. (shrink)

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. (shrink)

Conceptual spaces have become an increasingly popular modeling tool in cognitive psychology. The core idea of the conceptual spaces approach is that concepts can be represented as regions in similarity spaces. While it is generally acknowledged that not every region in such a space represents a natural concept, it is still an open question what distinguishes those regions that represent natural concepts from those that do not. The central claim of this paper is that natural concepts are represented by the (...) cells of an optimally designed similarity space. (shrink)

We trace the difference between the ways in which apes and humans co–operate to differences in communicative abilities, claiming that the pressure for future–directed co–operation was a major force behind the evolution of language. Competitive co–operation concerns goals that are present in the environment and have stable values. It relies on either signalling or joint attention. Future–directed co–operation concerns new goals that lack fixed values. It requires symbolic communication and context–independent representations of means and goals. We analyse these ways of (...) co–operating in game–theoretic terms and submit that the co–operative strategy of games that involve shared representations of future goals may provide new equilibrium solutions. (shrink)

In this entertaining work, Peter Grdenfors embarks on an evolutionary detective story to try and solve one of the big mysteries surrounding human existence - how has the modern human being's way of thinking come into existence. Immensely readable and full of humorous insights, the book will be valuable for students in psychology and biology, and accessible to readers of popular science.

Decision theory and the theory of rational choice have recently been the subjects of considerable research by philosophers and economists. However, no adequate anthology exists which can be used to introduce students to the field. This volume is designed to meet that need. The essays included are organized into five parts covering the foundations of decision theory, the conceptualization of probability and utility, pholosophical difficulties with the rules of rationality and with the assessment of probability, and causal decision theory. The (...) editors provide an extensive introduction to the field and introductions to each part. (shrink)

This paper offers a novel way of reconstructing conceptual change in empirical theories. Changes occur in terms of the structure of the dimensions—that is to say, the conceptual spaces—underlying the conceptual framework within which a given theory is formulated. Five types of changes are identified: (1) addition or deletion of special laws, (2) change in scale or metric, (3) change in the importance of dimensions, (4) change in the separability of dimensions, and (5) addition or deletion of dimensions. Given this (...) classification, the conceptual development of empirical theories becomes more gradual and rationalizable. Only the most extreme type—replacement of dimensions—comes close to a revolution. The five types are exemplified and applied in a case study on the development within physics from the original Newtonian mechanics to special relativity theory. (shrink)

Many animal species use tools, but human technical engagement is more complex. We argue that there is coevolution between technical engagement and advanced forms of causal cognition in the human lineage. As an analytic tool, we present a classification of different forms of causal thinking. Human causal thinking has become detached from space and time, so that instead of just reacting to perceptual input, our minds can simulate actions and forces and their causal consequences. Our main thesis is that, unlike (...) the situation for other primate species, an increasing emphasis on technical engagement made some hominins capable of reasoning about the forces involved in causal processes. This thesis is supported in three ways: We compare the casual thinking about forces of hominins with that of other primates. We analyze the causal thinking required for Stone Age hunting technologies such as throwing spears, bow hunting and the use of poisoned arrows, arguing that they may serve as examples of the expansion of casual cognition about forces. We present neurophysiological results that indicate the facilitation of advanced causal thinking. (shrink)

It is argued that early language learning in children emerges from five primary knowledge structures: Space, objects, actions, number and events. These structures constitute the basis for the semantic domains that are used to form categories that represent the meanings of early words. The domains are naturally modeled in conceptual spaces that are based on geometric notions rather than on symbolic representations. It is shown how these semantics domains can be used to generate an epigenetic model of language acquisition. The (...) four first primary knowledge systems are used for prepositions, nouns, verbs and quantifiers respectively, while events form the meanings of declarative sentences. This semantic model leads to direct recommendations for how the model can be implemented in robots and other artificial systems. (shrink)

Spaces in the brain can refer either to psychological spaces, which are derived from similarity judgments, or to neurocognitive spaces, which are based on the activities of neural structures. We want to show how psychological spaces naturally emerge from the underlying neural spaces by dimension reductions that preserve similarity structures and the relevant categorizations. Some neuronal representational formats that may generate the psychological spaces are presented, compared and discussed in relation to the mathematical principles of monotonicity, continuity and convexity. In (...) particular, we discuss the spatial structures involved in the connections between perception and action, for example eye-hand coordination, and argue that spatial organization of information makes such mappings more efficient. (shrink)

This article presents two learning processes in order to explain how children at an early age can transform a complex sensory input to concepts and categories. The first process constructs the perceptual structures that emerge in children’s cognitive development by detecting invariants in the sensory input. The invariant structures involve a reduction in dimensionality of the sensory information. It is argued that this process generates the primary domains of space, objects and actions and that these domains can be represented as (...) conceptual spaces. Once the primary domains have been established, the second process utilizes covariances between different dimensions of the domains in order to identify natural clusters of entities. The clusters are then are used to determine concepts as regions in the spaces. As an application, the processes are used to resolve the so-called ‘complex first paradox’ that emerges from the fact that children, in general, learn nouns earlier than adjectives, even though nouns are semantically more complex than adjectives. (shrink)

This edited book focuses on concepts and their applications using the theory of conceptual spaces, one of today’s most central tracks of cognitive science discourse. It features 15 papers based on topics presented at the Conceptual Spaces @ Work 2016 conference. The contributors interweave both theory and applications in their papers. Among the first mentioned are studies on metatheories, logical and systemic implications of the theory, as well as relations between concepts and language. Examples of the latter include explanatory models (...) of paradigm shifts and evolution in science as well as dilemmas and issues of health, ethics, and education. The theory of conceptual spaces overcomes many translational issues between academic theoretization and practical applications. The paradigm is mainly associated with structural explanations, such as categorization and meronomy. However, the community has also been relating it to relations, functions, and systems. The book presents work that provides a geometric model for the representation of human conceptual knowledge that bridges the symbolic and the sub-conceptual levels of representation. The model has already proven to have a broad range of applicability beyond cognitive science and even across a number of disciplines related to concepts and representation. (shrink)

Examines the link between nonmonotonic inference relations and theory revision operations, focusing on the correspondence between abstract properties which each may satisfy.

This paper concerns voting with logical consequences, which means that anybody voting for an alternative x should vote for the logical consequences of x as well. Similarly, the social choice set is also supposed to be closed under logical consequences. The central result of the paper is that, given a set of fairly natural conditions, the only social choice functions that satisfy social logical closure are oligarchic (where a subset of the voters are decisive for the social choice). The set (...) of conditions needed for the proof include a version of Independence of Irrelevant Alternatives that also plays a central role in Arrow's impossibility theorem. (Published Online July 11 2006) Footnotes1 Much of this article was written while the author was a fellow at the Swedish Collegium for Advanced Study in the Social Sciences (SCASSS) in Uppsala. I want to thank the Collegium for providing me with excellent working conditions. Wlodek Rabinowicz and other fellows gave me valuable comments at a seminar at SCASSS when an early version of the paper was presented. I also want to thank Luc Bovens, Franz Dietrich, Christian List and an anonymous referee for their excellent comments on a later version. The final version was prepared during a stay at Oxford University for which I am grateful to the British Academy. (shrink)

Within analytic philosophy, induction has been seen as a problem concerning inferences that have been analysed as relations between sentences. In this article, we argue that induction does not primarily concern relations between sentences, but between properties and categories. We outline a new approach to induction that is based on two theses. The first thesis is epistemological. We submit that there is not only knowledge-how and knowledge-that, but also knowledge-what. Knowledge-what concerns relations between properties and categories and we argue that (...) it cannot be reduced to knowledge-that. We support the partition of knowledge by mapping it onto the long-term memory systems: procedural, semantic and episodic memory. The second thesis is that the role of inductive reasoning is to generate knowledge-what. We use conceptual spaces to model knowledge-what and the relations between properties and categories involved in induction. (shrink)

Within analytic philosophy, induction has been seen as a problem concerning inferences that have been analysed as relations between sentences. In this article, we argue that induction does not primarily concern relations between sentences, but between properties and categories. We outline a new approach to induction that is based on two theses. The first thesis is epistemological. We submit that there is not only knowledge-how and knowledge-that, but also knowledge-what. Knowledge-what concerns relations between properties and categories and we argue that (...) it cannot be reduced to knowledge-that. We support the partition of knowledge by mapping it onto the long-term memory systems: procedural, semantic and episodic memory. The second thesis is that the role of inductive reasoning is to generate knowledge-what. We use conceptual spaces to model knowledge-what and the relations between properties and categories involved in induction. (shrink)

We present an account of semantics that is not construed as a mapping of language to the world but rather as a mapping between individual meaning spaces. The meanings of linguistic entities are established via a “meeting of minds.” The concepts in the minds of communicating individuals are modeled as convex regions in conceptual spaces. We outline a mathematical framework, based on fixpoints in continuous mappings between conceptual spaces, that can be used to model such a semantics. If concepts are (...) convex, it will in general be possible for interactors to agree on joint meaning even if they start out from different representational spaces. Language is discrete, while mental representations tend to be continuous—posing a seeming paradox. We show that the convexity assumption allows us to address this problem. Using examples, we further show that our approach helps explain the semantic processes involved in the composition of expressions. (shrink)

A general criterion for the theory of belief revision is that when we revise a state of belief by a sentence A, as much of the old information as possible should be retained in the revised state of belief. The motivating idea in this paper is that if a belief B is irrelevant to A, then B should still be believed in the revised state. The problem is that the traditional definition of statistical relevance suffers from some serious shortcomings and (...) cannot be used as a tool for defining belief revision processes. In particular, the traditional definition violates the requirement that if A is irrelevant to C and B is irrelevant to C, then A&B is irrelevant to C. In order to circumvent these drawbacks, I develop an amended notion of relevance which has the desired properties. On the basis of the new definition, I outline how it can be used to simplify a construction of a belief revision method. (shrink)

Several conditions for being an intrinsically intentional agent are put forward. On a first level of intentionality the agent has representations. Two kinds are described: cued and detached. An agent with both kinds is able to represent both what is prompted by the context and what is absent from it. An intermediate level of intentionality is achieved by having an inner world, that is, a coherent system of detached representations that model the world. The inner world is used, e.g., for (...) conditional and counterfactual thinking. Contextual or indexical representations are necessary in order that the inner world relates to the actual external world and thus can be used as a basis for action. To have full-blown intentionality, the agent should also have a detached self-awareness, that is, be able to entertain self-representations that are independent of the context. (shrink)

Using probability functions defined over a simple language as models of states of belief, my goal in this article has been to analyse contractions and revisions of beliefs. My first strategy was to formulate postulates for these processes. Close parallels between the postulates for contractions and the postulates for revisions have been established - the results in Section 5 show that contractions and revisions are interchangeable. As a second strategy, some suggestions for more or less explicit constructive definitions of the (...) revision process (and indirectly also of the contraction process) were then presented. However, the results in Section 6 are less conclusive than in the earlier ones. This problem area still awaits further development. (shrink)