Representing,Running, and Revising Mental Models: A Computational Model

People use commonsense science knowledge to flexibly explain, predict, and manipulate the world around them, yet we lack computational models of how this commonsense science knowledge is represented, acquired, utilized, and revised. This is an important challenge for cognitive science: Building higher order computational models in this area will help characterize one of the hallmarks of human reasoning, and it will allow us to build more robust reasoning systems. This paper presents a novel assembled coherence (AC) theory of human conceptual change, whereby people revise beliefs and mental models by constructing and evaluating explanations using fragmentary, globally inconsistent knowledge. We implement AC theory with Timber , a computational model of conceptual change that revises its beliefs and generates human‐like explanations in commonsense science. Timber represents domain knowledge using predicate calculus and qualitative model fragments, and uses an abductive model formulation algorithm to construct competing explanations for phenomena. Timber then (a) scores competing explanations with respect to previously accepted beliefs, using a cost function based on simplicity and credibility, (b) identifies a low‐cost, preferred explanation and accepts its constituent beliefs, and then (c) greedily alters previous explanation preferences to reduce global cost and thereby revise beliefs. Consistency is a soft constraint in Timber ; it is biased to select explanations that share consistent beliefs, assumptions, and causal structure with its other, preferred explanations. In this paper, we use Timber to simulate the belief changes of students during clinical interviews about how the seasons change. We show that Timber produces and revises a sequence of explanations similar to those of the students, which supports the psychological plausibility of AC theory.     

Reviving inert knowledge: analogical abstraction supports relational retrieval of past events

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.     

Solving geometric analogy problems through two-stage analogical mapping

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.     

Domain transfer via cross-domain analogy

Analogical learning has long been seen as a powerful way of extending the reach of one’s knowledge. We present the domain transfer via analogy (DTA) method for learning new domain theories via cross-domain analogy. Our model uses analogies between pairs of textbook example problems, or worked solutions, to create a domain mapping between a familiar and a new domain. This mapping allows us to initialize a new domain theory. After this initialization, another analogy is made between the domain theories themselves, providing additional conjectures about the new domain. We present two experiments in which our model learns rotational kinematics by an analogy with translational kinematics, and vice versa. These learning rates outperform those from a version of the system that is incrementally given the correct domain theory.     

The Roles of Similarity in Transfer: Separating Retrievability From Inferential Soundness

Similarity is universally acknowledged to be central in transfer, but recent research suggests that its role is complex. The present research attempts to isolate and compare the determinants of similarity-based access to memory and the determinants of the subjective soundness and similarity of a match. We predicted, based on structure-mapping theory, that subjective soundness would depend on the degree of shared relational structure, particularly higher-order structure such as causal bindings. In contrast, we predicted that memory retrieval would be highly sensitive to surface similarities such as common object attributes. To assess retrievability, in three studies, subjects were asked to read a large set of stories and were later given a set of probe stories that resembled the original stories in systematically different ways; e.g., purely relational analogies, surface-similarity matches, or overall (literal similarity) matches. Subjects were told to write out any of the original stories that came to mind. To assess subjective soundness, independent subjects (and also the same reminding subjects) were asked to rate the inferential soundness of each pair; i.e., how well inferences true of one story would apply to the other. As predicted, subjective soundness was highly related to the degree of common relational structure, while retrievability was chiefly related to the degree of surface similarity. Ratings of the similarity of the pairs did not predict the retrievability ordering, arguing against the possibility that the retrieval ordering simply reflected overall similarity. Further, a fourth study demonstrated that subjects given a forced-choice recognition task could discriminate between possible matches on the basis of relational structure, ruling out the possibility that the poor relational retrieval resulted from forgetting or failing to encode the relational structure. We conclude that there is a dissociation between the similarity that governs access to long-term memory and that which is used in evaluating and reasoning from a present match. We describe a model, called MAC/FAC ("any are called but few are chosen"), that uses a two-stage similarity retrieval process to model these findings. Finally, we speculate on the implications of this view for learning and transfer.     

Extending SME to Handle Large‐Scale Cognitive Modeling

Analogy and similarity are central phenomena in human cognition, involved in processes ranging from visual perception to conceptual change. To capture this centrality requires that a model of comparison must be able to integrate with other processes and handle the size and complexity of the representations required by the tasks being modeled. This paper describes extensions to Structure‐Mapping Engine (SME) since its inception in 1986 that have increased its scope of operation. We first review the basic SME algorithm, describe psychological evidence for SME as a process model, and summarize its role in simulating similarity‐based retrieval and generalization. Then we describe five techniques now incorporated into the SME that have enabled it to tackle large‐scale modeling tasks: (a) Greedy merging rapidly constructs one or more best interpretations of a match in polynomial time: O(n²log(n)); (b) Incremental operation enables mappings to be extended as new information is retrieved or derived about the base or target, to model situations where information in a task is updated over time; (c) Ubiquitous predicates model the varying degrees to which items may suggest alignment; (d) Structural evaluation of analogical inferences models aspects of plausibility judgments; (e) Match filters enable large‐scale task models to communicate constraints to SME to influence the mapping process. We illustrate via examples from published studies how these enable it to capture a broader range of psychological phenomena than before.     

Using analogical mapping to simulate time-course phenomena in perceptual similarity

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.     

MAC/FAC: A Model of Similarity-Based Retrieval

We present a model of similarity-based retrieval that attempts to capture three seemingly contradictory psychological phenomena: (a) structural commonalities are weighed more heavily than surface commonalities in similarity judgments for items in working memory; (b) in retrieval, superficial similarity is more important than structural similarity; and yet (c) purely structural (analogical) remindings e sometimes experienced. Our model, MAC/FAC, explains these phenomena in terms of a two-stage process. The first stage uses a computationally cheap, non-structural matcher to filter candidate long-term memory items. It uses content vectors, a redundant encoding of structured representations whose dot product estimates how well the corresponding structural representations will match. The second stage uses SME (structure-mapping engine) to compute structural matches on the handful of items found by the first stage. We show the utility of the MAC/FAC model through a series of computational experiments: (a) We demonstrate that MAC/FAC can model patterns of access found in psychological data; (b) we argue via sensitivity analyses that these simulation results rely on the theory; and (c) we compare the performance of MAC/FAC with ARCS, an alternate model of similarity-based retrieval, and demonstrate that MAC/FAC explains the data better than ARCS. Finally, we discuss limitations and possible extensions of the model, relationships with other recent retrieval models, and place MAC/FAC in the context of other recent work on the nature of similarity.