F. Electronic JournalsE-Journal Resource Listshttps://evidence.thinkportal.org/handle/123456789/9552023-03-21T14:44:05Z2023-03-21T14:44:05ZDeep Analogical Inference as the Origin of Hypotheseshttps://evidence.thinkportal.org/handle/123456789/323122020-02-25T12:42:25ZDeep Analogical Inference as the Origin of Hypotheses
The ability to generate novel hypotheses is an important problem-solving capacity of humans. This ability is vital for making sense of the complex and unfamiliar world we live in. Often, this capacity is characterized as an inference to the best explanation—selecting the “best” explanation from a given set of candidate hypotheses. However, it remains unclear where these candidate hypotheses originate from. In this paper we contribute to computationally explaining these origins by providing the contours of the computational problem solved when humans generate hypotheses. The origin of hypotheses, otherwise known as abduction proper, is hallmarked by seven properties: (1) isotropy, (2) open-endedness, (3) novelty, (4) groundedness, (5) sensibility, (6) psychological realism, and (7) computational tractability. In this paper we provide a computational-level theory of abduction proper that unifies the first six of these properties and lays the groundwork for the seventh property of computational tractability. We conjecture that abduction proper is best seen as a process of deep analogical inference.;
The Role of Problem Representation in Producing Near-Optimal TSP Tourshttps://evidence.thinkportal.org/handle/123456789/323112020-02-25T12:32:44ZThe Role of Problem Representation in Producing Near-Optimal TSP Tours
<p>Gestalt psychologists pointed out about 100 years ago that a key to solving difficult insight problems is to change the mental representation of the problem, as is the case, for example, with solving the six matches problem in 2D vs. 3D space. In this study we ask a different question, namely what representation is used when subjects solve search, rather than insight problems. Some search problems, such as the traveling salesman problem (TSP), are defined in the Euclidean plane on the computer monitor or on a piece of paper, and it seems natural to assume that subjects who solve a Euclidean TSP do so using a Euclidean representation. It is natural to make this assumption because the TSP task is defined in that space. We provide evidence that, on the contrary, subjects may produce TSP tours in the complex-log representation of the TSP city map. The complex-log map is a reasonable assumption here, because there is evidence suggesting that the retinal image is represented in the primary visual cortex as a complex-log transformation of the retina. It follows that the subject’s brain may be “solving” the TSP using complex-log maps. We conclude by pointing out that solving a Euclidean problem in a complex-log representation may be acceptable, even desirable, if the subject is looking for near-optimal, rather than optimal solutions.</p>; 1
The Role of the Goal in Solving Hard Computational Problems: Do People Really Optimize?https://evidence.thinkportal.org/handle/123456789/323102020-02-25T12:32:44ZThe Role of the Goal in Solving Hard Computational Problems: Do People Really Optimize?
<p>The role that the mental, or internal, representation plays when people are solving hard computational problems has largely been overlooked to date, despite the reality that this internal representation drives problem solving. In this work we investigate how performance on versions of two hard computational problems differs based on what internal representations can be generated. Our findings suggest that problem solving performance depends not only on the objective difficulty of the problem, and of course the particular problem instance at hand, but also on how feasible it is to encode the goal of the given problem. A further implication of these findings is that previous human performance studies using NP-hard problems may have, surprisingly, underestimated human performance on instances of problems of this class. We suggest ways to meaningfully frame human performance results on instances of computationally hard problems in terms of these problems’ computational complexity, and present a novel framework for interpreting results on problems of this type. The framework takes into account the limitations of the human cognitive system, in particular as it applies to the generation of internal representations of problems of this class.</p>; 1
Heuristics for Comparing the Lengths of Completed E-TSP Tours: Crossings and Areashttps://evidence.thinkportal.org/handle/123456789/323072020-02-25T12:32:43ZHeuristics for Comparing the Lengths of Completed E-TSP Tours: Crossings and Areas
<p>The article reports three experiments designed to explore heuristics used in comparing the lengths of completed Euclidean Traveling Salesman Problem (E-TSP) tours. The experiments used paired comparisons in which participants judged which of two completed tours of the same point set was shorter. The first experiment manipulated two factors, the presence/absence of crossed arcs, and the relative areas of the enclosed polygons. Both factors significantly influenced judgments, with the absence of crossings and smaller areas being associated with shorter tours. The second experiment examined the effects of crossings only, and compared stimulus pairs using all possible combinations of no, one, and more than one crossing. The results showed a significant tendency for tours with one or more crossings to be judged longer than tours with none, while tours with more crossings were not judged to be longer than tours with only one. Apparently the mere presence of a crossing is sufficient to cause a tour to be judged as longer. The third experiment examined the effects of area only, and consisted of two parts. In the first part, participants judged which of two tours that differed in area was shorter. The results supported those of the first experiment, by finding that tours with smaller areas tended to be judged as shorter. In the second part of the experiment, participants judged the relative areas of each pair, to determine whether people can reliably differentiate the areas of such complex polygons. The results confirmed that they can, thereby supporting the feasibility of using differences in area as a heuristic to judge relative lengths. The results were discussed in terms of Carruthers’s (2015) proposal of goal modification and the suggestion is made that applying heuristics of the type identified may represent a specific form of goal modification.</p>; 1