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. (shrink)

This article describes the path‐mapping theory of how humans integrate analogical mapping and general problem solving. The theory posits that humans represent analogs with declarative roles, map analogs by lower‐level retrieval of analogous role paths, and coordinate mappings with higher‐level organizational knowledge. Implemented in the ACT‐R cognitive architecture, the path‐mapping theory enables models of analogical mapping behavior to incorporate and interface with other problem‐solving knowledge. Path‐mapping models thus can include task‐specific skills such as (...) encoding analogs or generating responses, and can make behavioral predictions at the level of real‐world metrics such as latency or correctness. We show that the path‐mapping theory can successfully account for the major phenomena addressed by previous theories of analogy. We also describe a path‐mapping model that can account for subjects' incremental eye‐movement and typing behavior in a story‐mapping task. We discuss extensions and implications of this work to other areas of analogy and problem‐solving research. (shrink)

Evans’ 1968 ANALOGY system was the first computer model of analogy. This paper demonstrates that the structure mapping model of analogy, when combined with high‐level visual processing and qualitative representations, can solve the same kinds of geometric analogy problems as were solved by ANALOGY. Importantly, the bulk of the computations are not particular to the model of this task but are general purpose: We use our existing sketch understanding system, CogSketch, to compute visual structure that is used by our (...) existing analogical matcher, Structure Mapping Engine (SME). We show how SME can be used to facilitate high‐level visual matching, proposing a role for structural alignment in mental rotation. We show how second‐order analogies over differences computed via analogies between pictures provide a more elegant model of the geometric analogy task. We compare our model against human data on a set of problems, showing that the model aligns well with both the answers chosen by people and the reaction times required to choose the answers. (shrink)

(2013). Two facets of cognitive control in analogical mapping: The role of semantic interference resolution andgoal-driven structure selection. Thinking & Reasoning. ???aop.label???

Theories of analogical reasoning have assumed that a 1‐to‐1 constraint discourages reasoners from mapping a single element in 1 analog to multiple elements in another. Empirical evidence suggests that reasoners sometimes appear to violate the one‐to‐one constraint when asked to generate mappings, yet virtually never violate it when asked to generate analogical inferences. However, few studies have examined analogical inferences based on nonisomorphic analogs, and their conclusions are suspect due to methodological problems. We sought to elicit (...) mixed inferences that could result from combining information from 2 possible mappings. Participants generated 2‐to‐1 correspondences when asked for explicit mappings, but did not produce mixed inferences. Multiple correspondences appear to arise from multiple isomorphic mappings, rather than from a single homomorphic mapping. (shrink)

In this paper we present Drama, a distributed model of analogical mapping that integrates semantic and structural constraints on constructing analogies. Specifically, Drama uses holographic reduced representations (Plate, 1994), a distributed representation scheme, to model the effects of structure and meaning on human performance of analogical mapping. Drama is compared to three symbolic models of analogy (SME, Copycat, and ACME) and one partially distributed model (LISA). We describe Drama's performance on a number of example analogies and (...) assess the model in terms of neurological and psychological plausibility. We argue that Drama's successes are due largely to integrating structural and semantic constraints throughout the mapping process. We also claim that Drama is an existence proof of using distributed representations to model high‐level cognitive phenomena. (shrink)

A model of analogical mapping is proposed that uses five principles to generate consistent and conflicting hypotheses regarding assignments of elements of a source domain to analogous elements of a target domain. The principles follow the fine conceptual structure of the domains. The principles are: (1) the principle of proportional analogy; (2) the principle of mereological analogy, (3) the principle of chain reinforcement; (4) the principle of transitive reinforcement; and (5) the principle of mutual inconsistency. A constraint-satisfaction network (...) is used to find the set of assignments that preserves the greatest relational structure of the source. In contrast to the model proposed here, most models of analogical mapping use only the principle of proportional analogy. The use of many principles is shown to be superior in that it permits smoother integration of pragmatic factors and results in a more efficient mapping process. (shrink)

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. The human data were successfully simulated using a computational (...) analogy model (LISA) that treats both relational correspondences and object similarity as soft constraints that operate within a limited-capacity working memory; but not with a model (SME) that treats relational structure as pre-eminent. (shrink)

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)

Research in general, and research on friendship in particular, uses metaphors and analogies, and research itself can be seen in analogy with map making. This chapter takes us on a meandering walk along mono- and multidisciplinary inquiries into friendship as seen from many perspectives, like that of history and philosophy of science (that has analogical modelling as a canonical style of reasoning) and semiotics, to reflect on the uses of metaphor and analogy. Semiotics as founded by C. S. Peirce (...) is the science of representations, how representational devises relate to their objects and how the meaning generated depends upon context and interpretation. Metaphor and analogy are such representational tools, at once cognitive and common as we all use them to think with, but also specialized within the sciences and humanities where they can be used in effective and misleading ways. It is shown how the general map analogy can be semiotically analysed as a diagram and how its general form can be applied to the aspects of friendship that concern the friends’ knowledge of Self and Other. We not only think, but also do things with metaphors, such as transforming a friend into some kin, or vice versa. (shrink)

What mechanisms underlie children’s language production? Structural priming—the repetition of sentence structure across utterances—is an important measure of the developing production system. We propose its mechanism in children is the same as may underlie analogical reasoning: structure-mapping. Under this view, structural priming is the result of making an analogy between utterances, such that children map semantic and syntactic structure from previous to future utterances. Because the ability to map relationally complex structures develops with age, younger children are less (...) successful than older children at mapping both semantic and syntactic relations. Consistent with this account, 4-year-old children showed priming only of semantic relations when surface similarity across utterances was limited, whereas 5-year-olds showed priming of both semantic and syntactic structure regardless of shared surface similarity. The priming of semantic structure without syntactic structure is uniquely predicted by the structure-mapping account because others have interpreted structural priming as a reflection of developing syntactic knowledge. (shrink)

Advances in artificial intelligence have raised a basic question about human intelligence: Is human reasoning best emulated by applying task‐specific knowledge acquired from a wealth of prior experience, or is it based on the domain‐general manipulation and comparison of mental representations? We address this question for the case of visual analogical reasoning. Using realistic images of familiar three‐dimensional objects (cars and their parts), we systematically manipulated viewpoints, part relations, and entity properties in visual analogy problems. We compared human performance (...) to that of two recent deep learning models (Siamese Network and Relation Network) that were directly trained to solve these problems and to apply their task‐specific knowledge to analogical reasoning. We also developed a new model using part‐based comparison (PCM) by applying a domain‐general mapping procedure to learned representations of cars and their component parts. Across four‐term analogies (Experiment 1) and open‐ended analogies (Experiment 2), the domain‐general PCM model, but not the task‐specific deep learning models, generated performance similar in key aspects to that of human reasoners. These findings provide evidence that human‐like analogical reasoning is unlikely to be achieved by applying deep learning with big data to a specific type of analogy problem. Rather, humans do (and machines might) achieve analogical reasoning by learning representations that encode structural information useful for multiple tasks, coupled with efficient computation of relational similarity. (shrink)

We present five experiments and simulation studies to establish late analogical abstraction as a new psychological phenomenon: Schema abstraction from analogical examples can revive otherwise inert knowledge. We find that comparing two analogous examples of negotiations at recall time promotes retrieving analogical matches stored in memory—a notoriously elusive effect. Another innovation in this research is that we show parallel effects for real‐life autobiographical memory (Experiments 1–3) and for a controlled memory set (Experiments 4 and 5). Simulation studies (...) show that a unified model based on schema abstraction can capture backward (retrieval) effects as well as forward (transfer) effects. (shrink)

We argue that analogical reasoning, particularly Gentner's structure-mapping theory, provides an integrative theoretical framework through which we can better understand the development of symbol use. Analogical reasoning can contribute both to the understanding of others’ intentions and the establishment of correspondences between symbols and their referents, two crucial components of symbolic understanding. We review relevant research on the development of symbolic representations, intentionality, comparison, and similarity, and demonstrate how structure-mapping theory can shed light on several ostensibly (...) disparate findings in the literature. Focusing on visual symbols, we argue that analogy underlies and supports the understanding of both intention and correspondence, which may enter into a reciprocal bootstrapping process that leads children to gain the prodigious human capacity of symbol use. (shrink)

Analogical cognition refers to the ability to detect, process, and learn from relational similarities. The study of analogical and similarity cognition is widely considered one of the ‘success stories’ of cognitive science, exhibiting convergence across many disciplines on foundational questions. Given the centrality of analogy to mind and knowledge, it would benefit philosophers investigating topics in epistemology and the philosophies of mind and language to become familiar with empirical models of analogical cognition. The goal of this essay (...) is to describe recent empirical work on analogical cognition as well as model applications to philosophical topics. Topics to be discussed include the epistemological distinction between implicit knowledge and explicit knowledge, the debate between empiricists and nativists, the frame problem, expertise, creativity and autism, cognitive architecture, and relational knowledge. Particular attention is given to Dedre Gentner and colleague’s structure-mapping theory – the most developed and widely accepted model of analogical cognition. (shrink)

This paper aims at integrating the work onanalogical reasoning in Cognitive Science into thelong trend of philosophical interest, in this century,in analogical reasoning as a basis for scientificmodeling. In the first part of the paper, threesimulations of analogical reasoning, proposed incognitive science, are presented: Gentner''s StructureMatching Engine, Mitchel''s and Hofstadter''s COPYCATand the Analogical Constraint Mapping Engine, proposedby Holyoak and Thagard. The differences andcontroversial points in these simulations arehighlighted in order to make explicit theirpresuppositions concerning the nature (...) of analogicalreasoning. In the last part, this debate in cognitivescience is applied to some traditional philosophicalaccounts of formal and material analogies as a basisfor scientific modeling, like Mary Hesse`s, and tomore recent ones, that already draw from the work inArtificial Intelligence, like that proposed byAronson, Harré and Way. (shrink)

The present article is the first to investigate in any detail the plant–animal analogies that are integral to Nehemiah Grew's Anatomy of Plants (1682). It focuses on three analogies that Grew used (either productively or critically) to produce novel accounts of vegetative processes: those between sperm and pollen, blood and sap, and mouths and roots. I suggest that Grew's analogical approach and specific mappings allowed him, on the one hand, to “see” plant features and functions that other botanists had (...) overlooked, and, on the other, to determine when the analogies that other botanists deployed did not convincingly describe observable phenomena. On this basis, I argue, he was able to present what he, and several contemporaries, considered to be more accurate accounts of the nature of the vegetative parts and processes in question. More broadly, the article seeks to show that the analogical and observational were complementary aspects of Grew's method, and that, far from hindering his empirical endeavour, his analogies were crucial to it. (shrink)

The ability to reason by analogy is particularly important because it permits the extension of knowledge of a target domain by virtue of its similarity to a base domain via a process of analogical inference. The general procedure for analogical inference involves copying structure from the base to the target in which missing information is generated, and substitutions are made for items for which analogical correspondences have already been found. A pure copying with substitution and generation process (...) is too profligate to be useful, and so constraints must be placed on what information is to be carried over. In this paper, the importance of systematicity as a constraint on inference is explored in four studies in which subjects find correspondences between domains and also make inferences. This work suggests that people prefer to make inferences of information connected to systematic correspondences between domains. A second important theme of this paper is that violations of one‐to‐one mapping can lead to inconsistent object substitutions in inference. The data reveal no such inconsistent substitutions in people's inferences, suggesting that they do respect one‐to‐one mapping in analogical inference. These findings are discussed relative to four prominent computational models of analogical mapping and inference. (shrink)

In attempting to fit a model of analogical problem solving to protocol data of students solving physics problems, several unexpected observations were made. Analogies between examples and exercises (a form of case‐based reasoning) consisted of two distinct types of events. During an initialization event, the solver retrieved an example, set up a mapping between it and the problem, and decided whether the example was useful. During a transfer event, the solver inferred something about the problem's solution. Many different (...) types of initialization and transfer events were observed. Poor solvers tended to follow the example verbatim, copying each solution line over to the problem. Good solvers tried to solve the problem themselves, but referred to the example when they got stuck, or wanted to check a step, or wanted to avoid a detailed calculation. Rather than learn from analogies, both Good and Poor solvers tended to repeat analogies at subsequent similar situations. A revised version of the model is proposed (but not yet implemented) that appears to be consistent with all the findings observed in this and other studies of the same subjects. (shrink)

High-level perception--”the process of making sense of complex data at an abstract, conceptual level--”is fundamental to human cognition. Through high-level perception, chaotic environmen- tal stimuli are organized into the mental representations that are used throughout cognitive pro- cessing. Much work in traditional artificial intelligence has ignored the process of high-level perception, by starting with hand-coded representations. In this paper, we argue that this dis- missal of perceptual processes leads to distorted models of human cognition. We examine some existing artificial-intelligence models--”notably (...) BACON, a model of scientific discovery, and the Structure-Mapping Engine, a model of analogical thought--”and argue that these are flawed pre- cisely because they downplay the role of high-level perception. Further, we argue that perceptu- al processes cannot be separated from other cognitive processes even in principle, and therefore that traditional artificial-intelligence models cannot be defended by supposing the existence of a --œrepresentation module--� that supplies representations ready-made. Finally, we describe a model of high-level perception and analogical thought in which perceptual processing is integrated with analogical mapping, leading to the flexible build-up of representations appropriate to a given context. (shrink)

Maps and mapping raise questions about models and modeling and in science. This chapter archives map discourse in the founding generation of philosophers of science (e.g., Rudolf Carnap, Nelson Goodman, Thomas Kuhn, and Stephen Toulmin) and in the subsequent generation (e.g., Philip Kitcher, Helen Longino, and Bas van Fraassen). In focusing on these two original framing generations of philosophy of science, I intend to remove us from the heat of contemporary discussions of abstraction, representation, and practice of science and (...) thereby see in a more distant and neutral light the many productive ways in which maps can stand in analytically for scientific theories and models. The chapter concludes by complementing the map analogy – i.e., a scientific theory is a map of the world – with a model analogy, viz., a scientific model is a vehicle for understanding. (shrink)

Analogies are partial similarities between different situations that support further inferences. Specifically, analogy is a kind of similarity in which the same system of relations holds across different objects. Analogies thus capture parallels across different situations.

Carey proposes that the acquisition of the natural numbers relies on the interaction between language and analogical processes: specifically, on an analogical mapping from ordinal linguistic structure to ordinal conceptual structure. We suggest that this analogy in fact requires several steps. Further, we propose that additional analogical processes enter into the acquisition of number.

In this paper, I try to accomplish two goals. The first is to provide a general characterization of a method of proofs called — in mathematics — the diagonal argument. The second is to establish that analogical thinking plays an important role also in mathematical creativity. Namely, mathematical research make use of analogies regarding general strategies of proof. Some of mathematicians, for example George Polya, argued that deductions is impotent without analogy. What I want to show is that there (...) exists a direct line leading from Cantor’s diagonal argument to constructions that underlies of the proofs of several important theorems of the mathematical logic (in particular, Church’s theorem concerning the undecidability of formal arithmetic, Gödel’s theorem concerning the incopleteness of formal arithmetic, Tarski’s theorem concerning truth, and Turing’s theorem concerning the Halting Problem), and that the line could be described as an analogical mapping. In other words, Cantor’s diagonal argument and the proofs of the limitative theorems are structurally the same. Hence they can be represented as instances (or special cases) of the same general scheme. (shrink)

Human cognition is striking in its brilliance and its adaptability. How do we get that way? How do we move from the nearly helpless state of infants to the cognitive proficiency that characterizes adults? In this paper I argue, first, that analogical ability is the key factor in our prodigious capacity, and, second, that possession of a symbol system is crucial to the full expression of analogical ability.

Empirical studies indicate that analogy consists of two main processes: retrieval and mapping. While current theories and models of analogy have revealed much about the mainly structural constraints that govern the mapping process, the similarities that underpin the correspondences between individual representational elements and drive retrieval are understood in less detail. In existing models symbol similarities are externally defined but neither empirically grounded nor theoretically justified. This paper introduces a new model (EMMA: the environmental model of analogy) which (...) relies on co‐occurrence information provided by LSA (Latent Semantic Analysis; Landauer & Dumais, 1997) to ground the relations between the symbolic elements aligned in analogy. LSA calculates a contextual distribution for each word encountered in a corpus by counting the frequency with which it co‐occurs with other words. This information is used to define a model that locates each word encountered in a high‐dimensional space, with relations between elements in this space representing contextual similarities between words. A series of simulation experiments demonstrate that the environmental approach to semantics embodied in LSA can produce appropriate patterns of analogical retrieval, but that this semantic measure is not sufficient to model analogical mapping. The implications of these findings, both for theories of representation in analogy research and more general theories of semantics in cognition, are explored. (shrink)

People are habitual explanation generators. At its most mundane, our propensity to explain allows us to infer that we should not drink milk that smells sour; at the other extreme, it allows us to establish facts (e.g., theorems in mathematical logic) whose truth was not even known prior to the existence of the explanation (proof). What do the cognitive operations underlying the inference that the milk is sour have in common with the proof that, say, the square root of two (...) is irrational? Our ability to generate explanations bears striking similarities to our ability to make analogies. Both reflect a capacity to generate inferences and generalizations that go beyond the featural similarities between a novel problem and familiar problems in terms of which the novel problem may be understood. However, a notable difference between analogy-making and explanation-generation is that the former is a process in which a single source situation is used to reason about a single target, whereas the latter often requires the reasoner to integrate multiple sources of knowledge. This seemingly small difference poses a challenge to the task of marshaling our understanding of analogical reasoning to understanding explanation. We describe a model of explanation, derived from a model of analogy, adapted to permit systematic violations of this one-to-one mapping constraint. Simulation results demonstrate that the resulting model can generate explanations for novel explananda and that, like the explanations generated by human reasoners, these explanations vary in their coherence. (shrink)

Analogical reasoning is often employed in problem-solving and metaphor interpretation. This paper submits that, as a default, analogical reasoning addressing these different tasks employs different mapping strategies: In problem-solving, it employs analogy-maximising strategies (like structure mapping, Gentner & Markman 1997); in metaphor interpretation, analogy-minimising strategies (like ATT-Meta, Barnden 2015). The two strategies interact in analogical reasoning with conceptual metaphors. This interaction leads to predictable fallacies. The paper supports these hypotheses through case-studies on ‘mind’-metaphors from ordinary (...) discourse, and abstract problem-solving in the philosophy of mind, respectively: It shows that (1) default metaphorical interpretations for vision- and space-cognition metaphors can be derived with a variant of the analogy-minimising ATT-Meta approach, (2) philosophically influential introspective conceptions of the mind can be derived with conceptual metaphors only through an analogy-maximising strategy, and (3) the interaction of these strategies leads to hitherto unrecognised fallacies in analogical reasoning with metaphors. This yields a debunking explanation of introspective conceptions. (shrink)

The theory of mind debate has reached a “hybrid consensus” concerning the status of theory-theory and simulation-theory. Extant hybrid models either specify co-dependency and implementation relations, or distribute mentalizing tasks according to folk-psychological categories. By relying on a non-developmental framework these models fail to capture the central connection between simulation and theory. I propose a “dynamic” hybrid that is informed by recent work on the nature of similarity cognition. I claim that Gentner’s model of structure-mapping allows us to understand (...) simulation as a process in which psychological representations are aligned, causing the spontaneous abstraction of theoretical generalizations about the psychological domain. (shrink)

The development of analogical reasoning has traditionally been understood in terms of theories of adult competence. This approach emphasizes structured representations and structure mapping. In contrast, we argue that by taking a developmental perspective, analogical reasoning can be viewed as the product of a substantially different cognitive ability – relational priming. To illustrate this, we present a computational (here connectionist) account where analogy arises gradually as a by-product of pattern completion in a recurrent network. Initial exposure to (...) a situation primes a relation that can then be applied to a novel situation to make an analogy. Relations are represented as transformations between states. The network exhibits behaviors consistent with a broad range of key phenomena from the developmental literature, lending support to the appropriateness of this approach (using low-level cognitive mechanisms) for investigating a domain that has normally been the preserve of high-level models. Furthermore, we present an additional simulation that integrates the relational priming mechanism with deliberative controlled use of inhibition to demonstrate how the framework can be extended to complex analogical reasoning, such as the data from explicit mapping studies in the literature on adults. This account highlights how taking a developmental perspective constrains the theory construction and cognitive modeling processes in a way that differs substantially from that based purely on adult studies, and illustrates how a putative complex cognitive skill can emerge out of a simple mechanism. (shrink)

Analogical reasoning is a foundational tool for human learning, allowing learners to recognize relational structures in new events and domains. Here I sketch some grounds for understanding and applying analogical reasoning in social learning. The social world is fundamentally characterized by relations between people, with common relational structures—such as kinships and social hierarchies—forming social units that dictate social behaviors. Just as young learners use analogical reasoning for learning relational structures in other domains—spatial relations, verbs, relational categories—analogical (...) reasoning ought to be a useful cognitive tool for acquiring social relations and structures. (shrink)

Abstractabstract:This article presents previous attempts to map Utopia, a fictional island in the book Utopia by Thomas More, and proposes another possibility, based on the assumption that Utopia is an enclosed garden on an artificial island that is not flat, but has piedmont slopes of 2.5:1. Our mapping experiment is founded on the Renaissance analogy between the domestication of wild nature, and the civilization of the human beings in More’s enclosed garden; and on the anecdotal similarities between the Inca (...) Empire and Utopia. This approach is not only consistent with the island’s dimensional specifications, which have hampered previous mapping attempts due to their mathematical incompatibility, but it also addresses the educative capacity of utopian life not considered by previous mapping efforts. Utopia, as a result, is to be understood as a series of performative spatial arrangements where the physical and geographical specifications would inform the vernacular life of its inhabitants in the direction of self-enhancement. (shrink)

While extremes tend to capture attention, the ordinary is often most of the story. So it may be with the structure-mapping process. The structure-mapping process can account for such pinnacles of thinking as analogy and metaphor, which can lead to overlooking the mundane, incremental use of structure mapping. Consequently, the current discussion shifts focus to the value of close comparisons between literally similar items for the development of knowledge. The intent is to foster greater integration between process (...) and content as well as between individuals and collectives. The payoff is identifying some undue simplifications and some promising new directions. (shrink)