We propose that similarity judgments are inferences about generative processes, and that two objects appear similar when they are likely to have been generated by the same process. We present a formal model based on this idea, and suggest that it may be particularly useful for explaining high-level judgments of similarity. We compare our model to featural and transformational accounts, and describe an experiment where it outperforms a transformational model.

An Integrated Architecture for Engineering Problem Solving Yusuf Pisan Problem solving is an essential function of human cognition. To build intelligent systems that are capable of assisting engineers and tutoring students, we need to develop an information processing model that captures the skills used in engineering problem solving. This thesis describes the Integrated Problem Solving Architecture (IPSA) that combines qualitative, quantitative and diagrammatic reasoning skills to produce annotated solutions to engineering problems. We focus on representing expert knowledge, and examine how control knowledge provides the structure for using domain knowledge. To demonstrate our architecture for engineering problem solving, we present a Thermodynamics Problem Solver (TPS) that uses the IPSA architecture. TPS solves over 150 thermodynamics problems taken from the first four chapters of a common thermodynamics textbook and produces expert-like solutions. iv ACKNOWLEDGMENTS I would l...

The results of two experiments suggest that strong constraints on the ability to imagine rotations extend to the perception of rotations. Participants viewed stereographic perspective views of rotating squares, regular polyhedra, and a variety of polyhedral generalized cones, and attempted to indicate the orientation of the axis and planes of rotation in terms of one of the 13 canonical directions in 3D space. When the axis and planes of a rotation were aligned with principal directions of the environment, participants could indicate the orientation of the motion well. When a rotation was oblique to the environment, the orientation of the object to the motion made a very large difference to performance. Participants were fast and accurate when the object was a generalized cone about the axis of rotation or was elongated along the axis. Variation of the amount of rotation and reflection symmetry of the object about the axis of rotation was not powerful. The study of motion and spatial transformation has long been central in mathematics and the physical sciences, and recently it has become the focus of much work in the study of perception and spatial cognition. Rotation, for example, is a fundamental form of motion (e.g., Gibson, 1957; Shepard, 1984), and the study of mental imagery has benefited greatly from the investigation of mental imagery of rotation (see Shepard & Cooper, 1982). Across the study of spatial cognition, it has become clear that some forms of spatiotemporal structure are cognitively simple for the typical person, whereas other forms are quite complex and difficult. This distinction is familiar from work on the spatial organization of elementary forms (e.g., Garner, 1974; Palmer, 1977; Wertheimer, 1950), but it applies also to a great variety of familiar or three-dimensional (3D) structures and

ssing. We suggest that some types of similarity are determined automatically. When the cognitive system recognizes similarities, they influence cognitive processing, even when the person does not intend for their processing to be affected by similarities. In order to support this claim, we first outline three different approaches to similarity. Then, we examine how similarity can influence both low-level processes like attention and memory retrieval and higher cognitive processes like analogical reasoning and decision making. Next, we explore a number of examples in which cognitive processing is influenced by the presence of similarities in a stimulus set. Finally, we broaden the discussion to include similarities in more deliberate cognitive processes. Three Approaches to Similarity Representation and Similarity When a person makes a similarity comparison, the result is typically both a judgment of similarity and also some awareness of the commonalities and differences of the pair com

v Declaration .................................... ix Acknowledgements................................ xi 1Prelude 1 TheVeryIdeaofRepresentation......................... 2 TypesofSimilarity ................................ 8 IsSimilarityIndeterminate? ........................... 11 TheRoleofSimilarityinCognition....................... 11 Summary&GeneralDiscussion......................... 14 2 Theories of Similarity 17 SimilarityDataSets................................ 17 SpatialRepresentation .............................. 21 FeaturalRepresentation.............................. 31 TreeRepresentation................................ 40 NetworkRepresentation ............................. 47 Alignment-BasedSimilarityModels....................... 48 TransformationalSimilarityModels ....................... 50 Summary&GeneralDiscussion......................... 54 i 3 On Representational Complexity 55 ApproachestoModelSelection ......................... 57 ChoosinganAdditiveClusteringRepresentation ................ 67 ChoosinganAdditiveTreeRepresentation ................... 82 ChoosingaSpatialRepresentation........................ 94 Summary&GeneralDiscussion......................... 95 4 Featural Representation 97 AMenagerieofFeaturalModels......................... 98 ClusteringModels.................................104 GeometricComplexityCriteria..........................106 AlgorithmsforFittingFeaturalModels .....................107 MonteCarloStudyI:DotheAlgorithmsWork? ................109 RepresentationsofKinshipTerms ........................117 MonteCarloStudyII:Complexity........................122 ExperimentI:Faces................................125 ExperimentII:Countries .............................1...

In this paper, a model is proposed for bilateral symmetry detection in images consisting of dense arrangements of local features. The model is elaborated on the basis of a psychophysical experiment showing that grouping precedes and facilitates symmetry detection. The proposed computational model consists of three stages: a grouping stage, a symmetry-detection stage, and a symmetry-subsumption stage. Reliance upon a preliminary grouping stage enables a significant reduction of the computational load for detecting symmetry. An implementation of the model is described, and results are presented, showing a good agreement of the model performance with human symmetry perception. * Part of the work in this paper has been presented at the IEEE 4 th International Conference on Computer Vision, Berlin 1993. 1 Introduction In this paper, we propose a model for global bilateral symmetry detection in dense images. Dense arrangements of local features, such as dots or oriented segments, are en...

The aim of this paper is to present an evolutionary framework for categorization. Evolution needs an evaluation mechanism to work, and it is argued that primary values that the organism needs for its survival -- such as food, mates for reproduction, and shelter -- can drive the evolution of categories. Sensory stimulation is needed to build up the cognitive apparatus, but cannot in itself provide the evaluation mechanism for evolution. Categorization constrained by values will be dependent on the availability of sensory information, and its power as predictive of values. As perception and categorization are tied to the actions of the organism, it is argued that the unit of perception should be seen as larger than the usual singledimension stimulus, and evidence is reviewed to support this claim. Covarying stimuli will also provide a much greater predictive power than single-dimension stimuli alone.

. The purpose of this paper is to propose a refinement of the notion of innateness. If we merely identify innateness with bias, then we obtain a poor characterisation of this notion, since any learning device relies on a bias that makes it choose a given hypothesis instead of another. We show that our intuition of innateness is better captured by a characteristic of bias, related to isotropy. Generalist models of learning are shown to rely on an "isotropic" bias, whereas the bias of specialised models, which include some specific a priori knowledge about what is to be learned, is necessarily "anisotropic". The so-called generalist models, however, turn out to be specialised in some way: they learn "symmetrical" forms preferentially, and have strictly no deficiencies in their learning ability. Because some learning beings do not always show these two properties, such generalist models may be sometimes ruled out as bad candidates for cognitive modelling. 1 Introduction In cognitive mode...

Most people would agree that the shape of an object is one of its most perceptually important attributes, and some researchers have argued that it is the primary attribute by which observers are able to recognize objects �e.g., Biederman, 1987). Given the ubiquity of this common intuition, it is somewhat puzzling to note that the concept of ``shape' ' has no formal mathematical definition that can adequately characterize its intended meaning when used colloquially. For example, almost everyone would concur that a big sphere and a small sphere both have the same shape, yet by most of the standard measures used in geometry they are quite different. The abstract nature of the concept of shape is perhaps best revealed by the perceptual classification of biological forms �e.g., see Thompson, 1942). Consider, for example, the ability of normal individuals to identify their friends and loved ones under a variety of different viewing conditions. We are able to identify people from different vantage points, and with different facial expressions, hairstyles, make-up, or clothing accessories, such as hats or jewellery. We

. The purpose of this paper is to propose a refinement of the notion of innateness. If we merely identify innateness with bias, then we obtain a poor characterisation of this notion, since any learning device relies on a bias that makes it choose a given hypothesis instead of another. We show that our intuition of innateness is better captured by a characteristic of bias, related to isotropy. Generalist models of learning are shown to rely on an "isotropic" bias, whereas the bias of specialised models, which include some specific a priori knowledge about what is to be learned, is necessarily "anisotropic". The socalled generalist models, however, turn out to be specialised in some way: they learn "symmetrical" forms preferentially, and have strictly no deficiencies in their learning ability. Because some learning beings do not always show these two properties, such generalist models may be sometimes ruled out as bad candidates for cognitive modelling. 1