Keith J. Holyoak

Overview of Research Career

Keith Holyoak's career in cognitive science and cognitive neuroscience has been devoted to understanding the representation of knowledge in the human mind and brain. Over the past four decades, working with an evolving network of outstanding collaborators, he has made a series of important contributions to our understanding of how people think and reason. A key focus of his work has been on how people learn and use abstract relationships that depend on more than direct similarity—relations of the sort required to grasp social regulations, category membership, causality, and analogies. An overarching theme has been that such relational knowledge underlies induction, which encompasses "all inferential processes that expand knowledge in the face of uncertainty" (Holland, Holyoak, Nisbett & Thagard, 1986, p. 1). Holyoak has aimed to understand the cognitive skills that endow humans with what the philosopher Charles Peirce called "special aptitudes for guessing right."


Semantic Memory and Mental Comparisons

As a PhD student at Stanford University in the early 1970s, Holyoak and fellow student Arnold Glass (both advised by Gordon Bower) investigated how people answer simple factual questions based on their general world knowledge, or semantic memory (Collins & Quillian, 1969). They were particularly fascinated by the human ability to rapidly and accurately decide that novel statements are false, without needing to search (laboriously and futilely) through every fact they know to be true. Holyoak and Glass (1975) identified two major strategies that people use: detecting semantic contradictions and finding counterexamples. These strategies illustrate how people can use knowledge about relations between concepts flexibly to make novel inferences.

In his PhD dissertation, completed in 1976, and his early work as an assistant professor at the University of Michigan, Holyoak explored the special properties of concepts that can be ordered along a unidimensional continuum of magnitude. An intriguing phenomenon, termed the "symbolic distance effect" (Moyer & Landauer, 1967), is that speed and accuracy of judging which of two concepts is the greater (or lesser) increases with the difference between their magnitudes. Holyoak and Walker (1976) showed that the same phenomenon (previously observed with digit magnitudes and animal sizes) is also obtained with abstract concepts such as adjectives of quality or terms for time intervals. Another standard finding with comparative judgments is the "semantic congruity effect"—it is easier (for example) to select the larger (rather than the smaller) of two large animals, whereas the reverse pattern holds when comparing two small animals. Holyoak (1978; Holyoak & Mah, 1982) introduced a variant of this paradigm in which people are asked to judge which of two concepts is closer to a third (the latter providing an explicit reference point). He found that judgments were easier for items relatively close in magnitude to the reference point. Based on these findings, Holyoak proposed that the endpoints of continua routinely are used as implicit reference points, in effect stretching subjective distances between concepts close to the reference point, thereby creating a congruity effect. In related work, Holyoak and Gordon (1983) showed that the self serves as a reference point in social judgments, leading to asymmetries in perceived similarity. The reference point theory became an influential interpretation of how symbolic magnitude comparisons are linked to processes akin to an internal psychophysics (e.g., Petrusic, 1992).


Analogies and Schemas

In the early 1980s Holyoak's research branched out in several new directions. Together with his graduate student Mary Gick, Holyoak began modern work on the use of analogies to solve problems (Gick & Holyoak, 1980, 1983). Inspired by ideas from Gestalt psychology (Duncker, 1945), they had college students role-play solving a problem faced by a doctor who needed to find a way to use rays to destroy a stomach tumor without damaging the surrounding healthy tissue. Shortly before encountering this tumor problem, the students might read a story that potentially provided a source analog (e.g., a story about a general who had his troops attack a fortress using small groups that advanced simultaneously along multiple converging roads). The story was presented in an incidental context (e.g., as a memory experiment). Gick and Holyoak found that a minority of college students spontaneously used the story as a cue to create an analogous "convergence" solution to the tumor problem (apply low-intensity rays simultaneously from multiple directions), but that many more were able to use the analogy after a hint that the prior story might be helpful. Later work showed that analogical transfer can be enhanced by comparing multiple source analogs, thereby creating a more abstract schemas for a class of problems (Gick & Holyoak, 1983; Catrambone & Holyoak, 1989).

A key idea in Holyoak's approach to analogical reasoning and schema induction was that learning and transfer is guided by the reasoner's goals (Holyoak, 1985). In collaboration with Patricia Cheng, this pragmatic approach was extended to types of reasoning generally viewed as deductive. They focused on Wason's (1966) deceptively simple "card task" (given a conditional rule such as, "If a card has a vowel on one side then it has an even number on the other," together with the four logically possible types of cards each with one face visible, select all and only those cards that need to be turned over to determine whether the rule holds). Previous studies had painted a confusing picture of human deductive inference in this deceptively simple task—performance was invariably poor with arbitrary rules, though sometimes but not always enhanced by meaningful content. Cheng and Holyoak (1985, 1989) developed the theory of pragmatic reasoning schemas, arguing that human inference was guided by rules that were neither fully abstract nor tied to specific cases, but rather were defined in terms of broad classes of situations linked to recurring social goals (e.g., checking that a precondition was satisfied before taking a restricted action). Cheng and Holyoak showed that people reasoned very effectively about rules that could be interpreted in terms of social regulations, such as conditional permissions and obligations. Moreover, training in terms of pragmatic schemas further enhanced reasoning performance (Cheng, Holyoak, Nisbett & Oliver, 1986). In later work, Holyoak and Cheng (1995) extended the theory to account for the influence of the reasoner's perspective (e.g., the way the differing goals of a landlord and a tenant alter their focus in evaluating compliance with a contract).

The pragmatic approach to reasoning became the core of a more general treatment of human induction. With John Holland in computer science, Richard Nisbett in social psychology and Paul Thagard in philosophy of science, Holyoak co-authored Induction (1986), which dealt with the general problem of achieving effective inference despite inherent uncertainty. In addition to his work on analogy and deductive reasoning, this treatise was influenced by another thread of Holyoak's work, which focused on human category learning. With Peter Gordon, Holyoak showed that perceptual category learning influences affective as well as cognitive judgments about category members (Gordon & Holyoak, 1983). In collaboration with Lisbeth Fried, he developed and tested the earliest Bayesian model of human category learning, the category density model (Fried & Holyoak, 1984). This model was able to account for learning about distributions (as well as central tendencies) of the features of perceptual categories, even when error feedback was not provided. Moreover, this work established that people have very general prior expectations about the abstract form of category distributions, favoring distributions that are unimodal and symmetrical (Flannagan, Fried & Holyoak, 1986). This early line of work on category learning anticipated subsequent dramatic advances in Bayesian approaches to human induction (Anderson, 1990; Tenenbaum, 1999).

Over the 1980s, Holyoak and his collaborators extended their work on analogical problem solving in several directions. Foreshadowing his future development as a poet, Holyoak (1982) analyzed the connections between psychological work on analogy and the role of comparison in literary symbolism. Holyoak and Koh (1987) identified multiple types of similarity that have dissociable influences on analogical retrieval versus mapping. His group also began to investigate developmental changes in analogy ability (Holyoak, Junn & Billman, 1984), as well as implications for education. With Miriam Bassok, he found intriguing asymmetries in analogical transfer between equations taught in the context of algebra versus physics. With Laura Novick, he began to explore the potential role of analogical reasoning in teaching mathematics (Novick & Holyoak, 1991). All of these early research directions set the stage for subsequent work in the field of analogical reasoning and learning over the next two decades (e.g., Richland, Zur & Holyoak, 2007).


Reasoning by Constraint Satisfaction

In the process of working on the Induction book, Holyoak became convinced that understanding human thinking and reasoning required the development of detailed computational models that would make human-like inferences. He and Paul Thagard developed a computer simulation called PI (Processes of Induction) that attempted to model analogical problem solving within a production-system architecture. However, even before their book was completed, Holyoak grew dissatisfied with this approach. Among other limitations, the model was not able to flexibly find correspondences based on partial matches of relational structure. Whereas Holyoak (1985) had emphasized the importance of pragmatic constraints on analogy, Gentner (1983) had stressed the role of structure. It seemed that a human-like model would need to integrate multiple types of constraints.

Beginning in fall of 1984, Holyoak spent a year as a visitor in the Department of Psychology at Carnegie-Mellon University. Jay McClelland joined the CMU faculty that same year, and in their early conversations Holyoak learned about McClelland's work on parallel distributed processing (PDP), which would appear as a two-volume book (McClelland, Rumelhart & the PDP Research Group, 1986). Because the PDP approach appeared to replace symbolic with "subsymbolic", neural-like processes, a great deal of controversy ensued at CMU and elsewhere. In the spring of 1985, Holyoak and Walter Schneider co-organized a one-time seminar that brought together the local experts in both symbolic and PDP modeling. Holyoak moved to UCLA in 1986, where he participated in a seminar on the PDP books organized as part of an emerging cognitive science program. Around this time he was also invited to write a review of the books (Holyoak, 1987).

After this extended period of grappling with PDP and its implications, Holyoak realized early in 1987 that the symbolic versus subsymbolic debate could be set aside (for a time). Instead of using PDP to replace symbolic processing, it could be used to implement it. In particular, PDP-style models naturally operated by parallel constraint satisfaction, using excitatory and inhibitory connections to allow a global solution to emerge from many local constraints. This insight led Holyoak to work with Paul Thagard to create a new model of analogical mapping, ACME (Analogical Constraint Satisfaction Engine). ACME (Holyoak & Thagard, 1989) was quickly followed by ARCS (Analogical Retrieval by Constraint Satisfaction; Thagard, Holyoak, Nelson & Gochfeld, 1990). Both models were viewed as instantiations of a "multiconstraint theory" of analogy, in which relational structure, direct similarity of objects, and pragmatic links to goals all worked together to retrieve useful source analogs stored in memory, find a sensible mapping between a source and a target analog, and then use the mapping to make plausible and useful inferences about the source. In their monograph Mental Leaps, Holyoak and Thagard (1995) used the multiconstraint theory as a qualitative description of the real-world use of analogies for purposes such as scientific discovery, explanation, metaphor, and ritual.

Other work continued to develop implications of the view that analogy, and perhaps reasoning more generally, could be viewed as constraint satisfaction. The stages of analogical transfer, and a basic algorithm for analogical inferences called "copy with substitution and generation" (CWSG), were described by Holyoak, Novick and Melz (1994). With his graduate students, Holyoak performed a series of experiments showing the conditions under which analog retrieval (as well as mapping) is guided by relational parallels (Wharton et al., 1994), and established that shared relations can yield semantic priming (Spellman, Holyoak & Morrison, 2001). Spellman and Holyoak (1992) analyzed the constraints that governed analogical mappings related to the first Persian Gulf War, and demonstrated experimentally that pragmatic constraints interact with other types of constraints to guide mapping (Spellman & Holyoak, 1996).

Meanwhile, the idea that complex human reasoning can emerge from interactions between multiple local constraints was explored in other domains besides analogy, as reviewed by Spellman and Holyoak (1993). Thagard (1989) developed ECHO (Explanatory Coherence by Harmony Optimization), a model of the evaluation of competing explanations based on the same type of algorithm used in ACME. Holyoak (1991) coined the term "symbolic connectionism" to characterize the general possibility that connectionist (PDP) models could be usefully integrated with symbolic knowledge representations. Together with law professor Dan Simon, Holyoak provided experimental evidence that complex decisions, such as legal cases, are made in accord with principles of constraint satisfaction (Holyoak & Simon, 1999).


Causal Models

A foundational type of abstract relation used in human thinking is that between cause and effect. In the late 1980s, a number of researchers argued that causal relations are not special, but rather are simply a special case of the elementary associative links that might underlie conditioning in nonhuman animals (a possibility consistent with then-current PDP models). In contrast, Judea Pearl (1988), working in artificial intelligence, proposed that causal knowledge is based on representations of cause-effect relations organized into networks, serving as internal models of how causes seem to operate in the external world. Michael Waldmann and Holyoak (1992; Waldmann, Holyoak & Fratianne, 1995) proposed that humans learn and reason using causal models. They performed a series of experiments demonstrating that the psychological representation of cause-effect relations can be dissociated from the overt temporal order of presented cues and their outcomes (e.g., a doctor may use symptoms to infer diseases, even though the causal arrow runs from diseases to symptoms). A vigorous debate ensued over the next two decades. The development of causal models as a psychological theory was later influenced by Cheng's (1997) theory of causal power. The evidence is now overwhelming that humans learn and reason about explicit cause-effect relations (Holyoak & Cheng, 2011).


Neurocomputational Model of Relational Reasoning

Despite the successes of ACME and related models as formulations of reasoning as constraint satisfaction, Holyoak was keenly aware of their limitations. In particular, ACME did not aim to operate within realistic working-memory limits, and lacked representations of the meanings of individual concepts. Holyoak believed that these limitations stemmed in part from the unsolved problem of how explicit symbolic representations could be reconciled with a neural architecture. Working with John Hummel, he was no longer content to simply assume that symbolic processing could be "hybridized" with a connectionist architecture. Rather, Hummel and Holyoak aimed to create a new type of symbolic-connectionist model in which relational reasoning emerged from a neural system. The result was LISA (Learning and Inference with Schemas and Analogies), which provided an integrated account of analog retrieval and mapping (Hummel & Holyoak, 1997) and also inference and schema induction (Hummel & Holyoak, 2003). LISA codes relations by binding distributed representations of roles to distributed representations of their fillers (coded on separate pools of semantic units). By using neural synchrony to impose a hierarchical temporal structure on knowledge representations within working memory, LISA operates under natural capacity limits. The model was able to account for numerous empirical phenomena related to relational reasoning.


Neural Substrate of Relational Reasoning

During this same time period, Holyoak began to explore the basis for relational thinking in the human brain. A theoretical paper by Robin and Holyoak (1995) set the stage by relating the cognitive processes underlying relational reasoning to functions of subregions within the prefrontal cortex. Their analysis was guided primarily by data from non-human primates. In the next phase of his research, together with neuropsychologist Barbara Knowlton and others, Holyoak investigated relational reasoning in patients suffering from Frontotemporal Lobar Degeneration. These studies revealed that patients with extensive damage to the prefrontal cortex were selectively impaired at integrating multiple relations (Waltz et al., 1999) and handling interference (Morrison et al., 2004). In related work with college students, neuroimaging showed that the rostrolateral subregion of the prefrontal cortex is especially important in reasoning with multiple relations (Christoff et al., 2001; Kroger et al., 2002), whereas more posterior subregions are involved in inhibitory control during relational reasoning (Cho et al., 2010).

These and other new findings from cognitive neuroscience provided vehicles to link the LISA model more closely to brain processes. LISA was used to model the loss of relational reasoning in populations with forms of brain damage, as well as changes in relational reasoning during cognitive development (Richland, Morrison & Holyoak, 2006) and normal aging (Viskontas et al., 2006). Knowlton, Morrison, Holyoak and Hummel (2012) reviewed neural evidence for mechanisms postulated by the LISA model. In a broad review of the literature in comparative psychology, Penn, Holyoak and Povinelli (2007) argued that the capacity to re-represent perceptual relations in a more abstract form, enabling analogical reasoning based on higher-order relations, distinguishes human intelligence from the cognitive abilities of other animal species. Thus the core mechanisms of LISA may reflect evolutionarily late developments in the human prefrontal cortex.


Bayesian Models of Reasoning and Learning

In recent years, working with Hongjing Lu and others, Holyoak has applied Bayesian methods to model various forms of inductive learning. Learning within causal models was formulated within a Bayesian framework to represent uncertainty, providing compelling evidence that associative learning (even when formulated within the same Bayesian framework) is inadequate as an account of human causal learning (Lu et al., 2008). Extending their Bayesian model of causal learning, Holyoak and his collaborators then developed a theoretical bridge between causal models and analogical inference (Holyoak, Lee & Lu, 2010). Lu, Chen and Holyoak (2012) developed a Bayesian model of how comparative relations (e.g., larger, fiercer) could be learned from non-relational inputs (feature vectors representing individual animal concepts). The BART model (Bayesian Analogy with Relational Transformations) can solve structured analogy problems using relational representations the model learned itself from unstructured inputs that were independently generated. No previous model of analogy had demonstrated a comparable capability, which arguably is an essential precursor to a comprehensive account of complex human analogical reasoning. A simpler version of the BART model (Chen, Lu & Holyoak, 2014) was developed to model how symbolic magnitudes can be learned and compared (returning to a problem Holyoak had first considered decades earlier).

Relational Reasoning in Mathematics
Another current research area concerns the role of relational reasoning in mathematics. With collaborators Melissa DeWolf and Miriam Bassok, Holyoak has been investigating the impact of different formats for expressing rational numbers across a variety of reasoning tasks. When people are required to compare the magnitudes of numbers, decimals yield much faster and more accurate responding that do fractions (DeWolf et al., 2014). But when the task requires processing relations between quantities (e.g., distinguishing between types of ratios), fractions are often more effective (DeWolf, Bassok & Holyoak, 2015a). Children’s understanding of the relational aspects of rational numbers may serve as an important stepping stone towards learning more advanced mathematical topics, such as algebra (DeWolf, Bassok & Holyoak, 2015b).

Other Contributions and Awards
In addition to the books already mentioned, Holyoak co-authored the earliest textbook in cognitive psychology to include comprehensive coverage of thinking and reasoning, as well as relevant work in neuropsychology (Glass, Holyoak & Santa, 1979; Glass & Holyoak, 1986). He also co-edited the first major handbooks in the field of thinking and reasoning (Holyoak & Morrison, 2005, 2012), as well as several other integrative books. Many early position papers on causal learning appeared in Shanks, Holyoak and Medin (1996). Holyoak co-edited an early collection of papers addressing the role of the prefrontal cortex in human cognition (Grafman, Holyoak & Boller, 1995), as well as a major collection of papers on analogical reasoning (Gentner, Holyoak & Kokinov, 2001).

Holyoak has been a recipient of a John Simon Guggenheim Fellowship and a James McKeen Cattell Fellowship. He is a Fellow of AAAS, the Association for Psychological Science, the Cognitive Science Society, and the Society for Experimental Psychology. In 2015 he became the incoming Editor of Psychological Review. He previously served as Editor of Cognitive Psychology, Senior Editor of Cognitive Science, Associate Editor of Psychological Science, and as editorial board member of numerous other journals.
In a parallel career as a poet and translator, Holyoak has published Facing the Moon: Poems of Li Bai and Du Fu (Oyster River Press, 2007), My Minotaur: Selected Poems 1998–2006 (Dos Madres Press, 2010), Foreigner: New English Poems in Chinese Old Style (Dos Madres Press, 2012), and The Gospel According to Judas (Dos Madres Press, 2015).

Representative Publications (chronological order)
Holyoak, K. J., & Glass, A. L. (1975).  The role of contradictions and counterexamples in the rejection of false sentences. Journal of Verbal Learning and Verbal Behavior, 4, 215-239.
Holyoak, K. J., & Walker, J. H. (1976).  Subjective magnitude information in semantic orderings. Journal of Verbal Learning and Verbal Behavior, 15, 287-299.
Holyoak, K. J. (1978).  Comparative judgments with numerical reference points. Cognitive Psychology, 10, 203-243.
Glass, A. L., Holyoak, K. J., & Santa, J. L. (1979). Cognition. Reading, MA: Addison-Wesley.
Gick, M. L., & Holyoak, K. J. (1980).  Analogical problem solving. Cognitive Psychology, 12, 306-355. 
Holyoak, K. J.,& Mah, W. A. (1982).  Cognitive reference points in judgments of symbolic magnitude. Cognitive Psychology, 14, 328-352.
Holyoak, K. J. (1982).  An analogical framework for literary interpretation. Poetics, 11, 105-126.
Fried, L. S., & Holyoak, K. J. (1984).  Induction of category distributions: A framework for classification learning. Journal of Experimental Psychology: Learning, Memory and Cognition, 10, 234-257.
Gick, M. L., & Holyoak, K. J. (1983).  Schema induction and analogical transfer. Cognitive Psychology, 15, 1-38.
Gordon, P. C., & Holyoak, K. J. (1983).  Implicit learning and generalization of the "mere exposure" effect. Journal of Personality and Social Psychology, 45, 492-500.
Holyoak, K. J., & Gordon, P. C. (1983).  Social reference points. Journal of Personality and Social Psychology, 44, 881-887.
Holyoak, K. J., Junn, E. N., & Billman, D. O. (1984).  Development of analogical problem-solving skill. Child Development, 55, 2042-2055.
Cheng, P. W., & Holyoak, K. J. (1985).  Pragmatic reasoning schemas. Cognitive Psychology, 17, 391-416.
Holyoak, K. J. (1985).  The pragmatics of analogical transfer. In G. H. Bower (Ed.), The psychology of learning and motivation, Vol. 19 (pp. 59-87).  New York: Academic Press.
Cheng, P. W., Holyoak, K. J., Nisbett, R. E., & Oliver, L. M. (1986).  Pragmatic versus syntactic approaches to training deductive reasoning.  Cognitive Psychology, 18, 293-328.
Flannagan, M. J., Fried, L. S., & Holyoak, K. J. (1986).  Distributional expectations and the induction of category structure. Journal of Experimental Psychology: Learning, Memory, and Cognition, 12, 241-256.
Glass, A. L., & Holyoak, K. J. (1986). Cognition, 2nd edition. New York: Random House.
Holland, J. H., Holyoak, K. J., Nisbett, R. E., & Thagard, P. (1986). Induction: Processes of inference, learning, and discovery.  Cambridge, MA: MIT Press.
Holyoak, K. J.(1987).  A connectionist view of cognition (review of Parallel distributed processing by D. E. Rumelhart, J. L. McClelland, and the PDP Research Group). Science, 236,992-996.
Holyoak, K. J., & Koh, K. (1987).  Surface and structural similarity in analogical transfer. Memory & Cognition, 15, 323-340.
Cheng, P. W., & Holyoak, K. J. (1989).  On the natural selection of reasoning theories.  Cognition, 33, 285-313.
Catrambone, R., & Holyoak, K. J. (1989).  Overcoming contextual limitations on problem-solving transfer.  Journal of Experimental Psychology: Learning, Memory, and Cognition, 15, 1147-1156.
Holyoak, K. J., & Thagard, P. (1989).  Analogical mapping by constraint satisfaction.  Cognitive Science, 13, 295-355.
Bassok, M., & Holyoak, K. J. (1989).  Interdomain transfer between isomorphic topics in algebra and physics.  Journal of Experimental Psychology: Learning: Memory, and Cognition, 15, 153-166.
Thagard, P., Holyoak, K. J., Nelson, G., & Gochfeld, D. (1990).  Analog retrieval by constraint satisfaction.  Artificial Intelligence, 46, 259-310.
Holyoak, K. J. (1991).  Symbolic connectionism: Toward third-generation theories of expertise.  In A. Ericsson & J. Smith (Eds.), Toward a general theory of expertise: Prospects and limits (pp. 301-355).  Cambridge, UK: Cambridge University Press.
Novick, L. R., & Holyoak, K. J. (1991).  Mathematical problem solving by analogy. Journal of Experimental Psychology: Learning, Memory, and Cognition, 17, 398-415.
Spellman, B. A., & Holyoak, K. J. (1992).  If Saddam is Hitler then who is George Bush?:  Analogical mapping between systems of social roles. Journal of Personality and Social Psychology, 62, 913-933.
Waldmann, M. R., & Holyoak, K. J. (1992).  Predictive and diagnostic learning within causal models: Asymmetries in cue competition.  Journal of Experimental Psychology: General, 121, 222-236.
Holyoak, K. J., & Spellman, B. A. (1993).  Thinking.  Annual Review of Psychology, 44, 265-315.
Wharton, C. M., Holyoak, K. J., Downing, P. E., Lange, T. E., Wickens, T. D., & Melz, E. R. (1994).  Below the surface: Analogical similarity and retrieval competition in reminding.  Cognitive Psychology, 26, 64-101.
Holyoak, K. J., Novick, L. R., & Melz, E. R. (1994).  Component processes in analogical transfer: Mapping, pattern completion, and adaptation.  In K. J. Holyoak & J. A. Barnden (Eds.), Advances in connectionist and neural computation theory, Vol. 2:  Analogical connections (pp. 113-180)Norwood, N.J.: Ablex.
Waldmann, M. R., Holyoak, K. J., & Fratianne, A. (1995).  Causal models and the acquisition of category structure.  Journal of Experimental Psychology: General, 124, 181-206.
Robin, N., & Holyoak, K. J. (1995).  Relational complexity and the functions of prefrontal cortex.  In M. S. Gazzaniga (Ed.), The cognitive neurosciences (pp. 987-997).  Cambridge, MA: MIT Press.
Grafman, J., Holyoak, K. J., & Boller, F. (Eds.) (1995).  Structure and functions of the human prefrontal cortex.  New York: New York Academy of Sciences.
Holyoak, K. J., & Cheng, P. W. (1995).  Pragmatic reasoning with a point of view. Thinking & Reasoning, 1, 289-313.
Holyoak, K. J., & Thagard, P. (1995).  Mental leaps: Analogy in creative thought. Cambridge, MA: MIT Press.
Shanks, D. R., Holyoak, K. J., & Medin, D. L. (Eds.) (1996). The psychology of learning and motivation, Vol. 34: Causal learning.  San Diego: Academic Press.
Spellman, B. A., & Holyoak, K. J. (1996).  Pragmatics in analogical mapping.  Cognitive Psychology, 31, 307-346.
Hummel, J. E., & Holyoak, K. J. (1997).  Distributed representations of structure: A theory of analogical access and mapping.  Psychological Review, 104, 427-466.
Waltz, J. A., Knowlton, B. J., Holyoak, K. J., Boone, K. B., Mishkin, F. S., de Menezes Santos, M., Thomas, C. R., & Miller, B. L. (1999). A system for relational reasoning in human prefrontal cortex. Psychological Science, 10, 119-125.
Holyoak, K. J., & Simon, D. (1999).  Bidirectional reasoning in decision making by constraint satisfaction.  Journal of Experimental Psychology: General, 128, 3-31.
Gentner, D., Holyoak, K. J., & Kokinov, B. N. (Eds.) (2001). The analogical mind: Perspectives from cognitive science.  Cambridge, MA: MIT Press.
Spellman, B. A., Holyoak, K. J., & Morrison, R. G. (2001). Analogical priming via semantic relations.  Memory & Cognition, 29, 383-393.
Christoff, K., Prabhakaran, V., Dorfman, J., Zhao, Z., Kroger, J. K., Holyoak, K. J., & Gabrieli, J. D. E. (2001). Rostrolateral prefrontal cortex involvement in relational integration during reasoning. NeuroImage, 14, 1136-1149.
Kroger, J. K., Saab, F. W., Fales, C. L., Bookheimer, S. Y., Cohen, M. S., & Holyoak, K. J. (2002). Recruitment of anterior dorsolateral prefrontal cortex in human reasoning: A parametric study of relational complexity. Cerebral Cortex, 12, 477-485.
Hummel, J. E., & Holyoak, K. J. (2003). A symbolic-connectionist theory of relational inference and generalization. Psychological Review, 110, 220-264.
Morrison, R. G., Krawczyk, D. C., Holyoak, K. J., Hummel, J. E., Chow, T. W., Miller, B. L., & Knowlton, B. J. (2004). A neurocomputational model of analogical reasoning and its breakdown in Frontotemporal Lobar Degeneration. Journal of Cognitive Neuroscience, 16, 260-271.

Viskontas, I. V., Morrison, R. G., Holyoak, K. J., Hummel, J. E., & Knowlton, B. J.  (2004). Relational integration, inhibition and analogical reasoning in older adults. Psychology and Aging, 19, 581-591.
Holyoak, K. J., & Morrison, R. G. (Eds.) (2005). The Cambridge handbook of thinking and reasoning. Cambridge, UK: Cambridge University Press.
Richland, L. E., Morrison, R. G., & Holyoak, K. J. (2006). Children’s development of analogical reasoning: Insights from scene analogy problems. Journal of Experimental Child Psychology, 94, 249-271.
Richland, L. E., Zur, O., & Holyoak, K. J. (2007). Cognitive supports for analogy in the mathematics classroom. Science, 316, 1128-1129.
Holyoak, K. (translator) (2007). Facing the Moon: Poems of Li Bai and Du Fu. Durham, NH: Oyster River Press.
Lu, H., Yuille, A. L., Liljeholm, M., Cheng, P. W., & Holyoak, K. J. (2008). Bayesian generic priors for causal learning. Psychological Review, 115, 955-982.
Penn, D. C., Holyoak, K. J., & Povinelli, D. J. (2008). Darwin’s mistake: Explaining the discontinuity between human and nonhuman minds. Behavioral and Brain Sciences, 31, 109-178 (with 24 commentaries and authors’ response).
Cho, S., Moody, T. D., Fernandino, L., Mumford, J. A., Poldrack, R. A., Cannon, T. D., Knowlton, B. J., & Holyoak, K. J. (2010). Common and dissociable prefrontal loci associated with component mechanisms of analogical reasoning.  Cerebral Cortex, 20, 524-533.
Holyoak, K. J., Lee, H. S., & Lu, H. (2010). Analogical and category-based inference: A theoretical integration with Bayesian causal models. Journal of Experimental Psychology: General, 139, 702-727.
Holyoak, K. (2010). My Minotaur: Selected Poems 1998-2006. Loveland, OH: Dos Madres Press.
Holyoak, K. J., & Cheng, P. W. (2011). Causal learning and inference as a rational process: The new synthesis. Annual Review of Psychology, 62, 135-163.
Holyoak, K. J., & Morrison, R. G. (Eds.) (2012). The Oxford handbook of thinking and reasoning. New York: Oxford University Press.
Holyoak, K. (2012). Foreigner: New English Poems in Chinese Old Style. Loveland, OH: Dos Madres Press.
Lu, H., Chen, D., & Holyoak, K. J. (2012). Bayesian analogy with relational transformations. Psychological Review, 119, 617-648.
Knowlton, B. J., Morrison, R. G., Hummel, J. E., & Holyoak, K. J. (2012). A neurocomputational system for relational reasoning. Trends in Cognitive Sciences, 16, 373-381.
Chen, D., Lu, H., & Holyoak, K. J. (2014). The discovery and comparison of symbolic magnitudes. Cognitive Psychology, 71, 27-54.
DeWolf, M., Grounds, M. A., Bassok, M., & Holyoak, K. J. (2014). Magnitude comparison with different types of rational numbers. Journal of Experimental Psychology: Human Perception and Performance, 40, 71-82.
DeWolf, M., Bassok, M., & Holyoak, K. J. (2015a). Conceptual structure and the procedural affordances of rational numbers: Relational reasoning with fractions and decimals. Journal of Experimental Psychology: General, 144, 127-150.
DeWolf, M., Bassok, M., & Holyoak, K. J. (2015b). From rational numbers to algebra: Separable contributions of decimal magnitude and relational understanding of fractions. Journal of Experimental Child Psychology.
Holyoak, K. (2015). The Gospel According to Judas. Loveland, OH: Dos Madres Press.

Other References
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