Keith J. Holyoak

Schema induction and analogical transfer.

An analysis of the process of analogical thinking predicts that analogies will be noticed on the basis of semantic retrieval cues and that the induction of a general schema from concrete analogs will facilitate analogical transfer. These predictions were tested in experiments in which subjects first read one or more stories illustrating problems and their solutions and then attempted to solve a disparate but analogous transfer problem. The studies in Part I attempted to foster the abstraction of a problem schema from a single story analog by means of summarization instructions, a verbal statement of the underlying principle, or a diagrammatic representation of it. None of these devices achieved a notable degree of sucess. In contrast, the experiments in Part II demonstrated that if two prior analogs were given, subjects often derived a problem schema as an incidental product of describing the similarities of the analogs. The quality of the induced schema was highly predictive of subsequent transfer performance. Furthermore, the verbal statements and diagrams that had failed to facilitate transfer from one analog proved highly beneficial when paired with two. The function of examples in learning was discussed in light of the present study.

Analogical problem solving

Abstract The use of an analogy from a semantically distant domain to guide the problemsolving process was investigated. The representation of analogy in memory and processes involved in the use of analogies were discussed theoretically and explored in five experiments. In Experiment I oral protocols were used to examine the processes involved in solving a problem by analogy. In all experiments subjects who first read a story about a military problem and its solution tended to generate analogous solutions to a medical problem (Dunckers “radiation problem”), provided they were given a hint to use the story to help solve the problem. Transfer frequency was reduced when the problem presented in the military story was substantially disanalogous to the radiation problem, even though the solution illustrated in the story corresponded to an effective radiation solution (Experiment II). Subjects in Experiment III tended to generate analogous solutions to the radiation problem after providing their own solutions to the military problem. Subjects were able to retrieve the story from memory and use it to generate an analogous solution, even when the critical story had been memorized in the context of two distractor stories (Experiment IV). However, when no hint to consider the story was given, frequency of analogous solutions decreased markedly. This decrease in transfer occurred when the story analogy was presented in a recall task along with distractor stories (Experiment IV), when it was presented alone, and when it was presented in between two attempts to solve the problem (Experiment V). Component processes and strategic variations in analogical problem solving were discussed. Issues related to noticing analogies and accessing them in memory were also examined, as was the relationship of analogical reasoning to other cognitive tasks.

Pragmatic reasoning schemas

We propose that people typically reason about realistic situations using neither content-free syntactic inference rules nor representations of specific experiences. Rather, people reason using knowledge structures that we term pragmatic reasoning schemas, which are generalized sets of rules defined in relation to classes of goals. Three experiments examined the impact of a “permission schema” on deductive reasoning. Experiment 1 demonstrated that by evoking the permission schema it is possible to facilitate performance in Wasons selection paradigm for subjects who have had no experience with the specific content of the problems. Experiment 2 showed that a selection problem worded in terms of an abstract permission elicited better performance than one worded in terms of a concrete but arbitrary situation, providing evidence for an abstract permission schema that is free of domain-specific content. Experiment 3 provided evidence that evocation of a permission schema affects not only tasks requiring procedural knowledge, but also a linguistic rephrasing task requiring declarative knowledge. In particular, statements in the form if p then q were rephrased into the form p only if q with greater frequency for permission than for arbitrary statements, and rephrasings of permission statements produced a pattern of introduction of modals (must, can) totally unlike that observed for arbitrary conditional statements. Other pragmatic schemas, such as “causal” and “evidence” schemas can account for both linguistic and reasoning phenomena that alternative hypotheses fail to explain.

Analogical Mapping by Constraint Satisfaction

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.

Distributed representations of structure : A theory of analogical access and mapping

We describe an integrated theory of analogical access and mapping, instantiated in a computational model called LISA (Learning and Inference with Schemas and Analogies). LISA represents predicates and objects as distributed patterns of activation over units representing semantic primitives. These representations are dynamically bound into propositional structures, thereby achieving the structure-sensitivity of a symbolic system and the flexibility of a connectionist system. LISA also has a number of inherent limitations, including capacity limits and sensitivity to the manner in which a problem is represented. A key theoretical claim is that similar limitations also arise in human reasoning, suggesting that the architecture of LISA can provide computational explanations of properties of the human cognitive architecture. We report LISAs performance in simulating a wide range of empirical phenomena concerning human analogical access and mapping. The model treats both access and mapping as types of guided pattern classification, differing only in that mapping is augmented by a capacity to learn new correspondences. Extensions of the approach to account for analogical inference and schema induction are also discussed.

Surface and structural similarity in analogical transfer.

Two experiments investigated factors that influence the retrieval and use of analogies in problem solving, Experiment 1 demonstrated substantial spontaneous analogical transfer with a delay of several days between presentation of the source and target analogues. Experiment 2 examined the influence of different types of similarity between the analogues. A mechanism for retrieval of source analogues is proposed, based on summation of activation from features shared with a target problem. The results of Experiment 2 indicated that both structural features, which play a causal role in determining possible problem solutions, and salient surface features, which do not have a causal role, influence spontaneous selection of an analogue. Structural features, however, have a greater impact than do surface features on a problem solver’s ability to use an analogue once its relevance has been pointed out.

Rostrolateral Prefrontal Cortex Involvement in Relational Integration during Reasoning

Patient and neuroimaging studies indicate that complex reasoning tasks are associated with the prefrontal cortex (PFC). In this study, we tested the hypothesis that the process of relational integration, or considering multiple relations simultaneously, is a component process of complex reasoning that selectively recruits PFC. We used fMRI to examine brain activation during 0-relational, 1-relational, and 2-relational problems adapted from the Ravens Progressive Matrices and hypothesized that PFC would be preferentially recruited by the 2-relational problem type. Event-related responses were modeled by convolving a canonical hemodynamic response function with the response time (RT) associated with each trial. The results across different analyses revealed the same pattern: PFC activation was specific to the comparison between 2- and 1-relational problems and was not observed in the comparison between 1- and 0-relational problems. Furthermore, the process of relational integration was specifically associated with bilateral rostrolateral PFC (RLPFC; lateral area 10) and right dorsolateral PFC (areas 9 and 46). Left RLPFC showed the greatest specificity by remaining preferentially recruited during 2-relational problems even after comparisons were restricted to trials matched for RT and accuracy. The link between RLPFC and the process of relational integration may be due to the associated process of manipulating self-generated information, a process that may characterize RLPFC function.

A System for Relational Reasoning in Human Prefrontal Cortex

The integration of multiple relations between mental representations is critical for higher level cognition. For both deductive- and inductive-reasoning tasks, patients with prefrontal damage exhibited a selective and catastrophic deficit in the integration of relations, whereas patients with anterior temporal lobe damage, matched for overall IQ but with intact prefrontal cortex, exhibited normal relational integration. In contrast, prefrontal patients performed more accurately than temporal patients on tests of both episodic memory and semantic knowledge. These double dissociations suggest that integration of relations is a specific source of cognitive complexity for which intact prefrontal cortex is essential. The integration of relations may be the fundamental common factor linking the diverse abilities that depend on prefrontal function, such as planning, problem solving, and fluid intelligence.

A symbolic-connectionist theory of relational inference and generalization

The authors present a theory of how relational inference and generalization can be accomplished within a cognitive architecture that is psychologically and neurally realistic. Their proposal is a form of symbolic connectionism: a connectionist system based on distributed representations of concept meanings, using temporal synchrony to bind fillers and roles into relational structures. The authors present a specific instantiation of their theory in the form of a computer simulation model, Learning and Inference with Schemas and Analogies (LISA). By using a kind of self-supervised learning, LISA can make specific inferences and form new relational generalizations and can hence acquire new schemas by induction from examples. The authors demonstrate the sufficiency of the model by using it to simulate a body of empirical phenomena concerning analogical inference and relational generalization.

The Cognitive Basis of Knowledge Transfer

Publisher Summary This chapter discusses the interrelationships between task structure, encoding and retrieval processes, and the prior knowledge of the learner, as these factors relate to transfer. It presents a distinction between perceived similarity of the training and transfer situations, based on salient common features of their representations, and objective structural similarity, based on the actual nature of the task components determining appropriate responses. Transfer is affected by both types of similarity. Perceived similarity determines whether transfer is attempted, whereas objective structural similarity determines whether transfer is positive or negative. The encoding of the training task fosters subsequent transfer to the extent that the learner acquires rules that are applicable to a range of superficially different tasks with structural commonalities. If the transfer task evokes similar goals and processing mechanisms, or has salient surface resemblances to the training task, these common components then serve as the basis for retrieval of the acquired knowledge in the transfer context. Several factors that influence learning and retention merit more extensive investigation in relation to transfer. One such factor is the role of context and contrast in determining the learners representation of the training task.