Abstract. The aim of this paper is to present a topological method for constructing discretizations (tessellations) of conceptual spaces. The method works for a class of topological spaces that the Russian mathematician Pavel Alexandroff defined more than 80 years ago. Alexandroff spaces, as they are called today, have many interesting properties that distinguish them from other topological spaces. In particular, they exhibit a 1-1 correspondence between their specialization orders and their topological structures. Recently, a special type of Alexandroff spaces was (...) used by Ian Rumfitt to elucidate the logic of vague concepts in a new way. According to his approach, conceptual spaces such as the color spectrum give rise to classical systems of concepts that have the structure of atomic Boolean algebras. More precisely, concepts are represented as regular open regions of an underlying conceptual space endowed with a topological structure. Something is subsumed under a concept iff it is represented by an element of the conceptual space that is maximally close to the prototypical element p that defines that concept. This topological representation of concepts comes along with a representation of the familiar logical connectives of Aristotelian syllogistics in terms of natural settheoretical operations that characterize regular open interpretations of classical Boolean propositional logic. In the last 20 years, conceptual spaces have become a popular tool of dealing with a variety of problems in the fields of cognitive psychology, artificial intelligence, linguistics and philosophy, mainly due to the work of Peter Gärdenfors and his collaborators. By using prototypes and metrics of similarity spaces, one obtains geometrical discretizations of conceptual spaces by so-called Voronoi tessellations. These tessellations are extensionally equivalent to topological tessellations that can be constructed for Alexandroff spaces. Thereby, Rumfitt’s and Gärdenfors’s constructions turn out to be special cases of an approach that works for a more general class of spaces, namely, for weakly scattered Alexandroff spaces. This class of spaces provides a convenient framework for conceptual spaces as used in epistemology and related disciplines in general. Alexandroff spaces are useful for elucidating problems related to the logic of vague concepts, in particular they offer a solution of the Sorites paradox (Rumfitt). Further, they provide a semantics for the logic of clearness (Bobzien) that overcomes certain problems of the concept of higher2 order vagueness. Moreover, these spaces help find a natural place for classical syllogistics in the framework of conceptual spaces. The crucial role of order theory for Alexandroff spaces can be used to refine the all-or-nothing distinction between prototypical and nonprototypical stimuli in favor of a more fine-grained gradual distinction between more-orless prototypical elements of conceptual spaces. The greater conceptual flexibility of the topological approach helps avoid some inherent inadequacies of the geometrical approach, for instance, the so-called “thickness problem” (Douven et al.) and problems of selecting a unique metric for similarity spaces. Finally, it is shown that only the Alexandroff account can deal with an issue that is gaining more and more importance for the theory of conceptual spaces, namely, the role that digital conceptual spaces play in the area of artificial intelligence, computer science and related disciplines. Keywords: Conceptual Spaces, Polar Spaces, Alexandroff Spaces, Prototypes, Topological Tessellations, Voronoi Tessellations, Digital Topology. (shrink)

The aim of this paper is to reconcile two claims that have long been thought to be incompatible: that we compositionally determine the meaning of complex expressions from the meaning of their parts, and that prototypes are components of the meaning of lexical terms such as fish, red, and gun. Hypotheses and are independently plausible, but most researchers think that reconciling them is a difficult, if not hopeless task. In particular, most linguists and philosophers agree that is not negotiable; so (...) they tend to reject. Recently, there have been some attempts to reconcile these claims, but they all adopt an implausibly weak notion of compositionality. Furthermore, parties to this debate tend to fall into a problematic way of individuating prototypes that is too externalistic. In contrast, I propose that we can reconcile and if we adopt, instead, an internalist and pluralist conception of prototypes and a context-sensitive but strong notion of compositionality. I argue that each of this proposals is independently plausible, and that, when taken together, provide the basis for a satisfactory account of prototype compositionality. (shrink)

In this contribution the prototypical argumentative patterns are discussed in which pragmatic argumentation is used in the context of legal justification in hard cases. First, the function and implementation of pragmatic argumentation in prototypical argumentative patterns in legal justification are addressed. The dialectical function of the different parts of the complex argumentation are explained by characterizing them as argumentative moves that are put forward in reaction to certain forms of critique. Then, on the basis of an exemplary case, the famous (...) Holy Trinity case, the way in which the U.S. Supreme Court uses pragmatic argumentation in this case is discussed by showing how the court instantiates general prototypical argumentative patterns in light of the institutional preconditions of the justification in the context of the specific case. (shrink)

The aim of this paper is to present a topological method for constructing discretizations of topological conceptual spaces. The method works for a class of topological spaces that the Russian mathematician Pavel Alexandroff defined more than 80 years ago. The aim of this paper is to show that Alexandroff spaces, as they are called today, have many interesting properties that can be used to explicate and clarify a variety of problems in philosophy, cognitive science, and related disciplines. For instance, recently, (...) Ian Rumfitt used a special type of Alexandroff spaces to elucidate the logic of vague concepts in a new way. Moreover, Rumfitt’s class of Alexandroff spaces can be shown to provide a natural topological semantics for Susanne Bobzien’s “logic of clearness”. Mainly due to the work of Peter Gärdenfors and his collaborators, conceptual spaces have become an increasingly popular tool of dealing with a variety of problems in the fields of cognitive psychology, artificial intelligence, linguistics and philosophy. For Gärdenfors’s conceptual spaces, geometrically defined discretizations play an essential role. These tessellations can be shown to be extensionally equivalent to topological tessellations that can be constructed for Alexandroff spaces in general. Thereby, Rumfitt’s and Gärdenfors’s constructions turn out to be special cases of an approach that works for a more general class of spaces, namely, for weakly scattered Alexandroff spaces. The main aim of this paper is to show that this class of spaces provides a convenient framework for conceptual spaces as used in epistemology and related disciplines in general. Weakly scattered Alexandroff spaces are useful for elucidating problems related to the logic of vague concepts, in particular they offer a solution of the Sorites paradox. Further, they provide a semantics for the logic of clearness that overcomes certain problems of the concept of higher-order vagueness. Moreover, these spaces help find a natural place for classical syllogistics in the framework of conceptual spaces. The specialization order of Alexandroff spaces can be used to refine the all-or-nothing distinction between prototypical and non-prototypical stimuli in favor of a gradual distinction between more or less prototypical elements of conceptual spaces. The greater conceptual flexibility of the topological approach helps avoid some inherent inadequacies of the geometrical approach, for instance, the so-called “thickness problem”. Finally, it is shown that the Alexandroff spaces offer an appropriate framework to deal with digital conceptual spaces that are gaining more and more importance in the areas of artificial intelligence, computer science and related disciplines. (shrink)

In this paper, I explore the implications of recent empirical research on concept representation for the philosophical enterprise of conceptual analysis. I argue that conceptual analysis, as it is commonly practiced, is committed to certain assumptions about the nature of our intuitive categorization judgments. I then try to show how these assumptions clash with contemporary accounts of concept representation in cognitive psychology. After entertaining an objection to my argument, I close by considering ways in which conceptual analysis might be altered (...) to accord better with the empirical work. (shrink)

Combining typical knowledge to generate novel concepts is an important creative trait of human cognition. Dealing with such ability requires, from an AI perspective, the harmonization of two conflicting requirements that are hardly accommodated in symbolic systems: the need of a syntactic compositionality (typical of logical systems) and that one concerning the exhibition of typicality effects (see Frixione and Lieto, 2012). In this work we provide a logical framework able to account for this type of human-like concept combination. We propose (...) a nonmonotonic Description Logic of typicality called TCL (Typicality-based Compositional Logic). (shrink)

Prototype theory makes a crucial distinction between central and peripheral sense of words. Geeraerts explores the implications of this model for a theory of semantic change, in the first full-scale treatment of the impact of the most recent developments in lexicological theory on the study of meaning change. He identifies structural features of the development of word meanings which follow from a prototype-theoretical model of semantic structure, and incorporates these diachronic prototypicality effects into a theory of meaning change.

An integrated representation of large‐scale space, or cognitive map, colled PLAN, is presented that attempts to address a broader spectrum of issues than has been previously attempted in a single model. Rather than examining way‐finding as a process separate from the rest of cognition, one or the fundamental goals of this work is to examine how the wayfinding process is integrated into general cognition. One result of this approach is that the model is “heads‐up,” or scene‐based, because it takes advantage (...) of the properties of the human visual system and, particularly, the visual system's split into two pathways. The emphasis on the human location or “where” system is new to cognitive mapping and is port of an attempt to synthesize prototype theory, associative networks and location together in a connectionist system. Not all of PLAN is new, however. Many of its parts have analogues in one or another preexisting theory. What makes PLAN unique is integrating the various components into a coherent whole, and the capacity of this resulting system to speak to a wide range of constraints. Our approach emphasizes adaptiveness; thus, our focus on such issues as ease of use and efficiency of learning. The result is a model that has a stronger relationship both to the environment, and to the ways that humans interact with it, compared with previous models. The resulting model is examined in some detail and compared to other systems. (shrink)

The species problem is often described as the abundance of conflicting definitions of _species_, such as the biological species concept and phylogenetic species concepts. But biologists understand the notion of species in a non-definitional as well as a definitional way. In this article I argue that when they understand _species_ without a definition in their mind, their understanding is often mediated by the notion of _good species_, or prototypical species, as the idea of ``prototype'' is explicated in cognitive psychology. (...) This distinction helps us make sense of several puzzling phenomena regarding biologists' dealing with species, such as the fact that in everyday research biologists often behave as if the species problem is solved, while they should be fully aware that it is not. I also briefly discuss implications of this finding, including that some extant attempts to answer what the nature of species is have an inadequate assumption about how the notion of species is represented in biologists' minds. (shrink)

In a previous paper the concept of disease was fuzzy-logically analyzed and a sketch was given of a prototype resemblance theory of disease (Sadegh-Zadeh (2000). J. Med. Philos., 25:605–38). This theory is outlined in the present paper. It demonstrates what it means to say that the concept of disease is a nonclassical one and, therefore, not amenable to traditional methods of inquiry. The theory undertakes a reconstruction of disease as a category that in contradistinction to traditional views is not (...) based on a set of common features of its members, that is individual diseases, but on a few best examples of the category, called its prototypes, and a similarity relationship such that a human condition is considered a disease if it resembles a prototype. It enables new approaches to resolving many of the stubborn problems associated with the concept of disease. (shrink)

In this paper I evaluate the soundness of the prototype paradigm, in particular its basic assumption that there are pan-human psychological essences or core meanings that refer to basic-level natural kinds, explaining why, on the whole, human communication and learning are successful. Instead I argue that there are no particular pan-human basic elements for thought, meaning and cognition, neither prototypes, nor otherwise. To illuminate my view I draw on examples from anthropology. More generally I argue that the prototype (...) paradigm exemplifies two assumptions that dominate cognitive science: (1) If human beings use words they mean something particular and what they mean can be discovered by scientific methods. (2) There is a fixed number of domains of categorization, each made up of a fixed number of basic categories. I suggest that these two assumptions lead to Brave New World. (shrink)

In this paper I evaluate the soundness of the prototype paradigm, in particular its basic assumption that there are pan-human psychological essences or core meanings that refer to basic-level natural kinds, explaining why, on the whole, human communication and learning are successful. Instead I argue that there are no particular pan-human basic elements for thought, meaning and cognition, neither prototypes, nor otherwise. To illuminate my view I draw on examples from anthropology. More generally I argue that the prototype (...) paradigm exemplifies two assumptions that dominate cognitive science: (1) If human beings use words they mean something particular and what they mean can be discovered by scientific methods. (2) There is a fixed number of domains of categorization, each made up of a fixed number of basic categories. I suggest that these two assumptions lead to Brave New World. (shrink)

As it emerged from philosophical analyses and cognitive research, most concepts exhibit typicality effects, and resist to the efforts of defining them in terms of necessary and sufficient conditions. This holds also in the case of many medical concepts. This is a problem for the design of computer science ontologies, since knowledge representation formalisms commonly adopted in this field do not allow for the representation of concepts in terms of typical traits. However, the need of representing concepts in terms of (...) typical traits concerns almost every domain of real world knowledge, including medical domains. In particular, in this article we take into account the domain of mental disorders, starting from the DSM-5 descriptions of some specific mental disorders. On this respect, we favor a hybrid approach to the representation of psychiatric concepts, in which ontology oriented formalisms are combined to a geometric representation of knowledge based on conceptual spaces. (shrink)

Concepts are mental representations that are the constituents of thought. EdouardMachery claims that psychologists generally understand concepts to be bodies of knowledge or information carrying mental states stored in long term memory that are used in the higher cognitive competences such as in categorization judgments, induction, planning, and analogical reasoning. While most research in the concepts field generally have been on concrete concepts such as LION, APPLE, and CHAIR, this paper will examine abstract moral concepts and whether such concepts may (...) have prototype and exemplar structure. After discussing the philosophical importance of this project and explaining the prototype and exemplar theories, criticisms will be made against philosophers, who without experimental support from the sciences of the mind, contend that moral concepts have prototype and/or exemplar structure. Next, I will scrutinize Mark Johnson’s experimentally-based argument that moral concepts have prototype structure. Finally, I will show how our moral concepts may indeed have prototype and exemplar structure as well as explore the further ethical implications that may be reached by this particular moral concepts conclusion. (shrink)

Prototypes and fuzziness are regarded in this paper as fundamental phenomena in the inherent logic of concepts whose relationship, however, has not been sufficiently clarified. Therefore, modifications are proposed in the definition of both. Prototypes are defined as the elements possessing maximal degree of membership in the given category such thatthis membership has maximal cognitive efficiency in representing theelement. A modified fuzzy set (m-fuzzy set) is defined on aclass (possibly self-contradictory collection) such that its core (the collection of elements with (...) full membership) is aset (self-consistent collection) comprising the finite set of the prototypes. In this scheme of recursive representation the possibility of contradictions, which has been proven to be inevitable in the logic of concepts, islocalized. Finally a related model of the brain''s pattern recognition mechanism is briefly summarized. (shrink)

An argument that makes use of a generalization activates the prototype for the category used in the generalization. We conducted two experiments that investigated how the activation of the prototype affects the persuasiveness of the argument. The results of the experiments suggest that the features of the prototype overshadow and partly overwrite the actual facts of the case. The case is, to some extent, judged as if it had the features of the prototype instead of the (...) features it actually has. This prototype effect increases the persuasiveness of the argument in situations where the audience finds the judgment more warranted for the prototype than for the actual case, but decreases persuasiveness in situations where the audience finds the judgment less warranted for the prototype than for the actual case. (shrink)

The foregoing considerations support the conjecture that prototypes are semi-compositional in the sense that there exist unboundedly many combinations of nouns with non-exceptional adjectives, which satisfy the rule default-to-prototype and hence are compositional. Presumably there also exist unboundedly many combinations of nouns with exceptional adjectives, which violate DP and hence are non-compositional. An analysis of the connection between productivity and compositionality has been suggested by Robbins. He argues that, for the explanation of productivity, one need not assume that conceptual (...) meanings always compose—it is enough that they compose in infinitely many cases. Since semi-compositionality entails the existence of unboundedly many non-compositional cases, non-compositionality cannot be dealt away with a finite list of idiomatic exceptions, but is a genuine feature of prototype semantics in natural language. (shrink)

Human cloning until recently has been considered to belong to the domain of science fiction; now it is a tangible possibility, a hopeful as well as a fearsome one. One of the fears that necessarily come along with it is about the peril cloning might represent for human uniqueness, since the clones are expected to be identical to their prototypes; this would unavoidably compromise moral agents’ right to a unique identity. In this paper I will put under examination the argument (...) against cloning that is based upon the right to a unique identity; I will argue that cloning represents no actual threat for anybody’s unique identity, therefore this argument is futile. I will also support the view that the so-called right to a unique identity is not as indisputable as to serve as the basis of a moral argument against human reproductive cloning. (shrink)

Although we have gained great insight into the variety of cultural influences on emotion concept prototypes from a plethora of studies examining such cross-cultural effects, there has been relatively little academic focus on the nature of emotion concept prototypes within a cultural perspective. Our discussion of the nature of emotion concept prototypes centres on essentialist versus non-essentialist principles. We argue that at a general, decontextualised level, essentialist and non-essentialist principles predict similarity in the structure of emotion concept prototypes. We further (...) argue that context is central in assessments of the nature of emotion concept prototypes from a cultural perspective. Rather than asking how emotion concept prototypes differ as a consequence of how certain influences might vary from one culture to another, a key question is whether emotion concept prototypes vary in different contexts within and between cultures and what this might inform us about the nature of emotion concept prototypes. (shrink)

This article demonstrates the potential of using hierarchical Bayesian methods to relate models and data in the cognitive sciences. This is done using a worked example that considers an existing model of category representation, the Varying Abstraction Model (VAM), which attempts to infer the representations people use from their behavior in category learning tasks. The VAM allows for a wide variety of category representations to be inferred, but this article shows how a hierarchical Bayesian analysis can provide a unifying explanation (...) of the representational possibilities using 2 parameters. One parameter controls the emphasis on abstraction in category representations, and the other controls the emphasis on similarity. Using 30 previously published data sets, this work shows how inferences about these parameters, and about the category representations they generate, can be used to evaluate data in terms of the ongoing exemplar versus prototype and similarity versus rules debates in the literature. Using this concrete example, this article emphasizes the advantages of hierarchical Bayesian models in converting model selection problems to parameter estimation problems, and providing one way of specifying theoretically based priors for competing models. (shrink)

Our goal is to use prototype analysis to distinguish the folk or culturally held understandings of love, romantic love, and sex and to specify, from the obtained data, the semantic relationship among these three associated concepts. By considering the semantic distinctions between these three concepts, we come to an unintended insight: if romantic love is a socio-cultural universal it does not appear to have the same evolutionary history as love or sex and this may account for its somewhat ambiguous (...) status in the scholarly literature on romantic love. We demonstrate that, in the United States, sex, in and of itself, is seldom conceived of as a relationship while love and romantic love are primarily viewed as relational. Our findings, though preliminary, strongly suggest that romantic love is a synthesis of two evolutionary drives: love and sex. (shrink)

It has been claimed that the prototype theory of concepts supports two controversial claims in the philosophy of art: that art cannot be defined, and that the possession of a certain sort of historical narrative is a sufficient but not necessary means of determining the art status of contested works. It is argued here that two sorts of considerations undermine the thesis that prototype theory offers significant support to anti-definitionism and historical narrativism. First, there is reason to think (...) that prototype theory is as a psychological theory not the sort of view that can support philosophical theories like anti-definitionism and historical narrativism. Second, well-known objections and theoretical alternatives to prototype theory theory raise serious questions about that theory’s own credentials. (shrink)

Resumen: La tragedia clásica en China, como forma literaria única, encarna el espíritu cultural de la nación y posee un profundo patrimonio histórico y un valor estético distintivo. Desde tiempos antiguos, la tragedia ha ocupado un lugar importante en la historia de la literatura China, reflejlas preocupaciones públicas sobre la realidad social y su contemplación del destino humano. Como método de investigación interdisciplin, el análisis de prototipos proporciona nuevas perspectivas y herramientas teóricas para profundizar en las connode la tragedia. El (...) estudio de los prototipos de la tragedia clásica en China ayuda a revelar la trayectoria de desarrollo y las leyes inherentes de la tragedia clásica en la historia. Este artículo toma el marco de la teoría de prototipos para analizar los prototipos de la tragedia clásica en China, con el objetivo de proporcionar la base teórica para la investigación relacionada. (shrink)

The question of how people represent emotions is eminently important for a number of different domains of psychological research. The present study tested the assumption that emotion concepts are represented similar to theories in that they are comprised of a set of causally interrelated features. Using emotional scenarios and investigating the emotion concepts of anger, anxiety, and sadness it was found that people's representations of emotion concepts essentially involved the representation of the causal relation of emotion features and that the (...) causal status of a feature determined the feature's centrality in the concept. Moreover, people's representations of emotion concepts corresponded to basic assumptions of cognitive emotion theories, namely that cognitive appraisals cause other surface features of emotion, like expression and behaviour. By providing evidence for a theory-based representation, the present results show that the classical and the prototype approach are insufficient to model the representation of emotion concepts. (shrink)

Elimination of imaginaries for 1-variable definable equivalence relations is proved for a theory of algebraically closed valued fields with new sorts for the disc spaces. The proof is constructive, and is based upon a new framework for proving elimination of imaginaries, in terms of prototypes which form a canonical family of formulas for defining each set that is definable with parameters. The proof also depends upon the formal development of the tree-like structure of valued fields, in terms of valued trees, (...) and a decomposition of valued trees which is used in the coding of certain sets of discs. (shrink)

The Page target article is interesting because of apparent coverage of many psychological phenomena with simple, unified neural techniques. However, prototype phenomena cannot be covered because the strongest response would be to the first-learned stimulus in each category rather than to a prototype stimulus or most frequently presented stimuli. Alternative methods using distributed coding can also achieve portability of network knowledge.

Machery’s argument that concepts split into different kinds is bold and inspiring but not fully persuasive. We will focus on the lack of evidence for the fourth tenet of Machery’s..

In the present paper, we shall discuss the notion of prototype and show its benefits. First, we shall argue that the prototypes of common-sense concepts are necessary for making prompt and reliable categorisations and inferences. However, the features constituting the prototype of a particular concept are neither necessary nor sufficient conditions for determining category membership; in this sense, the prototype might lead to conclusions regarded as wrong from a theoretical perspective. That being said, the prototype remains (...) essential to handling most ordinary situations and helps us to perform important cognitive tasks. To exemplify this point, we shall focus on disease concepts. Our analysis concludes that the prototypical conception of disease is needed to make important inferences from a practical and clinical point of view. Moreover, it can still be compatible with a classical definition of disease, given in terms of necessary and sufficient conditions. In the first section, we shall compare the notion of stereotype, as it has been introduced in philosophy of language by Hilary Putnam, with the notion of prototype, as it has been developed in the cognitive sciences. In the second section, we shall discuss the general role of prototypical information in cognition and stress its centrality. In the third section, we shall apply our previous discussion to the specific case of medical concepts, before briefly summarising our conclusions in section four. (shrink)

This Discussion Note calls for attention to the cultural practices of Neural Engineering as part of the life sciences as practices and technologies of manufacturing life. Through focusing on Disability, Ableism, and especially Technoableism within the field, I point out instances of onto-epistemological violence, which influence the likelihood of survival of disabled people individually and as a group. By drawing on Crip Technoscience, a method assemblage is introduced that allows to address these issues in an intersectional-kyriarchal understanding of interlocking systems (...) of privilege and oppression through generative critique and productive collaborative work. Criptical Neural Engineering is dedicated to disability justice and disability gain. It centers disabled people as epistemic activists and demands response-ability and accountability from non-disabled people, specifically engineers that want to build adaptive technologies with disabled people. (shrink)

In this article we present an engineering approach for the integration of social group dynamics in the behavior modeling of multiagent systems. To this end, a toolbox was created that brings together several theories from the social sciences, each focusing on different aspects of group dynamics. Due to its modular approach, the toolbox can either be used as a central control component of an application or it can be employed temporarily to rapidly test the feasibility of the incorporated theories for (...) a given application domain. This is exemplified by applying the toolbox to different applications. (shrink)