A focused review of the literature on reasoning suggests that mechanisms based upon contraries are of fundamental importance in various abilities. At the same time, the importance of contraries in the human perceptual experience of space has been recently demonstrated in experimental studies. Solving geometry problems represents an interesting case as both reasoning abilities and the manipulation of perceptual–figural aspects are involved.In this study we focus on perceptual changes in geometrical problem solving processes in order to (...) understand whether a mental manipulation in terms of opposites might help. Four conditions were studied, two of which concerned the search for contraries as an implicit or explicit strategy.Results demonstrated that contraries, when used explicitly in solution processes, constitute an effective heuristic: The number of correct solutions increased, less time was needed to find a solution and participants were oriented towards the use of perception-based solutions—not only wer.. (shrink)

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. (shrink)

Packing optimization problems have a wide spectrum of real-word applications. One of the applications of the problems is problem of placement of containers with spent nuclear fuel on the storage platform. The solution of the problem can be reduced to the solution of the problem of finding the optimal placement of a given set of congruent circles into a multiconnected domain taking into account technological restrictions. A mathematical model of the prob-lem is constructed and its peculiarities are (...) considered. Our approach is based on the mathematical modelling of rela-tions between geometric objects by means of phi-function technique. That allowed us to reduce the problem solving to nonlinear programming. Today, an important scientific problem is the problem of creating conditions for safe storage of spent nuclear fuel. In the process of creating any dry spent nuclear fuel storage, the following main stages can be identified: site selection, storage design, construction, operation and decommissioning. A full check for compliance of the repository and its elements with these standards usually begins at the design stage. At the stage of site selection, the inspection for compliance with safety standards is carried out only in terms of the impact of the repository as a whole on the environment. This approach cannot be considered fully appropriate, because, taking into account, for example, all the climatic features of the future storage site, it is possible to adjust the thermal storage regimes of spent nuclear fuel. Similarly, it can be considered necessary to analyze and select the shape of the storage site in order to accommo-date the maximum possible number of spent fuel containers. Such a choice, obviously, should be made taking into ac-count the norms of nuclear, radiation and thermal safety, as well as in compliance with technological limitations. The problem of finding the optimal placement of containers taking into account the given technological limitations can be formulated in the form of the problem of optimization of geometric design. Therefore, the purpose of the study is to build a mathematical model of the problem and study its characteristics to develop effective methods of solution. The proposed approach is based on mathematical modeling of relations between geometric objects using the method of phi-functions. This allowed to reduce the solution of the problem to the problem of nonlinear programming. (shrink)

When classical mechanics is seen as the short-wavelength limit of quantum mechanics (i.e., as the limit of geometrical optics), it becomes clear just how serious and all-pervasive the measurement problem is. This formulation also leads us into the Bohm theory. But this theory has drawbacks: its nonuniqueness, in particular, and its nonlocality. I argue that these both reflect an underlying problem concerning information, which is actually a deeper version of the measurement problem itself.

This paper examines the second geometrical problem in the Meno. Its purpose is to explore the implication of Cook Wilson’s interpretation, which has been most widely accepted by scholars, in relation to the nature of hypothesis. I argue that (a) the geometrical hypothesis in question is a tentative answer to a more basic problem, which could not be solved by available methods at that time, and that (b) despite the temporary nature of a hypothesis, there is (...) a rational process for formulating it. The paper also contains discussion of the method of analysis, problem reduction and a diorism, which have often been ambiguously explained in relation to the geometrical problem in question. (shrink)

ArgumentThe aim of this paper is to employ the newly contextualized historiographical category of “premodern algebra” in order to revisit the arguably most controversial topic of the last decades in the field of Greek mathematics, namely the debate on “geometrical algebra.” Within this framework, we shift focus from the discrepancy among the views expressed in the debate to some of the historiographical assumptions and methodological approaches that the opposing sides shared. Moreover, by using a series of propositions related toElem.II.5 (...) as a case study, we discuss Euclid's geometrical proofs, the so-called “semi-algebraic” alternative demonstrations attributed to Heron of Alexandria, as well as the solutions given by Diophantus, al-Sulamī, and al-Khwārizmī to the corresponding numerical problem. This comparative analysis offers a new reading of Heron's practice, highlights the significance of contextualizing “premodern algebra,” and indicates that the origins of algebraic reasoning should be sought in the problem-solving practice, rather than in the theorem-proving tradition. (shrink)

When people make sense of situations, illustrations, instructions and problems they do more than just think with their heads. They gesture, talk, point, annotate, make notes and so on. What extra do they get from interacting with their environment in this way? To study this fundamental problem, I looked at how people project structure onto geometric drawings, visual proofs, and games like tic tac toe. Two experiments were run to learn more about projection. Projection is a special capacity, similar (...) to perception, but less tied to what is in the environment. Projection, unlike pure imagery, requires external structure to anchor it, but it adds ‘mental’ structure to the external scene much like an augmented reality system adds structure to an outside scene. A person projects when they look at a chessboard and can see where a knight may be moved. Because of the cognitive costs of sustaining and extending projection, humans make some of their projections real. They create structure externally. They move the piece, they talk, point, notate, represent. Much of our interactivity during sense making and problem solving involves a cycle of projecting then creating structure. (shrink)

We establish a criterion for deciding whether a class of structures is the class of models of a geometric theory inside Grothendieck toposes; then we specialize this result to obtain a characterization of the infinitary first-order theories which are geometric in terms of their models in Grothendieck toposes, solving a problem posed by Ieke Moerdijk in 1989.

Permutative logic is a non-commutative conservative extension of linear logic suggested by some investigations on the topology of linear proofs. In order to syntactically reflect the fundamental topological structure of orientable surfaces with boundary, permutative sequents turn out to be shaped like q-permutations. Relaxation is the relation induced on q-permutations by the two structural rules divide and merge; a decision procedure for relaxation has been already provided by stressing some standard achievements in theory of permutations. In these pages, we provide (...) a parallel procedure in which the problem at issue is approached from the point of view afforded by geometry of 2-manifolds and solved by making specific surfaces interact. (shrink)

This paper develops the conjecture that the electromagnetic interaction is the manifestation of the torsion Ωμ of spacetime. This conjecture is made feasible by the natural separation of the connection ω μ v into “gravitational” and “electromagnetic” parts α μ v and β μ v , respectively, related to the metric and to the torsion. When α μ v is neglected in front of β μ v , the affine geodesics are shown to become the equations of motion of charged (...) particles with Lorentz force, for an appropriate choice of Ωμ. Since β μ v contains the factor q/m, neutral particles do not see the torsional part of the connection and behave as if Ωμ were zero, i.e., as in Einstein's theory of gravity (the same effect is obviously obtained for charged particles when β μ v 《 α μ v ).In addition to the factor q/m, the velocity of the test particle appears in Ωμ. This indicates that the appropriate context for this problem is to be found in velocity-dependent connections. The velocities are now coordinates and become the actual velocities of the test particles only in the system of equations that one solves for obtaining the affine geodesics in connections of this type.When written with differential forms, the combination of Maxwell's equations and of the pertinent form of the torsion suggests geometric field equations for electrodynamics. As for the gravitational part of the connection, it can be made to obey equations similar in form to the Einstein field equations. A unified geometric theory of electrodynamics and gravitation spontaneously emerges. The present state of the theory does not yet permit us to ascertain whether the right-hand side of the fully geometric, gravitational field equations corresponds to the energy-momentum tensor. (shrink)

When people make sense of situations, illustrations, instructions and problems they do more than just think with their heads. They gesture, talk, point, annotate, make notes and so on. What extra do they get from interacting with their environment in this way? To study this fundamental problem, I looked at how people project structure onto geometric drawings, visual proofs, and games like tic tac toe. Two experiments were run to learn more about projection. Projection is a special capacity, similar (...) to perception, but less tied to what is in the environment. Projection, unlike pure imagery, requires external structure to anchor it, but it adds ‘mental’ structure to the external scene much like an augmented reality system adds structure to an outside scene. A person projects when they look at a chessboard and can see where a knight may be moved. Because of the cognitive costs of sustaining and extending projection, humans make some of their projections real. They create structure externally. They move the piece, they talk, point, notate, represent. Much of our interactivity during sense making and problem solving involves a cycle of projecting then creating structure. (shrink)

The development of geometrical analysis in the 10th century was partly inspired by the reception of the works of Apollonius, which Arab mathematicians translated as early as the preceding century. Al-Qūhī contributed to this development by writing several collections of problems dealing with Apollonian themes and solved by the method of analysis; however, it seems that they do not all occupy the same place in his work. The author gives here the edition, translation, and mathematical commentary of a short (...) work, entitled The determination of two straight lines from a point along a known angle, which presents the particularity of providing problems as geometrical lemmas to other studies. Indeed, al-Qūhī uses two of these lemmas in more complex constructions which belong to his Treatise on the art of the astrolabe. In this same treatise on the astrolabe, as well as in his Treatise on the perfect compass, this scholar also uses as lemmas several problems solved in another of his works, entitled The generation of points on straight lines according to ratios of which the terms are surfaces. This work is unfortunately lost, and all that remains of it are the traces which subsist in other treatises in which it has been used. This study seems to be necessary if one wishes to understand the organization of the work of al-Qūhī, a mathematician of the first rank who was representative of his time. (shrink)

This article is a study of geometric constructions. We consider, as an illustration, the methods used for dividing the straight line into n equal parts (n-section). Architects and practicioners of classical Europe had at their disposal a broad range of geometric constructions: ancient ones were edited and translated, whereas new solutions were constantly published. The wide variety and reasons for selection of these geometric constructions are puzzling: the most widespread construction was not the simplest one. This article wonders why so (...) many constructions were used to solve the same problem and why tedious methods were used. It is argued that the practical conditions and scale at which the problem was tackled could account for such diversity. (shrink)

We define and study the notion of quantum polarity, which is a kind of geometric Fourier transform between sets of positions and sets of momenta. Extending previous work of ours, we show that the orthogonal projections of the covariance ellipsoid of a quantum state on the configuration and momentum spaces form what we call a dual quantum pair. We thereafter show that quantum polarity allows solving the Pauli reconstruction problem for Gaussian wavefunctions. The notion of quantum polarity exhibits (...) a strong interplay between the uncertainty principle and symplectic and convex geometry and our approach could therefore pave the way for a geometric and topological version of quantum indeterminacy. We relate our results to the Blaschke–Santaló inequality and to the Mahler conjecture. We also discuss the Hardy uncertainty principle and the less-known Donoho–Stark principle from the point of view of quantum polarity. (shrink)

This paper discusses some of the technical problems related to a Weylian geometrical interpretation of the Schrödinger and Klein-Gordon equations proposed by E. Santamato. Solutions to these technical problems are proposed. A general prescription for finding out the interdependence between a particle's effective mass and Weyl's scalar curvature is presented which leads to the fundamental equation of geometric quantum mechanics, $$m(R)\frac{{dm(R)}}{{dR}} = \frac{{\hbar ^2 }}{{c^2 }}$$ The Dirac equation is rigorously derived within this formulation, and further problems to be (...) solved are proposed in the conclusion. The main one is based on obtaining the relationship between Feynman's path integral quantization method, among others, and the methods of geometric quantum mechanics. The solution of this problem will be a crucial test for this theory that attempts to “geometrize” quantum mechanics rather than the conventional approach in the past of quantizing geometry. A numerical prediction of this theory yields a 3×10−35 eV correction to the ground-state energy of the hydrogen atom. (shrink)

Aristotle’s way of conceiving the relationship between mathematics and other branches of scientific knowledge is completely different from the way a contemporary scientist conceives it. This is one of the causes of the fact that we look at the mathematical passage we find in Aristotle’s works with the wrong expectation. We expect to find more or less stringent proofs, while for the most part Aristotle employs mere analogies. Indeed, this is the primary function of mathematics when employed in a philosophical (...) context: not a demonstrative tool, but a purely analogical model. In the case of the geometrical examples discussed in this paper, the diagrams are not conceived as part of a formalized proof, but as a work in progress. Aristotle is not interested in the final diagram but in the construction viewed in its process of development; namely in the figure a geometer draws, and gradually modifies, when he tries to solve a problem. The way in which the geometer makes use of the elements of his diagram, and the relation between these elements and his inner state of knowledge is the real feature which interests Aristotle. His goal is to use analogy in order to give the reader an idea of the states of mind involved in a more general process of knowing. (shrink)

The transformation of mathematics from ancient Greece to the medieval Arab-speaking world is here approached by focusing on a single problem proposed by Archimedes and the many solutions offered. In this trajectory Reviel Netz follows the change in the task from solving a geometrical problem to its expression as an equation, still formulated geometrically, and then on to an algebraic problem, now handled by procedures that are more like rules of manipulation. From a practice of (...) mathematics based on the localized solution we see a transition to a practice of mathematics based on the systematic approach. With three chapters ranging chronologically from Hellenistic mathematics, through late Antiquity, to the medieval world, Reviel Netz offers an alternate interpretation of the historical journey of pre-modern mathematics. (shrink)

The reach-avoid game theory is an ideal tool to handle the conflicts among intelligent agents and has been previously studied assuming full state information and no time limits on the players in the past decades. In this article, we extend the problem by requiring the defender to detect the attacker and adding maximum operation time constraints to the attacker. The attacker aims to reach the target region without being captured or reaching its time limit. The defender can employ strategies (...) to intercept the attacker only when the attacker is detected. A geometric method is proposed to solve this game qualitatively. By analyzing the geometric property of the Apollonian circle and the detection range, we give the barrier under the condition that the attacker is initially detected and the attacker’s shortest route which guarantees its arrival at the target region when it is initially outside the detection range. Then, a barrier that separates the game space into two respective winning regions of the players is constructed based on the shortest route and the time limit of the attacker. The main contributions of this work are that this paper provides the first attempt to introduce the abovementioned two concepts simultaneously, which makes the game more practical, and we provide the complete solution of the game in all possible situations. (shrink)

In the course of daily life we solve problems often enough that there is a special term to characterize the activity and the right to expect a scientific theory to explain its dynamics. The classical view in psychology is that to solve a problem a subject must frame it by creating an internal representation of the problem’s structure, usually called a problem space. This space is an internally generable representation that is mathematically identical to a graph structure (...) with nodes and links. The nodes can be annotated with useful information, and the whole representation can be distributed over internal and external structures such as symbolic notations on paper or diagrams. If the representation is distributed across internal and external structures the subject must be able to keep track of activity in the distributed structure. Problem solving proceeds as the subject works from an initial state in mentally supported space, actively constructing possible solution paths, evaluating them and heuristically choosing the best. Control of this exploratory process is not well understood, as it is not always systematic, but various heuristic search algorithms have been proposed and some experimental support has been provided for them. (shrink)

When adopting a sound logical system, reasonings made within this system are correct. The situation with reasonings expressed, at least in part, with natural language is much more ambiguous. One way to be certain of the correctness of these reasonings is to provide a logical model of them. To conclude that a reasoning process is correct we need the logical model to be faithful to the reasoning. In this case, the reasoning inherits, so to speak, the correctness of the logical (...) model. There is a weak link in this procedure, which we call the faithfulness problem: how do we decide that the logical model is faithful to the reasoning that it is supposed to model? That is an issue external to logic, and we do not have rigorous formal methods to make the decision. The purpose of this paper is to expose the faithfulness problem (not to solve it). For that purpose, we will consider two examples, one from the geometrical reasoning in Euclid’s Elements and the other from a study on deductive reasoning in the psychology of reasoning. (shrink)

In the movie The Gold Rush Charlie Chaplin and his friend are stranded in a log cabin in the middle of winter while a blizzard rages. The cabin is isolated, and they have a very big problem – there is nothing to eat. They pace around wondering what to do. Charlie's friend starts to see Charlie as a chicken, and he tries to kill him. He chases Charlie around the cabin many times. Eventually they hit upon the idea of (...) boiling an old boot and eating it for dinner. With great delicacy they sit at the table and eat the boot as if it were a gourmet meal. They solved the problem of having nothing to eat. While their solution to the problem did not result in a culinary feast, this example reveals two crucial features of problem solving. First, a problem exists when a goal must be achieved and the solution is not immediately obvious. Second, problem solving often involves attempting different ways to solve the problem. Put more formally, a problem has four components. First, there is an initial state. This is the person's state of knowledge at the start of a problem. Second, there is the goal state: the goal that the person wishes to achieve. Third are the actions or operations that the problem‐solver can use to get to the goal state. Fourth is the task environment that the solver is working in. The task environment consists of the features of the physical environment that can either directly or indirectly constrain or suggest different ways of solving a problem. I will sketch out the main currents of thinking in research in this area, beginning by reviewing the history of research on problem solving and then focusing on a number of important issues in problem‐solving research. Finally, I will give an overview of some recent developments. (shrink)

Computer-simulated scenarios have been part of psychological research on problem solving for more than 40 years. The shift in emphasis from simple toy problems to complex, more real-life oriented problems has been accompanied by discussions about the best ways to assess the process of solving complex problems. Psychometric issues such as reliable assessments and addressing correlations with other instruments have been in the foreground of these discussions and have left the content validity of complex problem (...) class='Hi'>solving in the background. In this paper, we return the focus to content issues and address the important features that define complex problems. (shrink)

Integrative systems biology is an emerging field that attempts to integrate computation, applied mathematics, engineering concepts and methods, and biological experimentation in order to model large-scale complex biochemical networks. The field is thus an important contemporary instance of an interdisciplinary approach to solving complex problems. Interdisciplinary science is a recent topic in the philosophy of science. Determining what is philosophically important and distinct about interdisciplinary practices requires detailed accounts of problem-solving practices that attempt to understand how specific (...) practices address the challenges and constraints of interdisciplinary research in different contexts. In this paper we draw from our 5-year empirical ethnographic study of two systems biology labs and their collaborations with experimental biologists to analyze a significant problem-solving approach in ISB, which we call adaptive problem solving. ISB lacks much of the methodological and theoretical resources usually found in disciplines in the natural sciences, such as methodological frameworks that prescribe reliable model-building processes. Researchers in our labs compensate for the lack of these and for the complexity of their problems by using a range of heuristics and experimenting with multiple methods and concepts from the background fields available to them. Using these resources researchers search out good techniques and practices for transforming intractable problems into potentially solvable ones. The relative freedom lab directors grant their researchers to explore methodological options and find good practices that suit their problems is not only a response to the complex interdisciplinary nature of the specific problem, but also provides the field itself with an opportunity to discover more general methodological approaches and develop theories of biological systems. Such developments in turn can help to establish the field as an identifiably distinct and successful approach to understanding biological systems. (shrink)

Multiple theories of problem-solving hypothesize that there are distinct qualitative phases exhibited during effective problem-solving. However, limited research has attempted to identify when transitions between phases occur. We integrate theory on collaborative problem-solving with dynamical systems theory suggesting that when a system is undergoing a phase transition it should exhibit a peak in entropy and that entropy levels should also relate to team performance. Communications from 40 teams that collaborated on a complex problem (...) were coded for occurrence of problem-solving processes. We applied a sliding window entropy technique to each team's communications and specified criteria for identifying data points that qualify as peaks and determining which peaks were robust. We used multilevel modeling, and provide a qualitative example, to evaluate whether phases exhibit distinct distributions of communication processes. We also tested whether there was a relationship between entropy values at transition points and CPS performance. We found that a proportion of entropy peaks was robust and that the relative occurrence of communication codes varied significantly across phases. Peaks in entropy thus corresponded to qualitative shifts in teams’ CPS communications, providing empirical evidence that teams exhibit phase transitions during CPS. Also, lower average levels of entropy at the phase transition points predicted better CPS performance. We specify future directions to improve understanding of phase transitions during CPS, and collaborative cognition, more broadly. (shrink)

Hamblin distinguished between formal and descriptive dialectic. Formal normative models of deliberation dialogue have been strongly emphasized as argumentation frameworks in computer science. But making such models of deliberation applicable to real natural language examples has reached a point where the descriptive aspect needs more interdisciplinary work. The new formal and computational models of deliberation dialogue that are being built in computer science seem to be closely related to some already existing and very well established computing technologies such as (...) class='Hi'>problem solving and decision making, but whether or how dialectical argumentation can be helpful to support these systems remains an open question. The aim of this paper is to examine some real examples of argumentation that seem to hover on the borderlines between deliberation, problem solving and decision making. (shrink)

Complex problem solving (CPS) emerged in the last 30 years in Europe as a new part of the psychology of thinking and problem solving. This paper introduces into the field and provides a personal view. Also, related concepts like macrocognition or operative intelligence will be explained in this context. Two examples for the assessment of CPS, Tailorshop and MicroDYN, are presented to illustrate the concept by means of their measurement devices. Also, the relation of complex cognition (...) and emotion in the CPS context is discussed. The question if CPS requires complex cognition is answered with a tentative “yes.”. (shrink)

The aim of this paper is to describe the way in which argumentative patterns come into being in plenary debate over legislative issues in the European Parliament. What kind of argumentative patterns are to be expected within this macro context? It is shown that the argumentative patterns that come into being in legislative debate in the European Parliament depend for the most part on the problem-solving argumentation that is put forward in the opening speech by the rapporteur of (...) the parliamentary committee report. This argumentation can be pragmatic problem-solving argumentation or complex problem-solving argumentation. The most important prototypical argumentative patterns are investigated in the argumentation put forward by the Members of parliament. This investigation is based on an inventory of the arguments that can in principle be used to support or attack the initial problem-solving argumentation put forward by the rapporteur. (shrink)

In the course of daily life we solve problems often enough that there is a special term to characterize the activity and the right to expect a scientific theory to explain its dynamics. The classical view in psychology is that to solve a problem a subject must frame it by creating an internal representation of the problem‘s structure, usually called a problem space. This space is an internally generable representation that is mathematically identical to a graph structure (...) with nodes and links. The nodes can be annotated with useful information, and the whole representation can be distributed over internal and external structures such as symbolic notations on paper or diagrams. If the representation is distributed across internal and external structures the subject must be able to keep track of activity in the distributed structure. Problem solving proceeds as the subject works from an initial state in this mentally supported space, actively construction possible solution paths, evaluating them and heuristically choosing the best. Control of this exploratory process is not well understood, as it is not always systematic, but various heuristic search algorithms have been proposed and some experimental support has been provided for them. (shrink)

According to Zagzebski, understanding something is justified by the exercise of cognitive skills and intellectual virtues the knower possesses. Zagzebski develops her view by suggesting that “understanding has internalist conditions for success”. Against this view, Grimm raises an objection: what justifies understanding is the reliability of the processes by which we come to understand, and we need not be aware of the outcome of all reliable processes. Understanding is no exception, so, given that understanding something results from reliable processes, we (...) need not always be aware of what we understand. I reply to Grimm’s objection; I argue that Zagzebski’s internalist requirement is best conceived as accessibility to conscious reflection. The accessibility condition is satisfied because understanding solves problems on the knower’s research agenda. And whenever problem-solving is non-trivial, the knower needs to reflect on what the best solving strategy is. (shrink)

Experimental research by social and cognitive psychologists has established that cooperative groups solve a wide range of problems better than individuals. Cooperative problem solving groups of scientific researchers, auditors, financial analysts, air crash investigators, and forensic art experts are increasingly important in our complex and interdependent society. This comprehensive textbook--the first of its kind in decades--presents important theories and experimental research about group problem solving. The book focuses on tasks that have demonstrably correct solutions within mathematical, (...) logical, scientific, or verbal systems, including algebra problems, analogies, vocabulary, and logical reasoning problems.The book explores basic concepts in group problem solving, social combination models, group memory, group ability and world knowledge tasks, rule induction problems, letters-to-numbers problems, evidence for positive group-to-individual transfer, and social choice theory. The conclusion proposes ten generalizations that are supported by the theory and research on group problem solving. Group Problem Solving is an essential resource for decision-making research in social and cognitive psychology, but also extremely relevant to multidisciplinary and multicultural problem-solving teams in organizational behavior, business administration, management, and behavioral economics. (shrink)

Problem Solving Technologies provides a user friendly understanding of technological objects including what they are and how the function in our lives.

How well can we explain natural occurrences of cognitive behaviours given the theoretical frameworks available to us today? The thesis explores what has to be assumed in cognitive theory in order to provide such an explanation, in contrast to being able to predict behaviour under controlled circumstances. The behaviours considered are all of the type described as involving higher level cognition or being representation hungry. Examples are problem solving and certain types of decision-making. Three different theoretical frameworks are (...) examined: general theories such as Newell and Simon’s Universal Problem Solver, the stances sometimes referred to as “situated cognition,” particularly those that try to exclude cognitive components from their explanatory framework ; and domain-specific theories of cognition. The last category can broadly be separated into two different types of theories: those who claim that specialised cognitive processes are activated through situational features and those who claim that specialised cognitive processes are successful relative such features. The conclusion is that none of the stances are sufficient on their own. The proposed solution is instead to take both the hypothesised domain-specific process and the information it utilises into account. If we allow for “high-quality” information of a more domain-general nature, that indicates which parts of the current situation are important, or makes it possible for the individual to assume certain relations in advance, then this information can account for parts of the flexibility and stability required of the cognitive processes. Examples of such information are causal relations and epistemic information connected to social information. Since these point us to how the features of the situation at hand were produced, they help us identify relevant aspects of, and relations between different situations. By utilising high-quality information, domain-specific processes can be made broader, and less specialised, while keeping a close tie to the situations in which they are active. In this way we can begin to explain real life cognitive behaviours. (shrink)

In adversarial problem solving (APS), one must anticipate, understand and counteract the actions of an opponent. Military strategy, business, and game playing all require an agent to construct a model of an opponent that includes the opponent's model of the agent. The cognitive mechanisms required for such modeling include deduction, analogy, inductive generalization, and the formation and evaluation of explanatory hypotheses. Explanatory coherence theory captures part of what is involved in APS, particularly in cases involving deception.

Anders, Rudi To solve a problem such as wars between nations and civil wars it is necessary to discover what causes the problem.

This paper presents an analysis of emotional and affectively toned discourse in biomedical engineering researchers’ accounts of their problem solving practices. Drawing from our interviews with scientists in two laboratories, we examine three classes of expression: explicit, figurative and metaphorical, and attributions of emotion to objects and artifacts important to laboratory practice. We consider the overall function of expressions in the particular problem solving contexts described. We argue that affective processes are engaged in problem (...) class='Hi'>solving, not as simply tacked onto reasoning but as integral to it. The examples we present illustrate the close relation of emotion to problem solving and experimentation; they also implicate social and cultural dimensions of emotion expression. The analysis underscores a need to consider emotional expression to be intimately and importantly tied to the cognitive achievements and social negotiations of laboratory practices. (shrink)

Learning to solve a class of problems can be characterized as a search through a space of hypotheses about the rules for solving these problems. A series of four experiments studied how different learning conditions affected the search among hypotheses about the solution rule for a simple computational problem. Experiment 1 showed that a problem property such as computational difficulty of the rules biased the search process and so affected learning. Experiment 2 examined the impact of examples (...) as instructional tools and found that their effectiveness was determined by whether they uniquely pointed to the correct rule. Experiment 3 compared verbal directions with examples and found that both could guide search. The final experiment tried to improve learning by using more explicit verbal directions or by adding scaffolding to the example. While both manipulations improved learning, learning still took the form of a search through a hypothesis space of possible rules. We describe a model that embodies two assumptions: the instruction can bias the rules participants hypothesize rather than directly be encoded into a rule; participants do not have memory for past wrong hypotheses and are likely to retry them. These assumptions are realized in a Markov model that fits all the data by estimating two sets of probabilities. First, the learning condition induced one set of Start probabilities of trying various rules. Second, should this first hypothesis prove wrong, the learning condition induced a second set of Choice probabilities of considering various rules. These findings broaden our understanding of effective instruction and provide implications for instructional design. (shrink)

Recent research on human problem solving has largely focused on laboratory tasks that do not demand from the subject much prior, task‐related information. This study seeks to extend the theory of human problem solving to semantically richer domains that are characteristic of professional problem solving. We discuss the behavior of a single subject solving problems in chemical engineering thermodynamics. We use as a protocol‐encoding device a computer program called SAPA which also doubles as (...) a theory of the subject's problem‐solving behavior. The subject made extensive use of means‐ends analysis, similar to that observed in semantically less rich domains, supplemented by recognition mechanisms for accessing information in semantic memory. (shrink)

A general model of problem‐solving processes based on misconception elimination is presented to simulate both impasses and solving processes. The model operates on goal‐related rules and a set of constraint rules in the form of “if (state or goal), do not (Action)” for the explicit constraints in the instructions and the implicit constraints that come from misconceptions of legal moves. When impasses occur, a constraint elimination mechanism is applied. Because successive eliminations of implicit constraints enlarge the (...) class='Hi'>problem space and have an effect on planning, the model integrates “plan‐based” and “constraint‐based” approaches to problem‐solving behavior.Simulating individual protocols of Tower of Hanoi situations shows that the model, which has a proper set of constraints, predicts a single move with no alternative on about 61% of the movements and that protocols are quite successfully simulated movement by movement. Finally, it is shown that many features of previous models are embedded in the constraint elimination model. (shrink)

A study is reported which focused on the problem-solving strategies employed by expert electronics engineers pursuing a real-world task: integrated-circuit design. Verbal protocol data were analysed so as to reveal aspects of the organisation and sequencing of ongoing design activity. These analyses indicated that the designers were implementing a highly systematic solution-development strategy which deviated only a small degree from a normatively optimal top-down and breadth-first method. Although some of the observed deviation could be described as opportunistic in (...) nature, much of it reflected the rapid depth-first exploration of tentative solution ideas. We argue that switches from a predominantly breadth-first mode of problem solving to depth-first or opportunistic modes may be an important aspect of the expert's strategic knowledge about how to conduct the design process effectively when faced with difficulties, uncertainties, and design impasses. (shrink)

Rather than being random deviation, student errors can be a source of insight into the nature of student difficulties. This paper reports on (and offers pedagogical advice concerning) many common student errors in the construction of proofs, in the application of inference and replacement rules, and in the choice of proof strategies. In addition, a detailed description of the bottom-up strategy for “working backwards” is supplied, along with a discussion of the main difficulties students face when trying to solve proofs (...) in this fashion. Ultimately, it is argued that students can employ both top-down and bottom-up proofs strategies by making use of a graphic proof representation. (shrink)

This paper reports on a study that was conducted on the effects of training students in specific strategic and meta-cognitive questioning strategies on the development of reasoning, problem-solving, and learning during cooperative inquiry-based science activities. The study was conducted in 18 sixth grade classrooms and involved 35 groups of students in three conditions: the cognitive questioning condition; the Philosophy for Children condition; and the comparison condition. The students were videotaped as they worked on a specific inquiry-science task once (...) each term for two consecutive school terms. The results show that the students in all conditions demonstrated more helping discourses or discourses known to mediate learning than any other of the discourse categories. This outcome is encouraging because it is the helping discourses where students provide explanations, elaborations, and reasons that promote follow-up learning. (shrink)