Innovation in design and technology, problem solving, and scientific discovery is often driven by analogical retrieval. When the current situation cues prior knowledge that shares underlying structural relationships, the retrieved relational structure can then be extended to the current situation to offer possible solutions or discoveries. For example, the bipolar plate of a fuel cell can be designed based on the structure of a leaf (see Chan et al., 2011). Although examples of real-world analogical problem solving have been well characterised and documented (e.g. Dunbar, 2000), analogical retrieval without supporting superficial similarity is relatively rare (e.g. Holyoak & Koh, 1987; Trench & Minervino, 2015). On the other hand, memories are frequently cued by situations that share superficial similarity without also sharing deeper structure (e.g. Gentner, Rattermann, & Forbus, 1993; Ross, 1989). When considering its elusiveness and utility, spontaneous analogical retrieval may be the biggest obstacle to overcome for successful problem solving (Gick & Holyoak, 1980).
Research in psychology, education, business, and design has developed methods to boost the chances of spontaneous analogical retrieval and problem solving (e.g. Catrambone & Holyoak, 1989; Gentner, Loewenstein, & Thompson, 2003; Kurtz & Loewenstein, 2007; Linsey, Markman, & Wood, 2012; Minervino, Olguín, & Trench, 2017). One of the most successful methods has been to encourage comparison of multiple analogue examples prior to problem solving. Comparing analogues highlights their common relational structure, which can both improve understanding of the relational structure in each example, and reify this common structure as a portable abstract schema (e.g. Gick & Holyoak, 1983; Goldwater & Gentner, 2015; Kurtz, Miao, & Gentner, 2001). Other manipulations can elicit similar benefits, such as framing a single learning example with an abstract schema (Mandler & Orlich, 1993), being trained to generate your own analogue problem (Bernardo, 2001) or fading out the concrete features of examples (e.g. Fyfe, McNeil, Son, & Goldstone, 2014). Like comparison of analogues, these other methods also encourage a focus on the abstract relational structure of examples, rather than superficial information. These robust, coherent, and abstract relational representations are then more likely to be cued by relevant future examples sharing relational structure and retrieved when useful (see Chen, Mo, & Honomichl, 2004 for analogical problem solving after long delays).
Encouraging comparison has been helpful both when the analogues share the key principle to solve the target problem (e.g. Gentner et al., 2003) and in open-ended problem solving when there exists no pre-established normative solution (e.g. Chan et al., 2011). However, in real-world problem-solving situations, there is no one to provide you with a useful analogue or abstract schema (Loewenstein, 2010). Furthermore, it is too late to go back and improve the quality of how you encoded the relational structure of your prior experiences. At the time of problem solving, is there anything to be done to increase the chances of retrieving the most useful prior knowledge?
One promising method comes from research suggesting it is possible to induce a relational mindset (Brown & Kane, 1988; Vendetti, Wu, & Holyoak, 2014; although see Minervino et al., 2017; Trench, Tavernini, & Goldstone, 2017; and our discussion below for different approaches). When analogical reasoning is elicited by particular task constraints or instructions, reasoners may continue to think relationally even after those task constraints or instructions are removed (hence, a relational mindset). Perhaps the earliest demonstration of a relational mindset was by Brown and Kane (1988) who showed that preschool-aged children given instruction on how to apply a solution from one problem to another would then spontaneously use an analogical strategy in further problems without similar instruction. Goldwater and Markman (2011) showed that people often use salient associations rather than relational commonalities when building categories. For example, with minimal instructional guidance on how to make categorization judgements, people were more likely to categorize a bodyguard with a celebrity (the two are associated) than a bodyguard with a force field (the two both play the same relational role—they protect others). However, when the task instructions encouraged people to compare all three before categorizing, the relational commonality between force fields and bodyguards then became the basis of categorization. Importantly for the current work, in a second set of categorization judgments, after comparison was no longer explicitly encouraged, people would continue to use relational commonalities when presented with new triplets (such as categorizing a vacuum cleaner with soap instead of vacuum cleaner with a carpet). Demonstrating that a relational mindset extends across modalities (from linguistic to visual), Vendetti et al. (2014) showed that after participants solved fill-in-the-blank analogy problems (e.g. blindness : sight :: poverty : ___), they were more likely to indicate that objects corresponded across visual scenes when they played the same role (e.g. a woman and a squirrel each receiving food) instead of sharing visual features (e.g. two women, even though one woman was giving food and the other was receiving food; task originally designed by Markman & Gentner, 1993; we will refer to this as “the picture-mapping task”).
There was a further intriguing result in that there was a correlation between fluid relational thinking ability (as measured by Raven’s Progressive Matrices (RPM); Raven, 2003) and the tendency to select the relational matches in the picture-mapping task for participants in the control condition, but there was no correlation between relational ability and relational tendency in the relational mindset condition. This pattern suggests that a relational mindset can support a focus on relational commonalities across a wide range of fluid abilities.
All of these prior results demonstrate that inducing a relational mindset increases recognition of relational commonalities among simultaneously presented stimuli. Unfortunately, as discussed above, the most difficult barrier to problem solving by analogy is not the failure to recognize the relational commonalities between multiple presented cases, but the failure of a single problem to cue an analogical match from prior knowledge (Gick & Holyoak, 1980). It is an open question whether a relational mindset might also aid relational retrieval. Why might we expect this to work, or why might we not?
A common explanation for the rarity of analogical retrieval is rooted in computational models of analogical reasoning (such as Falkenhainer, Forbus, & Gentner, 1989; Hummel & Holyoak, 1997). Critical to their explanation is that these models suggest that analogical reasoning processes are computationally intensive. Analogical reasoning requires aligning elements of two mental representations based on the common relations among them. This alignment process operates over structured mental representations, meaning that representational elements are bound together by how they relate to each other. There are three primary kinds of representational elements: entities, their attributes, and relations. Simulating this process is complex. Conceptual representations comprised of a large number of representational elements can be put into correspondence with each other in a vastly larger number of ways than smaller representations, so there are constraints on the sorts of correspondences that are preferred in this process.
Here, we will just consider a single model for brevity, the Structure Mapping Engine (SME; Falkenhainer et al., 1989; Forbus, Ferguson, Lovett, & Gentner, 2017). In the first phase of the alignment process, SME considers all possible matches between elements of the two representations (such as those based on shared attributes). Then, in a second phase to enforce structural consistency, there are two constraints. The first is “one-to-one mapping”, which ensures that an element in one representation only corresponds to one element in the other representation. The second constraint is “parallel connectivity”, which ensures that entities playing the same relational role in each representation are put into correspondence (e.g. if “Steve kissed Bill” was aligned with “Beth kissed Sally”, then Steve–Beth and Bill–Sally would be put into correspondence, and not Steve–Sally and Bill–Beth). Then a third phase imposes a third constraint, “systematicity”, that ensures more global levels of correspondence. Matches between two narratives that share higher-order themes and structure (e.g. between Star Wars and Lord of The Rings, because both depict the classic “hero’s journey” narrative) are preferred to matches where there are only superficial semantic similarities and shared lower-order relational correspondences (e.g. between Star Wars and 2001, because both involve space travel).
Simulating the process of aligning relational representations is computationally expensive, and empirical evidence from humans shows that deliberately aligning relational representations is working memory intensive (e.g. Waltz, Lau, Grewal, & Holyoak, 2000), largely because the process of binding entities into relations is arguably the primary constraint on working memory capacity (e.g. Chuderski, 2014; Halford, Wilson, & Phillips, 1998). Although this relational alignment is complex, the process is feasible when only considering a pair of active representations, and people tend to succeed. However, when considering a single example (e.g. a problem or passage of text) with the aim to draw upon prior experience to assist in reasoning or comprehension, there is a lot more than just one other representation to consider.
How could memory search discover only what is relevant to the current example? It is unfeasible to fully structurally align the representation of the current example with all prior experiences in memory. Thus, models of analogical reasoning and retrieval (see Forbus, Gentner, & Law, 1995; Hummel & Holyoak, 1997) are hybrids in that they can both simulate full structural alignment between pairs of representations, and the process by which a current representation can cue prior experiences in memory via more simple calculation of content overlap (e.g. by calculating how many representational elements are shared between representations in Forbus et al., 1995), ignoring distinctions between deep structural and more superficial commonalities. This content overlap calculation enables the rapid comparison of a cue stimulus with vast amounts of prior knowledge.
Memory search in these models initially only considers content overlap, not full structural correspondence. This explains the rarity of analogical retrieval because structurally similar examples that share few entities and attributes have little in common overall, and so are unlikely to be retrieved based on overlapping content. On the other hand, if a present example is highly similar in its entities and attributes with a prior experience, it is quite likely that prior experience will be cued in memory. Of course, prior experiences with commonalities in relations, entities, and attributes are the most likely to be retrieved (Holyoak & Koh, 1987).
If memory retrieval is based on the degree of content overlap, and does not entail analysing structural correspondence, then how could rates of analogical retrieval increase? According to this account, the best route to increasing analogical retrieval is by increasing the proportion of what people encode from example narratives, problems, and cases as abstract relational content likely to be shared with other structurally similar cases. In simpler terms, this means improving relational understanding. This involves recognising how abstract relational principles cohere narratives, problems, and cases. A rich understanding and repertoire of abstract, coherent, relational concepts should lead to uniform encoding across the examples to which these relational concepts apply. In fact, it is the support for uniform relational encoding that Gentner and colleagues propose as the reason why case comparison increases analogical retrieval (Gentner et al., 2003; Gentner, Loewenstein, Thompson, & Forbus, 2009).
How then, according to this account, could a relational mindset improve analogical retrieval? This account suggests that a relational mindset would be most able to help analogical retrieval by encouraging a greater focus on the relational structure of example cases when they are being encoded. This greater focus would support a more uniform relational encoding across examples that share relational structure, with predicted effects similar to those of case comparison.
Most of the research on uniform relational encoding has focussed on improving the representation of initial cases encoded before a retrieval or transfer task. However, there is also evidence that the representation of examples at the time of retrieval does matter. Gentner et al. (2009) showed that comparison of two cases could help retrieval of prior analogues. This benefit is called “the late abstraction principle”. By creating a more abstract relational representation of the cue cases, these cases can serve as better cues to prior examples with matching relational structure. Trench et al. (2017) advanced evidence for the late abstraction principle by training learners to generate schematic perceptual representations of target problems, fading away concrete features. Likewise, Minervino et al. (2017) trained leaners to generate analogue problems to their current target problem. Similar to case comparison, both of these methods increased analogical retrieval and transfer when most needed, during active problem solving. To date, these two methods (of generating schematic representations and analogue problems) may represent the best chance for people to boost analogical retrieval at the time of problem solving without a helper to provide an analogue case or abstract schema.
Given existing evidence, the “uniform relational encoding” account would suggest that the most effective time for a relational mindset to have an effect would be before initial cases were encoded. However, it is still possible that a relational mindset might encourage a more relationally focussed interpretation of a cue case and improve analogical retrieval by cuing prior cases. If memory search is driven by pure content overlap between cue and prior cases, and not a more sophisticated analysis of relational structure, then the only way to increase analogical retrieval is by changing the representation of prior and cue cases.
On other hand, there is research suggesting that memory search is not solely driven by calculation of content overlap, and that analogical retrieval is more sensitive to relational structure than the above account suggests. For example, Dunbar and Blanchette (2001) have argued that the rarity of analogical retrieval in many prior studies is an artefact of task design, and that the right kind of task or prompt can engage analogical retrieval of prior knowledge to a much greater degree. An implication of this account is that people are capable of strategically retrieving different kinds of information for different purposes. If people can strategically increase analogical retrieval, and analogical retrieval is not actually that rare in the right kinds of task environments, then there is no need for a computational explanation of the rarity of analogical retrieval positing that memory search does not involve an analysis of relational structure.
This strategic retrieval account offers additional ways that a relational mindset might increase analogical retrieval. Perhaps inducing a relational mindset at the time of retrieval could boost analogical retrieval without relying on changing the representation of any cases—cue or prior. If so, this could add to the evidence discussed by Dunbar and Blanchette (2001), and challenge the computational explanation of analogical retrieval described above. Furthermore, if inducing a relational mindset could encourage the strategic retrieval of useful prior analogies, this would suggest easy and practical exercises to engage in before problem solving.
The current research
The current experiments examined whether a relational mindset affects analogical retrieval using two sets of short passages designed by Jamrozik (2014). Pairs of passages (one in each set) expressed a specific relational concept, for example the pre-emption of something of lesser status or priority by something of higher status or priority. These concepts were selected because they are relevant to multiple domains of expertise, and thus relevant to educational or problem-solving settings (see Goldwater & Schalk, 2016, for a lengthy discussion). Each passage of the pair expressed the concept in a different domain, such as in law (how a federal law may pre-empt a local law when there are inconsistencies between the two) or in computer science (how a computer’s operating system may pre-empt an inessential series of computations to run a more critical program). In addition to pairs of passages sharing a relational concept from different domains, each passage shared a domain with another passage with a different relational concept. For example, the passage above on legal pre-emption shared a domain with a passage on legal proportionality—the severity of punishment should be in proportion to the severity of the crime. Across both sets of passages, every critical or “test” passage had a different relational and domain match in the other set. This allowed participants to initially read one set of passages and later read the second and report what earlier passage came to mind. Here, improved analogical retrieval was operationalized as recalling more relational matches.
We note here that we motivated this work by discussing the role of analogical retrieval and transfer in creative problem solving, and yet our task does not require any problems to be solved or new ideas to be generated. Instead, we just ask participants to say what they remember. We make this experimental choice for a couple of related reasons. First, prior research shows reminding and problem solving are intertwined processes (e.g. see Brian Ross’ research throughout the 80s and 90s: Ross, 1984, 1987, 1989; Ross & Kennedy, 1990; Ross & Bradshaw, 1994). In Mandler and Orlich (1993), all participants who explicitly recalled a prior analogue problem used that analogue to solve a current problem. In Bernardo (2001), the same experimental manipulations that boosted analogical retrieval boosted analogical problem solving.
There are obviously further important cognitive processes needed to assess the relevance of retrieved prior knowledge, and to formulate how to apply that knowledge to the present case. By focusing on retrieval, participants in the current study can report multiple cases they are reminded of without the additional demands to then draw out different solutions for each of them. It is quite possible that, with extra demands, they would only choose the first solution that came to mind. On the other hand, perhaps the pragmatics of retrieval tasks reduces analogical retrievals in comparison to problem solving tasks (see Dunbar & Blanchette, 2001). In that case, then, any evidence that a relational mindset could increase analogical retrieval could be valuable in showing that it works even when at odds with the task’s pragmatics.
Across two experiments, we examined whether and how a relational mindset may improve analogical retrieval by varying when the mindset was induced—either before encoding the first set of passages or after encoding the passages but before retrieval. Inducing a relational mindset before encoding the initial set of passages may increase analogical retrieval because of an increased focus on the relational structure in the passages, encouraging a representation in memory with robust and coherent relational structures. This novel effect would go beyond prior research showing how a relational mindset can increase a focus on the relational commonalities between co-presented examples, and offer a learning tool to make knowledge more accessible in relevant future situations.
Inducing a relational mindset after the initial encoding of passages might also improve relational retrieval. This pattern would suggest that an example with a given quality of relational encoding could be differentially accessed later. There would be two possible explanations for that effect. The first would be consistent with the late abstraction principle (Gentner et al., 2009), suggesting that changing the representation of cue cases is sufficient to help retrieval of prior analogues. The second possibility is that an induced relational mindset changes the memory search strategy of people, independent of (or in addition to) changing their representation of the cue case. If this manipulation succeeds, further research would be needed to tease these two explanations apart. Either way, these results would encourage work on how a relational mindset might improve problem solving when most needed—at the time of problem solving.
To maximise the chance of a relational mindset increasing relational retrieval after encoding, in experiment 1 all of the first set of passages included an explicit label for the relational concept they describe (such as pre-emption in the passage about pre-emption). Jamrozik (2014) showed that the use of a relational label at encoding increased the chances that the passage was cued by its relational match in the second set, even when the label was not present in the second passage. Jamrozik inferred that the relational label helped make the relational structure of the encoded example more prominent and coherent in memory, making it more likely to be directly cued by a later example sharing relational structure. We expected to replicate this finding (across experiments) and examined whether inducing a relational mindset would amplify this effect on the likelihood of analogical retrieval (while replicating Vendetti et al., 2014). Even with high-quality relational representations, past research shows below ceiling analogical retrieval, so an induced relational mindset could still be quite beneficial.