Analogy by Alignment: On Structure Mapping and Similarity
John Kelleher2004
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Abstract
This paper presents a novel domain independent algorithm for constructing analogies using relationship-based structure-mapping. This algorithm is used as a core component in a system that solves visual analogy IQ test problems.
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Structural constraints and object similarity in analogical mapping and inference
2004
Theories of analogical reasoning have viewed relational structure as the dominant determinant of analogical mapping and inference, while assigning lesser importance to similarity between individual objects. An experiment is reported in which these two sources of constraints on analogy are placed in competition under conditions of high relational complexity. Results demonstrate equal importance for relational structure and object similarity, both in analogical mapping and in inference generation.
Analogical Mapping by Constraint Satisfaction
Cognitive Science, 1989
A theory of analogical mapping between source and target analogs based upon interacting structural, semantic, and pragmatic constraints is proposed here. The structural constraint of isomorphism encourages mappings that maximize the consistency of relational corresondences between the elements of the two analogs. The constraint of semantic similarity supports mapping hypotheses to the degree that mapped predicates have similar meanings. The constraint of pragmatic centrality favors mappings involving elements the analogist believes to be important in order to achieve the purpose for which the analogy is being used. The theory is implemented in a computer program called ACME (Analogical Constraint Mapping Engine), which represents constraints by means of a network of supporting and competing hypotheses regarding what elements to map. A cooperative algorithm for parallel constraint satisfaction identities mapping hypotheses that collectively represent the overall mapping that best fits the interacting constraints. ACME has been applied to a wide range of examples that include problem analogies, analogical arguments, explanatory analogies, story analogies, formal analogies, and metaphors. ACME is sensitive to semantic and pragmatic information if it is available, and yet able to compute mappings between formally isomorphic analogs without any similar or identical elements. The theory is able to account for empirical findings regarding the impact of consistency and similarity on human processing of analogies.
Using analogical mapping to simulate time-course phenomena in perceptual similarity
Cognitive Systems Research, 2009
We present a computational model of visual similarity. The model is based upon the idea that perceptual comparisons may utilize the same mapping processes as are used in analogy. We use the Structure Mapping Engine (SME), a model of Gentner's structure-mapping theory of analogy, to perform comparison on representations that are automatically generated from visual input. By encoding visual scenes incrementally and sampling the output of SME at multiple stages in its processing, we are able to model not only the output of similarity judgments, but the time course of the comparison process. We demonstrate the model's effectiveness by replicating the results from three psychological studies that bear on the time course of comparison.
Producing and Recognizing Analogical Relations
Journal of the Experimental Analysis of Behavior, 2009
Analogical reasoning is an important component of intelligent behavior, and a key test of any approach to human language and cognition. Only a limited amount of empirical work has been conducted from a behavior analytic point of view, most of that within Relational Frame Theory (RFT), which views analogy as a matter of deriving relations among relations. The present series of four studies expands previous work by exploring the applicability of this model of analogy to topography-based rather than merely selectionbased responses and by extending the work into additional relations, including nonsymmetrical ones. In each of the four studies participants pretrained in contextual control over nonarbitrary stimulus relations of sameness and opposition, or of sameness, smaller than, and larger than, learned arbitrary stimulus relations in the presence of these relational cues and derived analogies involving directly trained relations and derived relations of mutual and combinatorial entailment, measured using a variety of productive and selection-based measures. In Experiment 1 participants successfully recognized analogies among stimulus networks containing same and opposite relations; in Experiment 2 analogy was successfully used to extend derived relations to pairs of novel stimuli; in Experiment 3 the procedure used in Experiment 1 was extended to nonsymmetrical comparative relations; in Experiment 4 the procedure used in Experiment 2 was extended to nonsymmetrical comparative relations. Although not every participant showed the effects predicted, overall the procedures occasioned relational responses consistent with an RFT account that have not yet been demonstrated in a behavior-analytic laboratory setting, including productive responding on the basis of analogies.
Analogical mapping during similarity judgments
We propose that carrying out a similarity comparison of two objects or scenes requires that their components be aligned in a manner akin to analogical mapping. We present an experiment which supports this claim and then examine a computer simulation of these results which is consistent with the idea that a process of mapping and alignment occurs during similarity judgments .
A theory of rerepresentation in analogical matching
2003
Psychologically, rerepresentation appears to be an important technique for achieving flexibility in analogical matching. This paper presents a concise theory of rerepresentation in analogical matching. It divides the problem into detecting opportunities for rerepresentation, generating rerepresentation suggestions based on libraries of general methods, and strategies for controlling the rerepresentation process. We show that the kinds of opportunities can be exhaustively derived from the principles of structuremapping, and the methods for detecting them derived from consideration of how the SME algorithm works. Four families of rerepresentation methods are proposed, as well as task-independent and task-dependent constraints on strategies. Implemented simulation examples are used for illustration.
Structural Alignment during Similarity Comparisons
Cognitive Psychology, 1993
Similarity comparisons are a basic component of cognition, and there are many elegant models of this process. None of these models describe comparisons of structured representations, although mounting evidence suggests that mental representations are well characterized by structured hierarchical systems of relations. We propose that structured representations can be compared via structural alignment, a process derived from models of analogical reasoning. The general prediction of structural alignment is that similarity comparisons lead subjects to attend to the matching relational structure in a pair of items. This prediction is illustrated with a computational simulation that also suggests that the strength of the relational focus is diminished when the relational match is impoverished, or when competing interpretations lead to rich object matches. These claims are tested in four experiments using the one-shot mapping paradigm, which places object similarity and relational similarity in opposition. The results support the hypothesis that similarity involves the alignment of structured representations .
Analogy–Watershed or Waterloo? Structural alignment and the development of connectionist models of analogy
Neural network models have been criticized for their inability to make use of compositional representations. In this paper, we describe a series of psychological phenomena that demonstrate the role of structured representations in cognition. These findings suggest that people compare relational representations via a process of structural alignment. This process will have to be captured by any model of cognition, symbolic or subsymbolic.
Analogical mapping using similarity of binary distributed representations
1993
We develop an approach to analogical reasoning with hierarchically structured descriptions of episodes and situations based on a particular form of vector representations-structure-sensitive sparse binary distributed representations known as code-vectors. We propose distributed representations of analog elements that allow finding correspondence between the elements for implementing analogical mapping, as well as analogical inference, based on similarity of those representations. The proposed methods are investigated using test analogs and the obtained results are as those of known mature analogy models. However, exploiting similarity properties of distributed representations provides a better scaling, enhances the semantic basis of analogs and their elements as well as neurobiological plausibility. The paper also provides a brief survey of analogical reasoning, its models, and representations employed in those models.
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A Multi-Strategy Approach to Structural Analogy Making
Journal of Intelligent Information Systems, 2017
Analogy is the cognitive process of matching the characterizing features of two different items. This may enable reuse of knowledge across domains , which can help to solve problems. Indeed, abstracting the 'role' of the features away from their specific embodiment in the single items is fundamental to recognize the possibility of an analogical mapping between them. The analogical reasoning process consists of five steps: retrieval, mapping, evaluation , abstraction and re-representation. This paper proposes two forms of an operator that includes all these elements, providing more power and flexibility than existing systems. In particular, the Roles Mapper leverages the presence of identical descriptors in the two domains, while the Roles Argumentation-based Mapper removes also this limitation. For generality and compliance with other reasoning operators in a multi-strategy inference setting, they exploit a simple formalism based on First-Order Logic and do not require any background knowledge or meta-knowledge. Applied to the most critical classical examples in the literature, they proved to be able to find insightful analogies.
Constraints on Analogical Mapping: A Comparison of Three Models
Cognitive Science, 1994
Three theories of analogy have been proposed which are supported by computational models and data from experiments on human analogical abilities. In this paper, we show how these theories can be unified within a common metatheoretical framework which distinguishes between levels of informational, behavioural and hardware constraints. This framework makes clear the distinctions between three computational models in the literature (the Analogical Constraint Mapping Engine, the Structure-Mapping Engine and the Incremental Analogy Machine) . The paper then goes on to develop a methodology for the comparative testing of these models. In two different manipulations of an analogical-mapping task we compare the results of computational experiments with these models against the results of psychological experiments. In the first experiment, we show that increasing the number of similar elements in two analogical domains, decreases the response time taken to reach the correct mapping
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Making analogies is an important way for people to explain and understand new concepts. Though making analogies is natural for human beings, it is not a trivial task for a dialogue agent. Making analogies requires the agent to establish a correspondence between concepts in two different domains. In this work, we explore a data-driven approach for making analogies automatically. Our proposed approach works with data represented as a flat graphical structure, which can either be designed manually or extracted from Internet data. For a given concept from the base domain, our analogy agent can automatically suggest a corresponding concept from the target domain, and a set of mappings between the relationships each concept has as supporting evidence. We demonstrate the working of this algorithm by both reproducing a classical example of analogy inference and making analogies in new domains generated from DBPedia data.
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APPLIED INFORMATICS-PROCEEDINGS-, 2001
retrieving analogies from presented problem data is an important phase of analogical reasoning, influencing many related cognitive processes. Existing models have focused on semantic similarity, but structural similarity is also a necessary requirement of any analogical comparison. We present a new technique for performing structure based analogy retrieval. This is founded upon derived attributes that explicitly encode elementary structural qualities of a domains representation. Crucially, these attributes are unrelated to the semantic content of the domain information, and encode only its structural qualities. We describe a number of derived attributes and detail the computation of the corresponding attribute values. We examine our models operation, detailing how it retrieves both semantically related and unrelated domains. We also present a comparison of our algorithms performance with existing models, using a structure rich but semantically impoverished domain.
Analogies – Integrating Cognitive Abilities
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Finding analogies within systems: Constraints on unsegmented matching
The complex structure and organization of knowledge in the human mind is one of the key facets of thought. One of the fundamental cognitive processes that operates over that structure is analogy. A typical computational model of analogy might juxtapose a source do- main and a target domain, such as the solar system and the Bohr-Rutherford (BR) model of an atom (Gentner, 1983). The goal is to find a correspondence mapping between these two domains. Determining a mapping between the source and target domains of a non-trivial size would be intractable without a set of constraints to restrict the set of correspondences that are considered by a human reasoner. Moreover, the mere presence of domains serve as a constraint on mapping. In this paper, we study an alternative problem called unsegmented mapping - correspondence without specification of domains. We show a series of three formal constraints that allow for analogical-like mappings without explicit segmentation. The result, correspondence is possible without domains, has implications for models of analogical reasoning as well as schema induction and inference.
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Journal of Experimental and Theoretical Artificial Intelligence , 2022
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.
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Abstract We review the work of Evans on graphical proportional analogies, identifying the object mappings that underlie many such comparisons. The limitations of Evans ANALOGY model are investigated. We then establish the role of attributes (colour, shape, pattern etc) in such analogies and identify two distinct mapping algorithms that are required by different classes of geometric analogy problems. We identify the conditions under which the alternate algorithms are required to produce a" best" answer.
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