A theory of analogy must describe how the meaning of an analogy is derived from the meanings of its parts. In the structure‐mapping theory, the interpretation rules are characterized as implicit rules for mapping knowledge about a base domain into a target domain. Two important features of the theory are (a) the rules depend only on syntactic properties of the knowledge representation, and not on the specific content of the domains; and (b) the theoretical framework allows analogies to be distinguished (...) cleanly from literal similarity statements, applications of abstractions, and other kinds of comparisons.Two mapping principles are described: (a) Relations between objects, rather than attributes of objects, are mapped from base to target; and (b) The particular relations mapped are determined by systematicity, as defined by the existence of higher‐order relations. (shrink)

Human cognition requires coping with a complex and uncertain world. This suggests that dealing with uncertainty may be the central challenge for human reasoning. In Bayesian Rationality we argue that probability theory, the calculus of uncertainty, is the right framework in which to understand everyday reasoning. We also argue that probability theory explains behavior, even on experimental tasks that have been designed to probe people's logical reasoning abilities. Most commentators agree on the centrality of uncertainty; some suggest that there is (...) a residual role for logic in understanding reasoning; and others put forward alternative formalisms for uncertain reasoning, or raise specific technical, methodological, or empirical challenges. In responding to these points, we aim to clarify the scope and limits of probability and logic in cognitive science; explore the meaning of the explanation of cognition; and re-evaluate the empirical case for Bayesian rationality. (shrink)

Ducks lay eggs' is a true sentence, and `ducks are female' is a false one. Similarly, `mosquitoes carry the West Nile virus' is obviously true, whereas `mosquitoes don't carry the West Nile virus' is patently false. This is so despite the egg-laying ducks' being a subset of the female ones and despite the number of mosquitoes that don't carry the virus being ninety-nine times the number that do. Puzzling facts such as these have made generic sentences defy adequate semantic treatment. (...) However complex the truth conditions of generics appear to be, though, young children grasp generics more quickly and readily than seemingly simpler quantifiers such as `all' and `some'. I present an account of generics that not only illuminates the strange truth conditions of generics, but also explains how young children find them so comparatively easy to acquire. I then argue that generics give voice to our most cognitively primitive generalizations and that this hypothesis accounts for a variety of facts ranging from acquisition patterns to cross-linguistic data concerning the phonological articulation of operators. I go on to develop an account of the nature of these cognitively fundamental generalizations and argue that this account explains the strange truth-conditional behavior of generics. (shrink)

In this paper, we outline a comprehensive approach to composed analogies based on the theory of conceptual spaces. Our algorithmic model understands analogy as a search procedure and builds upon the idea that analogical similarity depends on a conceptual phenomena called ‘dimensional salience.’ We distinguish between category-based, property-based, event-based, and part-whole analogies, and propose computationally-oriented methods for explicating them in terms of conceptual spaces.

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)

We propose a nonmonotonic Description Logic of typicality able to account for the phenomenon of the combination of prototypical concepts. The proposed logic relies on the logic of typicality ALC + TR, whose semantics is based on the notion of rational closure, as well as on the distributed semantics of probabilistic Description Logics, and is equipped with a cognitive heuristic used by humans for concept composition. We first extend the logic of typicality ALC + TR by typicality inclusions of the (...) form p :: T(C) v D, whose intuitive meaning is that “we believe with degree p about the fact that typical Cs are Ds”. As in the distributed semantics, we define different scenarios containing only some typicality inclusions, each one having a suitable probability. We then exploit such scenarios in order to ascribe typical properties to a concept C obtained as the combination of two prototypical concepts. We also show that reasoning in the proposed Description Logic is EXPTIME-complete as for the underlying standard Description Logic ALC. (shrink)

A number of theoretical positions in psychology—including variants of case‐based reasoning, instance‐based analogy, and connectionist models—maintain that abstract rules are not involved in human reasoning, or at best play a minor role. Other views hold that the use of abstract rules is a core aspect of human reasoning. We propose eight criteria for determining whether or not people use abstract rules in reasoning, and examine evidence relevant to each criterion for several rule systems. We argue that there is substantial evidence (...) that several different inferential rules, including modus ponens, contractual rules, causal rules, and the law of large numbers, are used in solving everyday problems. We discuss the implications for various theoretical positions and consider hybrid mechanisms that combine aspects of instance and rule models. (shrink)

It is widely agreed that generics tolerate exceptions. It turns out, however, that exceptions are tolerated only so long as they do not violate homogeneity: when the exceptions are not concentrated in a salient “chunk” of the domain of the generic. The criterion for salience of a chunk is cognitive: it is dependent on the way in which the domain is mentally represented. Findings of psychological experiments about the ways in which different domains are represented, and the actors affecting such (...) representations, account for judgments of generic sentences, facts which cannot be explained by linguistics alone. The reason for the homogeneity requirement itself is, in turn, also dependent on cognitive considerations. Generics express default rules, and psychological findings have shown that, the more homogeneous the domain, the easier it is for subjects to infer rules about it. Thus, cognitive results form a crucial part of a comprehensive account of the meaning of a linguistic expression. (shrink)

In Gärdenfors and Makinson :197–245, 1994) and Gärdenfors it was shown that it is possible to model nonmonotonic inference using a classical consequence relation plus an expectation-based ordering of formulas. In this article, we argue that this framework can be significantly enriched by adopting a conceptual spaces-based analysis of the role of expectations in reasoning. In particular, we show that this can solve various epistemological issues that surround nonmonotonic and default logics. We propose some formal criteria for constructing and updating (...) expectation orderings based on conceptual spaces, and we explain how to apply them to nonmonotonic reasoning about objects and properties. (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)

Generic sentences (e.g., bare plural sentences such as “dogs have four legs” and “mosquitoes carry malaria”) are used to talk about kinds of things. Three experiments investigated the conceptual foundations of generics as well as claims within the formal semantic approaches to generics concerning the roles of prevalence, cue validity and normalcy in licensing generics. Two classes of generic sentences that pose challenges to both the conceptually based and formal semantic approaches to generics were investigated. Striking property generics (e.g. “sharks (...) bite swimmers”) are true even though only a tiny minority of instances have the property and thus pose obvious problems for quantificational approaches, and they also do not seem to characterize kinds in terms of the principled or statistical connections investigated in previous research ( Prasada and Dillingham, 2006 ; Prasada and Dillingham, 2009). The second class — minority characteristic generics (e.g. “ducks lay eggs”) — also poses serious problems for quantificational accounts, and appears to involve principled connections even though fewer than half of its instances have the relevant property. The experiments revealed three principal discoveries: first, striking generics involve neither principled nor statistical connections. Instead, they involve a causal connection between a kind and a property. Second, minority characteristic generics exhibit the characteristics of principled connections, which suggests that principled connections license the expectation that most instances will have the property, but do not require it. Finally, the experiments also provided evidence that prevalence and the acceptability of generics may be dissociated and provided data that are problematic for normalcy approaches to generics, and for the idea that cue validity licenses low prevalence generics. As such, the studies provided evidence in favor of a conceptually based approach to the semantics of generics ( Leslie, 2007 ; Leslie, 2008; see also Carlson, 2009). (shrink)

Conceptual spaces are a frequently applied framework for representing concepts. One of its central aims is to find criteria for what makes a concept natural. A prominent demand is that natural concepts cover convex regions in conceptual spaces. The first aim of this paper is to analyse the convexity thesis and the arguments that have been advanced in its favour or against it. Based on this, I argue that most supporting arguments focus on single-domain concepts (e.g., colours, smells, shapes). Unfortunately, (...) these concepts are not the primary examples of natural concepts. Building on this observation, the second aim of the paper is to develop criteria for natural multi-domain concepts. The representation of such concepts has two main aspects: features that are associated with the concept and the probabilistic correlation pattern which the concept captures. Conceptual spaces, together with probabilistic considerations, provide a helpful framework to approach these aspects. With respect to feature representation, the existence of characteristic features (i.e., that apples have a specific taste) is essential. Moreover, natural concepts capture peaks of a probabilistic distribution over complex spaces. They carve up nature at its joints, that is, at areas with no or low probabilistic density. This last aspect is shown to be closely related to the convexity demand. (shrink)

This paper is concerned with a version of Kamp and Partee's account of graded membership that relies on the conceptual spaces framework. Three studies are reported, one to construct a particular shape space, one to detect which shapes representable in that space are typical for certain sorts of objects, and one to elicit degrees of category membership for the various shapes from which the shape space was constructed. Taking Kamp and Partee's proposal as given, the first two studies allowed us (...) to predict the degrees to which people would judge shapes representable in the space to be members of certain categories. These predictions were compared with the degrees that were measured in the third study. The comparison yielded a test of the account of graded membership at issue. The outcome of this test was found to support the conceptual spaces version of Kamp and Partee's account of graded membership. (shrink)

The present study examined the effects of semantic structure on simple inductive judgments about category members. For a particular category, subjects were told that one of the species had a given property and were asked to estimate the proportion of instances in the other species that possessed the property. The results indicated that category structure—in particular, the typicality of the species—influenced subjects' judgments. These results were interpreted by models based on the following assumption: When little is known about the underlying (...) distribution of a property, subjects assume that the distribution mirrors that of better-known properties. For this reason, if subjects learn that an unknown property is possessed by a typical species, they are more likely to generalize than if the same fact had been learned about an atypical species. (shrink)

Four experiments investigated how people judge the plausibility of category-based arguments, focusing on the diversity effect, in which arguments with diverse premise categories are considered particularly strong. In Experiment 1 we show that priming people as to the nature of the blank property determines whether sensitivity to diversity is observed. In Experiment 2 we find that people's hypotheses about the nature of the blank property predict judgements of argument strength. In Experiment 3 we examine the effect of our priming methodology (...) on people's tendency to bring knowledge about causality or similarity to bear when evaluating arguments, and in Experiment 4 we show that whether people's hypotheses about the nature of the blank property were causal predicted ratings of argument strength. Together these results suggest that diversity effects occur because diverse premises lead people to bring general features of the premise categories to mind. Although our findings are broadly consistent with Bayesian and Relevance-based approaches to category-based inductive reasoning, neither approach captures all of our findings. (shrink)

Conceptual features differ in how mentally tranformable they are. A robin that does not eat is harder to imagine than a robin that does not chirp. We argue that features are immutable to the extent that they are central in a network of dependency relations. The immutability of a feature reflects how much the internal structure of a concept depends on that feature; i.e., how much the feature contributes to the concept's coherence. Complementarily, mutability reflects the aspects in which a (...) concept is flexible. We show that features can be reliably ordered according to their mutability using tasks that require people to conceive of objects missing a feature, and that mutability (conceptual centrality) can be distinguished from category centrality and from diagnosticity and salience. We test a model of mutability based on asymmetric, unlabeled, pairwise dependency relations. With no free parameters, the model provides reasonable fits to data. Qualitative tests of the model show that mutability judgments are unaffected by the type of dependency relation and that dependency structure influences judgments of variability. (shrink)

In a famous critique, Goodman dismissed similarity as a slippery and both philosophically and scientifically useless notion. We revisit his critique in the light of important recent work on similarity in psychology and cognitive science. Specifically, we use Tversky’s influential set-theoretic account of similarity as well as Gärdenfors’s more recent resuscitation of the geometrical account to show that, while Goodman’s critique contained valuable insights, it does not warrant a dismissal of similarity.

1: Linguistic and Epistemological Background 1 . 1 : Generic Reference vs. Generic Predication 1 . 2 : Why are there any Generic Sentences at all? 1 . 3 : Generics and Exceptions, Two Bad Attitudes 1 . 4 : Exceptions and Generics, Some Other Attitudes 1 . 5 : Generics and Intensionality 1 . 6 : Goals of an Analysis of Generic Sentences 1 . 7 : A Little Notation 1 . 8 : Generics vs. Explicit Statements of Regularities..

This paper addresses theoretical problems arising from the vagueness of language terms, and intuitions of the vagueness of the concepts to which they refer. It is argued that the central intuitions of prototype theory are sufficient to account for both typicality phenomena and psychological intuitions about degrees of membership in vaguely defined classes. The first section explains the importance of the relation between degrees of membership and typicality (or goodness of example) in conceptual categorization. The second and third section address (...) arguments advanced by Osherson and Smith (1997), and Kamp and Partee (1995), that the two notions of degree of membership and typicality must relate to fundamentally different aspects of conceptual representations. A version of prototype theory—the Threshold Model—is proposed to counter these arguments and three possible solutions to the problems of logical selfcontradiction and tautology for vague categorizations are outlined. In the final section graded membership is related to the social construction of conceptual boundaries maintained through language use. (shrink)

A central question in human development is how young children gain knowledge so fast. We propose that analogical generalization drives much of this early learning and allows children to generate new abstractions from experience. In this paper, we review evidence for analogical generalization in both children and adults. We discuss how analogical processes interact with the child's changing knowledge base to predict the course of learning, from conservative to domain-general understanding. This line of research leads to challenges to existing assumptions (...) about learning. It shows that it is not enough to consider the distribution of examples given to learners; one must consider the processes learners are applying; contrary to the general assumption, maximizing variability is not always the best route for maximizing generalization and transfer. (shrink)

The modifier effect is the reduction in perceived likelihood of a generic property sentence, when the head noun is modified. We investigated the prediction that the modifier effect would be stronger for mutable than for central properties, without finding evidence for this predicted interaction over the course of five experiments. However Experiment 6, which provided a brief context for the modified concepts to lend them greater credibility, did reveal the predicted interaction. It is argued that the modifier effect arises primarily (...) from a general lack of confidence in generic statements about the typical properties of unfamiliar concepts. Neither prototype nor classical models of concept combination receive support from the phenomenon. 2010 Elsevier Inc. All rights reserved. (shrink)

This dissertation examines and discusses some phenomena related to the geometric representation of similarity. It takes its inspiration from the existing body of empirical research within the fields of perceptual and cognitive psychology, but also connects to certain areas of machine learning. The problems discussed concern the modelling of information integration behavior when concepts like asymmetry, integrality, separability and familiarity are taken into account. The dissertation investigates how these phenomena can be modelled using geometric representations in order to increase the (...) descriptive power of the models. The main conclusions that can be drawn from this dissertation are that the descriptive powers of geometric models can be increased in a number of ways: a) By augmenting traditional geometric models with parameters of prominence they can reflect asymmetric similarity at least as well as previously known asymmetric models which include more parameters. b) Some specific metric, for instance, the Euclidean metric, should not be used merely by tradition. If there is reason to believe that there are groupings of dimensions such that the most descriptive metric differs between groups, the distance may be better described with a combination rule adding the contribution of each group/subspace together. c) Aspects of familiarity with stimuli should be taken into consideration, even for familiarity built up during a short period of time. When taking familiarity into consideration it may be possible to describe information integration over time with a finer granularity. Furthermore, by focusing on the part of the phenomenological data that reflect a more stable behavior, which seems to occur first when subjects are sufficiently familiar with the stimuli, the more stable behavior can be more accurately described. (shrink)

This paper aims to introduce and discuss a geometrically based model, the relative prominence model, which is inspired by Tversky's finding that a factor behind asymmetric similarity seems to be the "relative prominence". The model proposes that the experienced directed similarity from I to J is proportional to some symmetric similarity measure between I and J, and the quotient between the "prominences" for J and I. Analysis of empirical data from different areas shows that it is possible for a procedure (...) to estimate the parameters of the model quite well. The paper is concluded with a discussion of the differences between the relative prominence model and related models that handle asymmetry in terms of "stimulus bias". (shrink)