In the late summer of 1998, the authors, a cognitive scientist and a logician, started talking about the relevance of modern mathematical logic to the study of human reasoning, and we have been talking ever since. This book is an interim report of that conversation. It argues that results such as those on the Wason selection task, purportedly showing the irrelevance of formal logic to actual human reasoning, have been widely misinterpreted, mainly because the picture of logic current in psychology (...) and cognitive science is completely mistaken. We aim to give the reader a more accurate picture of mathematical logic and, in doing so, hope to show that logic, properly conceived, is still a very helpful tool in cognitive science. The main thrust of the book is therefore constructive. We give a number of examples in which logical theorizing helps in understanding and modeling observed behavior in reasoning tasks, deviations of that behavior in a psychiatric disorder (autism), and even the roots of that behavior in the evolution of the brain. (shrink)

Shepard has argued that a universal law should govern generalization across different domains of perception and cognition, as well as across organisms from different species or even different planets. Starting with some basic assumptions about natural kinds, he derived an exponential decay function as the form of the universal generalization gradient, which accords strikingly well with a wide range of empirical data. However, his original formulation applied only to the ideal case of generalization from a single encountered stimulus to a (...) single novel stimulus, and for stimuli that can be represented as points in a continuous metric psychological space. Here we recast Shepard's theory in a more general Bayesian framework and show how this naturally extends his approach to the more realistic situation of generalizing from multiple consequential stimuli with arbitrary representational structure. Our framework also subsumes a version of Tversky's set-theoretic model of similarity, which is conventionally thought of as the primary alternative to Shepard's continuous metric space model of similarity and generalization. This unification allows us not only to draw deep parallels between the set-theoretic and spatial approaches, but also to significantly advance the explanatory power of set-theoretic models. Key Words: additive clustering; Bayesian inference; categorization; concept learning; contrast model; features; generalization; psychological space; similarity. (shrink)

We examine the verification of simple quantifiers in natural language from a computational model perspective. We refer to previous neuropsychological investigations of the same problem and suggest extending their experimental setting. Moreover, we give some direct empirical evidence linking computational complexity predictions with cognitive reality.<br>In the empirical study we compare time needed for understanding different types of quantifiers. We show that the computational distinction between quantifiers recognized by finite-automata and push-down automata is psychologically relevant. Our research improves upon hypothesis and (...) explanatory power of recent neuroimaging studies as well as provides<br>evidence. (shrink)

To the best of my knowledge, no one in recent decades has written a book of this magnitude about the semantics of natural language. Certainly, nothing available today matches this volume in depth, precision, and coherence. The authors present classical and recent results of linguistic semantics within the framework of interpretative T-theories and defend the philosophical foundations of their approach by showing how it fits into the larger enterprise of cognitive linguistics. The book also includes an array of excellent exercises (...) and a good list of references. (shrink)

Research on human infants has begun to shed light on early-developing processes for segmenting perceptual arrays into objects. Infants appear to perceive objects by analyzing three-dimensional surface arrangements and motions. Their perception does not accord with a general tendency to maximize figural goodness or to attend to nonaccidental geometric relations in visual arrays. Object perception does accord with principles governing the motions of material bodies: Infants divide perceptual arrays into units that move as connected wholes, that move separately from one (...) another, that tend to maintain their size and shape over motion, and that tend to act upon each other only on contact. These findings suggest that o general representation of object unity and boundaries is interposed between representations of surfaces and representations of objects of familiar kinds. The processes that construct this representation may be related to processes of physical reasoning. (shrink)

We address the problem of predicting how people will spontaneously divide into groups a set of novel items. This is a process akin to perceptual organization. We therefore employ the simplicity principle from perceptual organization to propose a simplicity model of unconstrained spontaneous grouping. The simplicity model predicts that people would prefer the categories for a set of novel items that provide the simplest encoding of these items. Classification predictions are derived from the model without information either about the number (...) of categories sought or information about the distributional properties of the objects to be classified. These features of the simplicity model distinguish it from other models in unsupervised categorization (where, for example, the number of categories sought is determined via a free parameter), and we discuss how these computational differences are related to differences in modeling objectives. The predictions of the simplicity model are validated in four experiments. We also discuss the significance of simplicity in cognitive modeling more generally. (shrink)

Inductive generalization, where people go beyond the data provided, is a basic cognitive capability, and it underpins theoretical accounts of learning, categorization, and decision making. To complete the inductive leap needed for generalization, people must make a key ‘‘sampling’’ assumption about how the available data were generated. Previous models have considered two extreme possibilities, known as strong and weak sampling. In strong sampling, data are assumed to have been deliberately generated as positive examples of a concept, whereas in weak sampling, (...) data are assumed to have been generated without any restrictions. We develop a more general account of sampling that allows for an intermediate mixture of these two extremes, and we test its usefulness. In two experiments, we show that most people complete simple one-dimensional generalization tasks in a way that is consistent with their believing in some mixture of strong and weak sampling, but that there are large individual differences in the relative emphasis different people give to each type of sampling. We also show experimentally that the relative emphasis of the mixture is influenced by the structure of the available information. We discuss the psychological meaning of mixing strong and weak sampling, and possible extensions of our modeling approach to richer problems of inductive generalization. (shrink)

The paper examines constraints and preferences employed by people in learning decision rules from preclassified examples. Results from four experiments with human subjects were analyzed and compared with artificial intelligence (AI) inductive learning programs. The results showed the people's rule inductions tended to emphasize category validity (probability of some property, given a category) more than cue validity (probability that an entity is a member of a category given that it has some property) to a greater extent than did the AI (...) programs. Although the relative proportions of different rule types (e.g., conjunctive vs. disjunctive) changed across experiments, a single process model provided a good account of the data from each study. These observations are used to argue for describing constraints in terms of processes embodied in models rather than in terms of products or outputs. Thus AI induction programs become candidate psychological process models and results from inductive learning experiments can suggest new algorithms. More generally, the results show that human inductive generalizations tend toward greater specificity than would be expected if conceptual simplicity were the key constraint on inductions. This bias toward specificity may be due to the fact that this criterion both maximizes inferences that may be drawn from category membership and protects rule induction systems from developing over‐generalizations. (shrink)

This book emphasizes the role of semantics as a bridge between the theory of language and the theories of other cognitive capacities such as visual perception...

Natural language is full of patterns that appear to fit with general linguistic rules but are ungrammatical. There has been much debate over how children acquire these “linguistic restrictions,” and whether innate language knowledge is needed. Recently, it has been shown that restrictions in language can be learned asymptotically via probabilistic inference using the minimum description length (MDL) principle. Here, we extend the MDL approach to give a simple and practical methodology for estimating how much linguistic data are required to (...) learn a particular linguistic restriction. Our method provides a new research tool, allowing arguments about natural language learnability to be made explicit and quantified for the first time. We apply this method to a range of classic puzzles in language acquisition. We find some linguistic rules appear easily statistically learnable from language experience only, whereas others appear to require additional learning mechanisms (e.g., additional cues or innate constraints). (shrink)

This paper describes a theory that explains both the creativity and the efficiency of people's conceptual combination. In the constraint theory, conceptual combination is controlled by three constraints of diagnosticity, plausibility, and informativeness. The constraints derive from the pragmatics of communication as applied to compound phrases. The creativity of combination arises because the constraints can be satisfied in many different ways. The constraint theory yields an algorithmic model of the efficiency of combination. The C3 model admits the full creativity of (...) combination and yet efficiently settles on the best interpretation for a given phrase. The constraint theory explains many empirical regularities in conceptual combination, and makes various empirically verified predictions. In computer simulations of compound phrase interpretation, the C3 model has produced results in general agreement with people's responses to the same phrases. (shrink)

Children's comprehension of the universal quantifiers all and each was explored in a series of experiments using a picture selection task. The first experiment examined children's ability to restrict a quantifier to the noun phrase it modifies. The second and third experiments examined children's ability to associate collective, distributive, and exhaustive representations with sentences containing universal quantifiers. The collective representation corresponds to the "group" meaning (for All the flowers are in a vase all of the flowers are in the same (...) vase). The distributive representation implies a pairing (e.g., each flower paired with a vase for Each flower is in a vase). The exhaustive representation exhausts both sets (e.g., for The flowers are in the vases all the flowers are in vases and all the vases have flowers in them). Four- to 10-year-olds children had little difficulty restricting the quantifier all to the noun it modified in a task which required them to attend to the group feature of all. In contrast, only 9- and 10-year-olds were able to solve the task when the quantifier was each and the pictures showed entities in partial one-to-one correspondence. Children showed a preference for associating collective pictures with sentences containing all and distributive pictures with sentences containing each. The results suggest that between the ages of 5 and 10 years, children's semantic representations undergo less radical changes than others have proposed. Instead, developmental change may occur gradually as children acquire linguistic cues which map onto existing semantic representations. (shrink)

This volume is a collection of original contributions about the core knowledge in fundamental domains. It includes work on naive physics, such as formal specifications of intuitive theories of spatial relations, time causality, substance and physical objects, and on naive psychology.

In this book, Newell makes the case for unified theories by setting forth a candidate.

In this study on deduction, the authors argue that people reason by imagining the relevant state of affairs, ie building an internal model of it, formulating a tentative conclusion based on this model and then searching for alternative models.

Lance Rips describes a unified theory of natural deductive reasoning and fashions a working model of deduction, with strong experimental support, that is capable of playing a central role in mental life.

Current textbooks in formal semantics are all versions of, or introductions to, the same paradigm in semantic theory: Montague Grammar. Knowledge of Meaning is based on different assumptions and a different history. It provides the only introduction to truth- theoretic semantics for natural languages, fully integrating semantic theory into the modern Chomskyan program in linguistic theory and connecting linguistic semantics to research elsewhere in cognitive psychology and philosophy. As such, it better fits into a modern graduate or undergraduate program in (...) linguistics, cognitive science, or philosophy. Furthermore, since the technical tools it employs are much simpler to teach and to master, Knowledge of Meaning can be taught by someone who is not primarily a semanticist. Linguistic semantics cannot be studied as a stand-alone subject but only as part of cognitive psychology, the authors assert. It is the study of a particular human cognitive competence governing the meanings of words and phrases. Larson and Segal argue that speakers have unconscious knowledge of the semantic rules of their language, and they present concrete, empirically motivated proposals about a formal theory of this competence based on the work of Alfred Tarski and Donald Davidson. The theory is extended to a wide range of constructions occurring in natural language, including predicates, proper nouns, pronouns and demonstratives, quantifiers, definite descriptions, anaphoric expressions, clausal complements, and adverbs. Knowledge of Meaning gives equal weight to philosophical, empirical, and formal discussions. It addresses not only the empirical issues of linguistic semantics but also its fundamental conceptual questions, including the relation of truth to meaning and the methodology of semantic theorizing. Numerous exercises are included in the book. (shrink)

Only human beings have a rich conceptual repertoire with concepts like tort, entropy, Abelian group, mannerism, icon and deconstruction. How have humans constructed these concepts? And once they have been constructed by adults, how do children acquire them? While primarily focusing on the second question, in The Origin of Concepts , Susan Carey shows that the answers to both overlap substantially. Carey begins by characterizing the innate starting point for conceptual development, namely systems of core cognition. Representations of core cognition (...) are the output of dedicated input analyzers, as with perceptual representations, but these core representations differ from perceptual representations in having more abstract contents and richer functional roles. Carey argues that the key to understanding cognitive development lies in recognizing conceptual discontinuities in which new representational systems emerge that have more expressive power than core cognition and are also incommensurate with core cognition and other earlier representational systems. Finally, Carey fleshes out Quinian bootstrapping, a learning mechanism that has been repeatedly sketched in the literature on the history and philosophy of science. She demonstrates that Quinian bootstrapping is a major mechanism in the construction of new representational resources over the course of childrens cognitive development. Carey shows how developmental cognitive science resolves aspects of long-standing philosophical debates about the existence, nature, content, and format of innate knowledge. She also shows that understanding the processes of conceptual development in children illuminates the historical process by which concepts are constructed, and transforms the way we think about philosophical problems about the nature of concepts and the relations between language and thought. (shrink)