Hyperproof is a system for learning the principles of analytical reasoning and proof construction, consisting of a text and a Macintosh software program. Unlike traditional treatments of first-order logic, Hyperproof combines graphical and sentential information, presenting a set of logical rules for integrating these different forms of information. This strategy allows students to focus on the information content of proofs, rather than the syntactic structure of sentences. Using Hyperproof the student learns to construct proofs of both consequence and nonconsequence using (...) an intuitive proof system that extends the standard set of sentential rules to incorporate information represented graphically. Hyperproof is compatible with various natural-deduction-style proof systems, including the system used in the authors' Language of First-Order Logic. (shrink)

"Its publication should be a major event for cognitive linguistics and should pose a major challenge for cognitive science. In addition, it should have repercussions in a variety of disciplines, ranging from anthropology and psychology to epistemology and the philosophy of science.... Lakoff asks: What do categories of language and thought reveal about the human mind? Offering both general theory and minute details, Lakoff shows that categories reveal a great deal."—David E. Leary, American Scientist.

. . . Unlike Dewey, he has provided detailed incisive argumentation, and has shown just where the dogmas and dualisms break down." -- Richard Rorty, The Yale Review.

SYMBOLIC LOGIC. CHAPTER I. ON THE FORMS OF LOGICAL PROPOSITION. IT has been mentioned in the Introduction that the System of Logic which this work is ...

What might a theory of mental imagery look like, and how might one begin formulating such a theory? These are the central questions addressed in the present paper. The first section outlines the general research direction taken here and provides an overview of the empirical foundations of our theory of image representation and processing. Four issues are considered in succession, and the relevant results of experiments are presented and discussed. The second section begins with a discussion of the proper form (...) for a cognitive theory, and the distinction between a theory and a model is developed. Following this, the present theory and computer simulation model are introduced. This theory specifies the nature of the internal representations (data structures) and the processes that operate on them when one generates, inspects, or transforms mental images. In the third, concluding, section we consider three very different kinds of objections to the present research program, one hinging on the possibility of experimental artifacts in the data, and the others turning on metatheoretical commitments about the form of a cognitive theory. Finally, we discuss how one ought best to evaluate theories and models of the sort developed here. (shrink)

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.

touch 27 Thirrdly, the straining of the eye 28 The occasions which suggest distance have in their own nature no relation to it 29 A difficult case proposed by Dr. Barrow as repugnant to all the known theories 30 This case contradicts a ...

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...

This paper reviews current psychological theories of syllogistic inference and establishes that despite their various merits they all contain deficiencies as theories of performance. It presents the results of two experiments, one using syllogisms and the other using three-term series problems, designed to elucidate how the arrangement of terms within the premises affects performance. These data are used in the construction of a theory based on the hypothesis that reasoners construct mental models of the premises, formulate informative conclusions about the (...) relations in the model, and search for alternative models that are counterexamples to these conclusions. This theory, which has been implemented in several computer programs, predicts that two principal factors should affect performance: the figure of the premises, and the number of models that they call for. These predictions were confirmed by a third experiment. Dans cet article sont passées en revue les théories psychologiques du traitement des syllogismes. On établit qu'en dépit de leurs mérites variés toutes sont en défaut en tant que théories de la performance. On présente les résultats de deux expériences, une utilisant des syllogismes et l'autre des problémes avec des séries de trois termes conçues pour élucider comment l'arrangement des termes dans les premises affecte la performance. Ces données sont utilisées pour construire une théorie fondée sur l'hypothése que les gens construisent des modèles mentaux des premises, formulent des conclusions explicites sur les relations dans le modèle et cherchent des modèles qui seraient des contre-exemples pour leurs conclusions. Cette théorie, utilisée dans plusieurs programmes d'ordinateur, prédit que deux principaux facteurs affectent la performance: la figure des premises et le nombre de; modèles qu'ils mettent en jeu. Cette prédiction est confirmée dans les trois expériences. (shrink)

Our long term goal is an understanding of human communication in terms which would provide the basis for rational design. The kernel would be a theory of the cognitive consequences of allocating the same information to different media and modalities, based on the user's information processing characterised in computational terms. Our theory of the cognitive consequences of media/modality allocation starts from an analysis of differences in logical expressiveness of graphical and linguistic representations (Stenning \& Oberlander (1994, 1995)). This semantic approach (...) requires conceptualisations of {\it medium} and {\it modality} that can be related to representation systems. We propose that media are the physical/perceptual aspects of representations; modalities are classes of interpretation function which map media onto meanings. These interpretations of the terms contrast with existing HCI usage. The curtailments of abstraction observed in graphics arise from interactions between medium and modality. Graphical modalities are distinguished from sentential languages by the nature of their interpretation functions. A hierarchy of expressiveness of interpretations of graphics is defined, and compared with interpretations of sentential languages. Using the expressiveness of representations to predict their cognitive properties also requires reference to the availability of constraints of their interpretation to users. Further contrasts between graphics and language emerge in the availability of their constraints. Three example domains of graphical representations are analysed from this perspective---matrix graphics; logic diagrams; and semantic networks. Some empirical evidence of the usability of these notations is reviewed as evidence that the proposed conceptualisation offers powerful generalisations. (shrink)

A visual imagery task is presented which is beyond the limits of normal human ability, and some of the factors contributing to its difficulty are isolated by comparing the difficulty of related tasks. It is argued that complex objects are assigned hierarchical structural descriptions by being parsed into parts, each of which has its own local system of significant directions. Two quite different schemas for a wire‐frame cube are used to illustrate this theory, and some striking perceptual differences to which (...) they give rise are described. The difficulty of certain mental imagery tasks is shown to depend on which of the alternative structural descriptions of an object is used, and this is interpreted as evidence that structural descriptions are an important component of mental images. Finally, it is argued that analog transformations like mental folding involve changing the values of continuous variables in a structural description. (shrink)