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Organizations routinely rely on work groups for creative solutions to the problems they face. This is because solving difficult problems is often assumed to require the talents and knowledge of multiple people working together. However, much research has shown over the years that groups frequently experience dysfunction when trying to collaborate and generate creative solutions. Organizational researchers have theorized that analogical reasoning may play an important role in promoting collective creativity, but these claims are for the most part untested in the literature. In this dissertation, I attempt to answer two questions. First, does analogical reasoning provide some functional benefits for groups solving creative problems? Second, does analogical reasoning give rise to synergistic effects when creative groups collaborate during ideation and problem-solving? I assessed these questions using a laboratory study designed to find the effects of analogical reasoning in interacting and non-interacting groups, and to test for potential synergistic effects of analogical reasoning as a group-level strategy for generating creative problem solutions. Findings of the study suggest that analogical reasoning may provide some benefits for creative group outputs, and it may also create synergistic effects for creative groups. / text

This thesis is concerned with reasoning by analogy within the context of auto-mated problem solving. In particular, we consider the provision of an analogical reasoning component to a resolution theorem proving system. The framework for reasoning by analogy which we use (called Basic APS) contains three major components -the finding of analogies (analogy matching), the construction of analogical plans, and the application of the plans to guide the search of a theorem prover. We first discuss the relationship of analogy to other machine learning techniques. We then develop programs for each of the component processes of Basic APS. First we consider analogy matching. We reconstruct, analyse and crticise two previous analogy matchers. We introduce the notion of analogy heuristics in order to understand the matchers. We find that we can explain the short-comings of the matchers in terms of analogy heuristics. We then develop a new analogy matching algorithm, based on flexible application of analogy heuristics, and demonstrate its superiority to the previous matchers. We go on to consider analogical plan construction. We describe procedures for constructing a plan for the solution of a problem, given the solution of a different problem and an analogy match between the two problems. Again, we compare our procedures with corresponding ones from previous systems. We then describe procedures for the execution of analogical plans. We demon-strate the procedures on a number of example analogies. The analogies involved are straightforward for a human, but the problems themselves involve.huge search spaees, if tackled directly using resolution. By comparison with unguided search, we demonstrate the dramatic reductfon in search entaile_d by the use of an ana-logical plan. We then consider some directions for development of our analogy systems, which have not yet been implemented. Firstly, towards more flexible and power-ful execution of analogical plans. Secondly, towards an analogy system which can improve its own ability to find and apply analogies over the course of experience.

There has been a great deal of research into students' use of examples when solving problems in textbooks. Much of this work has been within the framework of analogical problem solving (APS). Indeed many researchers believe they can build adequate models of how students learn and solve exercise problems by analogy to worked examples. In the first part of this thesis I argue that this view of problem solving from examples is inappropriate and often misleading. Most students learning a subject for the first time tend to imitate examples. Imitative Problem Solving UPS)is a weak form of analogical problem solving. APS accounts assume that a solver has a representation of an earlier problem in memory. The difficulties involved are accessing that source problem and adapting it to solve the current one. WS does not assume t at the source is represented in memory, and even when the source example is available( as in textbook examples), the student may not understand it well enough to be able to adapt it to new situations. The second part of the thesis presents an interpretation theory for analysing both texts and the behaviour of solvers using those texts to solve exercise problems. The third part applies the interpretation theory to the solution explanation of a simple algebra word problem. Where an example problem fails to map directly onto an exercise problem, or where inferences have to be made to understand it, the solver win be unable to imitate the example and hence will have difficulties in proportion to the mapping inequalities between the two problems. That is, the interpretation theory allows us to predict precisely where solvers will have difficulty using an example to solve an exercise problem of the same type. The final part presents experimental tests of these predictions. The results confirm that the interpretation theory analysis can correctly identify possible areas of difficulty for the student due to a) the way an example problem is structured, and b) the nature of the transfer task.

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The acquisition of relational concepts plays an integral role and is assumed to be a prerequisite for analogical reasoning. Language and token-trained apes (e.g. Premack, 1976; Thompson, Oden, and Boysen, 1997) are the only nonhuman animals to succeed in solving and completing analogies, thus implicating language as the mechanism enabling the phenomenon. In the present study, I examine the role of meaning in the analogical reasoning abilities of three different primate species. Humans, chimpanzees, and rhesus monkeys completed relational match-to-sample (RMTS) tasks with either meaningful or nonmeaningful stimuli. For human participants, meaningfulness facilitated the acquisition of analogical rules. Individual differences were evident amongst the chimpanzees suggesting that meaning can either enable or hinder their ability to complete analogies. Rhesus monkeys did not succeed in either condition, suggesting that their ability to reason analogically, if present at all, may be dependent upon a dimension other than the representational value of stimuli.

Ever since artifacts have been produced, improving them has been a common human activity. Improving an artifact refers to modifying it such that it will be either easier to produce, or easier to use, or easier to fix, or easier to maintain, and so on. In all of these cases, "easier" means fewer resources are required for those processes. While 'resources' is a general measure, which can ultimately be expressed by some measure of cost (such as time or money), we believe that at the core of many improvements is the notion of reduction of complexity, or in other words, simplification. This talk presents our research on performing design simplification using analogical reasoning. We first define the simplification problem as the problem of reducing the complexity of an artefact from a given point of view. We propose that a point of view from which the complexity of an artefact can be measured consists of a context, an aspect and a measure. Next, we describe an approach to solving simplification problems by goal-directed analogical reasoning, as our implementation of this approach. Finally, we present some experimental results obtained with the system. The research presented in this dissertation is significant as it focuses on the intersection of a number of important, active research areas - analogical reasoning, functional representation, functional reasoning, simplification, and the general area of AI in Design.

It is well documented that undergraduate students struggle with the more formal and abstract concepts of vector space theory in a first course on linear algebra. Some of these students continue on to classes in abstract algebra, where they learn about algebraic structures such as groups. It is clear to the seasoned mathematician that vector spaces are in fact groups, and so linear transformations are group homomorphisms with extra restrictions. This study explores the question of whether or not students see this connection as well. In addition, I probe the ways in which students’ stated understandings are the same or different across contexts, and how these differences may help or hinder connection making across domains. Students’ understandings are also briefly compared to those of mathematics professors in order to highlight similarities and discrepancies between reality and idealistic expectations. The data for this study primarily comes from clinical interviews with ten undergraduates and three professors. The clinical interviews contained multiple card sorts in which students expressed the connections they saw within and across the domains of linear algebra and abstract algebra, with an emphasis specifically on linear transformations and group homomorphisms. Qualitative data was analyzed using abductive reasoning through multiple rounds of coding and generating themes. Overall, I found that students ranged from having very few connections, to beginning to form connections once placed in the interview setting, to already having a well-integrated morphism schema across domains. A considerable portion of this paper explores the many and varied ways in which students succeeded and failed in making mathematically correct connections, using the language of research on analogical reasoning to frame the discussion. Of particular interest were the ways in which isomorphisms did or did not play a role in understanding both morphisms, how students did not regularly connect the concepts of matrices and linear transformations, and how vector spaces were not fully aligned with groups as algebraic structures.