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Title
Abstract
Figures
Case Study
Methodology
Sensor Data
Discussion and Conclusions
Background and Architecture Design
Materials and Methods
Conclusion
Introduction and Research Questions
Related Work
Conclusions and Future Work
Latent Semantic Analysis
Conclusion and Future Work
Conclusions and Further Research
Related Works
Results
Discussion
Conclusions
Introduction
Informational Analysis
Limitations and Potential of the Model
Background
References
All Topics
Psychology
Cognitive Psychology

Artificial Intelligence and Cognition

Profile image of Marco CrucianiMarco Cruciani

2013

Abstract

Spatial structures determine the ways we perceive our environment and the ways we act in it in important ways. Spatial structures also determine the ways we think about our environment and how we solve spatial problems abstractly. When we use graphics to visualize certain aspects of spatial and non-spatial entities, we exploit the power of spatial structures to better understand important relationships. We also are able to imagine spatial structures and to apply mental operations to them. Similarly, the structure of time determines the course of events in cognitive processing. In my talk I will present knowledge representation research in spatial cognition. I will demonstrate the power of spatial structures in comparison to formal descriptions that are conventionally used for spatial problem solving in computer science. I suggest that spatial and temporal structures can be exploited for the design of powerful spatial computers. I will show that spatial computers can be particularly ...

Figures (50)
Fig. 2. An A-SOM network connected with two other SOM networks. They provide the ancillary input to the main A-SOM (see the main text for more details). where m is the softmax exponent. The ancillary activity yp, (t), p=1,2,...,r is calculated by again using the standard cosine metric
Fig. 2. An A-SOM network connected with two other SOM networks. They provide the ancillary input to the main A-SOM (see the main text for more details). where m is the softmax exponent. The ancillary activity yp, (t), p=1,2,...,r is calculated by again using the standard cosine metric
Fig. 4. The walk action movie created with a reduced number of images. Fig. 5. a) The sequence of images depicting the check watch action; b) The sequence of images obtained by subtracting consecutive images of the check watch action.
Fig. 4. The walk action movie created with a reduced number of images. Fig. 5. a) The sequence of images depicting the check watch action; b) The sequence of images obtained by subtracting consecutive images of the check watch action.
Fig. 7. Simulation results: The tables show the ability of the A-SOM to continue the likely continuation of an observed behaviour. Dark green colour indicates that the A- SOM is able to simulate, light green colour indicates that the A-SOM predicts a value very close to the expected one, and red colour indicates that the A-SOM predicts the wrong value. The system needs between 4 and 9 inputs to internally simulate the rest of the sequence.
Fig. 7. Simulation results: The tables show the ability of the A-SOM to continue the likely continuation of an observed behaviour. Dark green colour indicates that the A- SOM is able to simulate, light green colour indicates that the A-SOM predicts a value very close to the expected one, and red colour indicates that the A-SOM predicts the wrong value. The system needs between 4 and 9 inputs to internally simulate the rest of the sequence.
Fig. 8. Similar images have similar centres of activity. The A-SOM elicits similar or equal centres of activity for images that are similar.
Fig. 8. Similar images have similar centres of activity. The A-SOM elicits similar or equal centres of activity for images that are similar.
Fig. 9. Images with the same centres of activity (winners). The frames present similar features which lead the A-SOM to elicit the same centre of activity.
Fig. 9. Images with the same centres of activity (winners). The frames present similar features which lead the A-SOM to elicit the same centre of activity.
Fig. 1. The human categorization system (extracted from Evans and Green 2006) those located in the lower vertical axis, which provide more detail, are called subordi- nate categories i (saloon, collie, and rocking chair). k On the other hand, horizontal dimension focuses on segmentation of categories in the same level of inclusiveness, that is:
Fig. 1. The human categorization system (extracted from Evans and Green 2006) those located in the lower vertical axis, which provide more detail, are called subordi- nate categories i (saloon, collie, and rocking chair). k On the other hand, horizontal dimension focuses on segmentation of categories in the same level of inclusiveness, that is:
Fig. 2. Methodology for extracting analytical definitions 5.2 Extraction of subordinate categories
Fig. 2. Methodology for extracting analytical definitions 5.2 Extraction of subordinate categories
Table 3. Extraction of analytical definitions 6.5 Extraction to subordinate categories
Table 3. Extraction of analytical definitions 6.5 Extraction to subordinate categories
This precision is compared with precision by setting several PMI thresholds (0, 0.10, 0.15, and 0.25) as shown in table 5. Results show a significant improvement in preci- sion from PMI 0.25, but recall is negatively affected as this threshold is increased. On the other hand, if we consider linguistic heuristics we obtain a trade-off between pre- cision and recall, as shown in table 6.
This precision is compared with precision by setting several PMI thresholds (0, 0.10, 0.15, and 0.25) as shown in table 5. Results show a significant improvement in preci- sion from PMI 0.25, but recall is negatively affected as this threshold is increased. On the other hand, if we consider linguistic heuristics we obtain a trade-off between pre- cision and recall, as shown in table 6.
Table 5. Precision (P), recall (R) and F-Measure (F) by PMI threshold
Table 5. Precision (P), recall (R) and F-Measure (F) by PMI threshold
Fig. 1. Diagram of the system developed
Fig. 1. Diagram of the system developed
The set of skills implemented and their associated actions are described it able 1
The set of skills implemented and their associated actions are described it able 1
Fig. 2. (a) Reem humanoid robot and (b) Reem head with kinect included The robot platform used for testing the system developed is called Reem 2, a humanoid service robot created by PAL Robotics. Its weight is about 90 Kg, 22 degrees of freedom and an autonomy of about 8 hours. Reem is controlled by OROCOS for real time operations and by ROS for skill depletion. Among other abilities, it can recognize and grasp objects, detect faces, follow a person and even clean a room of objects that do not belong to it. In order to include robust grasping and gesture detection, a kinnect sensor on a headset on her head has been added to the commercial version.
Fig. 2. (a) Reem humanoid robot and (b) Reem head with kinect included The robot platform used for testing the system developed is called Reem 2, a humanoid service robot created by PAL Robotics. Its weight is about 90 Kg, 22 degrees of freedom and an autonomy of about 8 hours. Reem is controlled by OROCOS for real time operations and by ROS for skill depletion. Among other abilities, it can recognize and grasp objects, detect faces, follow a person and even clean a room of objects that do not belong to it. In order to include robust grasping and gesture detection, a kinnect sensor on a headset on her head has been added to the commercial version.
Fig. 3. Reem robot at the experiments environment that mimics a home The whole architecture has been put to test in an environment that mimics that of the RoboCup@Home League at the GPSR test [25] (see figure 3). In this test, the robot has to listen three different types of commands with increased difficulty, and execute the required actions (skills) to accomplish the command. For our implementation, only the two first categories have been tested, as described in section 2.2.
Fig. 3. Reem robot at the experiments environment that mimics a home The whole architecture has been put to test in an environment that mimics that of the RoboCup@Home League at the GPSR test [25] (see figure 3). In this test, the robot has to listen three different types of commands with increased difficulty, and execute the required actions (skills) to accomplish the command. For our implementation, only the two first categories have been tested, as described in section 2.2.
Fig. 4. Sequence of actions done by Reem to solve the command Bring me an energy drink understand command, ask questions, acknowledge all information, navigate to location, search for seating, point at seating Carry a Snack to a table Sequence of actions performed by the robot: understand command, ask questions, acknowledge all information, navigate to location, search for snack, grasp snack, go to table, deliver snack Bring me an energy drink (figure 4) Sequence of actions performed by the robot: understand command, ask questions, acknowledge all information, navigate to location, search for energy drink, grasp energy drink, return to origin, deliver energy drink
Fig. 4. Sequence of actions done by Reem to solve the command Bring me an energy drink understand command, ask questions, acknowledge all information, navigate to location, search for seating, point at seating Carry a Snack to a table Sequence of actions performed by the robot: understand command, ask questions, acknowledge all information, navigate to location, search for snack, grasp snack, go to table, deliver snack Bring me an energy drink (figure 4) Sequence of actions performed by the robot: understand command, ask questions, acknowledge all information, navigate to location, search for energy drink, grasp energy drink, return to origin, deliver energy drink
Fig. 1. A sketch of the cognitive architecture.
Fig. 1. A sketch of the cognitive architecture.
Fig. 2. An evocative representation of a chord in the music conceptual space.
Fig. 2. An evocative representation of a chord in the music conceptual space.
Fig. 3. An evocative representation of a scattering between two chords in the music conceptual space.
Fig. 3. An evocative representation of a scattering between two chords in the music conceptual space.
Fig. 4. A fragment of the terminological KB along with its mapping into the conceptual space.
Fig. 4. A fragment of the terminological KB along with its mapping into the conceptual space.
Fig. 1: Architecture of the hybrid system.
Fig. 1: Architecture of the hybrid system.
Fig. 1. a) Cancellation task in which targets are open circles and full circles are distrac- tors; b) open circles canceled with a circular mark; c) cancellation task implemented in our experiments: grey filled circles are targets and black ones distractors The cancellation task is a well known diagnostic test used to detect neuropsy- chological deficits in human beings. The test material typically consists of a rectangular white sheet which contains randomly scattered visual stimuli. Stim- uli may be of two (or more) categories (for example triangles and squares, lines and dots, A and C letters, etc.). Figure 1a shows an example of the task. Sub- jects are asked to find and cancel by a pen stroke all the items of a given category (e.g. open circles). Fundamentally, it is a visual search task where some items are coded as distractors and other represent targets (the items to cancel). Brain- damaged patients can fail to cancel targets in a sector of space, typically the left half of the sheet after a lesion in the right hemisphere (visual neglect, see figure 1b).Here we simulated this task through a virtual sheet (a bitmap) in which a set of targets and distractors are randomly drawn (Fig. 1c), and trained neural agents provided with a specific sensory-motor apparatus, described in the next section, to perform the task.
Fig. 1. a) Cancellation task in which targets are open circles and full circles are distrac- tors; b) open circles canceled with a circular mark; c) cancellation task implemented in our experiments: grey filled circles are targets and black ones distractors The cancellation task is a well known diagnostic test used to detect neuropsy- chological deficits in human beings. The test material typically consists of a rectangular white sheet which contains randomly scattered visual stimuli. Stim- uli may be of two (or more) categories (for example triangles and squares, lines and dots, A and C letters, etc.). Figure 1a shows an example of the task. Sub- jects are asked to find and cancel by a pen stroke all the items of a given category (e.g. open circles). Fundamentally, it is a visual search task where some items are coded as distractors and other represent targets (the items to cancel). Brain- damaged patients can fail to cancel targets in a sector of space, typically the left half of the sheet after a lesion in the right hemisphere (visual neglect, see figure 1b).Here we simulated this task through a virtual sheet (a bitmap) in which a set of targets and distractors are randomly drawn (Fig. 1c), and trained neural agents provided with a specific sensory-motor apparatus, described in the next section, to perform the task.
Fig. 2. The sensory-motor apparatus: two motors control rotation around two axes, one motor controls the zoom and a supplementary motor (not depicted) triggers the cancellation behaviour. A neural agent is equipped with a pan/tilt camera provided with a motorized zoom and an actuator able to trigger the cancellation behavior (Fig.2). The camera has a resolution of 350x350 pixels. Two motors allow the camera to explore the visual scene by controlling rotation around x and y axes while a third motor controls the magnification of the observed scene. Finally, the fourth actuator triggers a cancellation movement that reproduces in a simplified fashion the behavior shown by human individuals when asked to solve the task. The
Fig. 2. The sensory-motor apparatus: two motors control rotation around two axes, one motor controls the zoom and a supplementary motor (not depicted) triggers the cancellation behaviour. A neural agent is equipped with a pan/tilt camera provided with a motorized zoom and an actuator able to trigger the cancellation behavior (Fig.2). The camera has a resolution of 350x350 pixels. Two motors allow the camera to explore the visual scene by controlling rotation around x and y axes while a third motor controls the magnification of the observed scene. Finally, the fourth actuator triggers a cancellation movement that reproduces in a simplified fashion the behavior shown by human individuals when asked to solve the task. The
Fig. 3. Right. Neural agent’s retina. Receptors are depicted as blue filled circle, recep- tive fields as dotted red circles. Left. Receptor activation is computed averaging the luminance value of the perceived stimuli.
Fig. 3. Right. Neural agent’s retina. Receptors are depicted as blue filled circle, recep- tive fields as dotted red circles. Left. Receptor activation is computed averaging the luminance value of the perceived stimuli.
Fig. 4. Random patterns of targets (gray filled circles) and distractors (black filled circles) distractors (black stimuli) and targets (grey stimuli) (Fig. 4) and rewarded neural agents for the ability to find (by putting the center of their retina over a target stimulus) and cancel/mark correct stimuli (activating the proper actuator).
Fig. 4. Random patterns of targets (gray filled circles) and distractors (black filled circles) distractors (black stimuli) and targets (grey stimuli) (Fig. 4) and rewarded neural agents for the ability to find (by putting the center of their retina over a target stimulus) and cancel/mark correct stimuli (activating the proper actuator).
Fig. 5. Networks trained for the cancellation task: a) Perceptron; b)Feed forward neural networks with a 10 neurons hidden layer; c) Network b with a recurrent connection; d) Network c with a direct input-output connection layer. first by the number of neurons and by their connections. In this case more complexity turns on more computational power that a controller can manage. Second, complexity can be related to the body in terms of sensory or motor resources that can be exploited to solve a particular task.
Fig. 5. Networks trained for the cancellation task: a) Perceptron; b)Feed forward neural networks with a 10 neurons hidden layer; c) Network b with a recurrent connection; d) Network c with a direct input-output connection layer. first by the number of neurons and by their connections. In this case more complexity turns on more computational power that a controller can manage. Second, complexity can be related to the body in terms of sensory or motor resources that can be exploited to solve a particular task.
Fig. 6. Boxplots containing the post evaluation performance for each evolutionary experiment. Each boxplot reports the performance of the best 10 individuals. evaluation is twofold. First, during evolution each agent experienced a small number of possible visual patterns (20); second, the reward function was made up of two parts so as to avoid bootstrapping problems: one component to re- ward exploration and the second one to reward correct cancellations. Results are reported as proportion correct in cancellation tests. Figure 6 reports the post- evaluation results for each architecture in each motor condition: with the ability to operate the zoom (Fig. 6 a,b,c and d) and without this ability (a-, b-, c- and d-).
Fig. 6. Boxplots containing the post evaluation performance for each evolutionary experiment. Each boxplot reports the performance of the best 10 individuals. evaluation is twofold. First, during evolution each agent experienced a small number of possible visual patterns (20); second, the reward function was made up of two parts so as to avoid bootstrapping problems: one component to re- ward exploration and the second one to reward correct cancellations. Results are reported as proportion correct in cancellation tests. Figure 6 reports the post- evaluation results for each architecture in each motor condition: with the ability to operate the zoom (Fig. 6 a,b,c and d) and without this ability (a-, b-, c- and d-).
Fig. 7. Individual proportion correct in the selection of left or right-sided targets as first visited item.
Fig. 7. Individual proportion correct in the selection of left or right-sided targets as first visited item.
Fig. 1. The purely objective view of the world. The door can have different states like open, close (and other ones in the middle, like half-close). Then, there exist different actions that may change its status, like “push” and “pull”. are the same and have the same meaning regardless of the agent performing the action. On the other hand, in a purely subjective scenario, we have a plurality of possibly inconsistent ontologies, one for each agent or species. Besides being too broad and complex to represent, the main problem would be that the same concept would be unrelated to the corresponding ones in the ontologies of other agents. This leads to disalignments, to the impossibility to reuse part of the representations even if the concepts are similar, and to difficulties in maintaining the knowledge base.
Fig. 1. The purely objective view of the world. The door can have different states like open, close (and other ones in the middle, like half-close). Then, there exist different actions that may change its status, like “push” and “pull”. are the same and have the same meaning regardless of the agent performing the action. On the other hand, in a purely subjective scenario, we have a plurality of possibly inconsistent ontologies, one for each agent or species. Besides being too broad and complex to represent, the main problem would be that the same concept would be unrelated to the corresponding ones in the ontologies of other agents. This leads to disalignments, to the impossibility to reuse part of the representations even if the concepts are similar, and to difficulties in maintaining the knowledge base.
Fig. 2. The purely subjective view of the world. The enumeration of all instances and relationships without any ontology alignments produce a huge object space that turns out to be impossible to treat computationally.
Fig. 2. The purely subjective view of the world. The enumeration of all instances and relationships without any ontology alignments produce a huge object space that turns out to be impossible to treat computationally.
Fig. 3. From an ontological point of view, when the subject takes part to the meaning of the situation under definition, there is no need of concept duplication. Instead, the ontology has to provide mechanisms to contextualize the relationships according tc the subject, eventually with the addition of specific properties or objects (as the doot handle for the human subject).
Fig. 3. From an ontological point of view, when the subject takes part to the meaning of the situation under definition, there is no need of concept duplication. Instead, the ontology has to provide mechanisms to contextualize the relationships according tc the subject, eventually with the addition of specific properties or objects (as the doot handle for the human subject).
Fig. 4. A classic ontological view of the printer scenario. An instance has to belong to one of the three classes, but none of them captures the semantics associated tc the interaction with the users. In case the new instance belongs to both printer pt1 and printer pt2, then it inherits all their methods, thus avoiding the differentiation at user-level. on how many number of remaining copies are printable (marked as nc within the figure). The third example we consider is of a totally different kind. There is no more physical object, since the artifact is an institution, i.e., an object of the socially constructed reality [6]. Consider a university, where each person can have different roles like professor, student, guardian, and so forth. Each one of these will be associated to different behaviours and properties: the professors teach courses and give marks, have an income; the students give exams, have an id number, and so forth. Here the behaviour does not depend anymore on the physical properties but on the social role of the agent.
Fig. 4. A classic ontological view of the printer scenario. An instance has to belong to one of the three classes, but none of them captures the semantics associated tc the interaction with the users. In case the new instance belongs to both printer pt1 and printer pt2, then it inherits all their methods, thus avoiding the differentiation at user-level. on how many number of remaining copies are printable (marked as nc within the figure). The third example we consider is of a totally different kind. There is no more physical object, since the artifact is an institution, i.e., an object of the socially constructed reality [6]. Consider a university, where each person can have different roles like professor, student, guardian, and so forth. Each one of these will be associated to different behaviours and properties: the professors teach courses and give marks, have an income; the students give exams, have an id number, and so forth. Here the behaviour does not depend anymore on the physical properties but on the social role of the agent.
Fig. 5. An intelligent system where a printer works differently depending on who is the user performing the action.
Fig. 5. An intelligent system where a printer works differently depending on who is the user performing the action.
Fig. 7. A mental model of an airplane when travelling. [15]
Fig. 7. A mental model of an airplane when travelling. [15]
Fig. 6. A mental model of an airplane to recognize it. [15] cognitive metaphor. A mental model is composed by tokens (elements) and re- lations which represent a specific state of things, structured in an appropriate manner to the processes that will have to operate on them. There is no a sin- gle mental model to which the answer is right and that corresponds to a certain state of things: a single statement can legitimately correspond to several models, although it is likely that one of these matches in the best way to describe the state of affairs. This allows to represent both the intension that the extension of a concept, namely the characteristic properties of the state described; the man- agement procedures of the model are used to define the extension of the same concept, that is, the set of all possible states that describe the concept. Figures 6 and 7 show the case of an airplane and the resulting mental models that we create according to different types of action: recognize it or travel with it. In- deed, the action changes the type of perception we have of an object and the action takes different meanings depending on the interaction with the subject that performs it.
Fig. 6. A mental model of an airplane to recognize it. [15] cognitive metaphor. A mental model is composed by tokens (elements) and re- lations which represent a specific state of things, structured in an appropriate manner to the processes that will have to operate on them. There is no a sin- gle mental model to which the answer is right and that corresponds to a certain state of things: a single statement can legitimately correspond to several models, although it is likely that one of these matches in the best way to describe the state of affairs. This allows to represent both the intension that the extension of a concept, namely the characteristic properties of the state described; the man- agement procedures of the model are used to define the extension of the same concept, that is, the set of all possible states that describe the concept. Figures 6 and 7 show the case of an airplane and the resulting mental models that we create according to different types of action: recognize it or travel with it. In- deed, the action changes the type of perception we have of an object and the action takes different meanings depending on the interaction with the subject that performs it.
Fig. 1. Figure 1 (a) shows the corpus containing all three assessment criteria. It is illustrated that document 0_Memorizing lies close to the origin. Figure 1 (b) shows the corpus without the document 0_Memorizing. In Figure (a) and (b) the crosses close to the origin mark the positions of the 20 queries.
Fig. 1. Figure 1 (a) shows the corpus containing all three assessment criteria. It is illustrated that document 0_Memorizing lies close to the origin. Figure 1 (b) shows the corpus without the document 0_Memorizing. In Figure (a) and (b) the crosses close to the origin mark the positions of the 20 queries.
Fig. 2. Each structure can be defined recursively as composed by its substructures. A structure can be decomposed into a collection of substructures. Each substructure can be defined separately, and the original structure can be defined as a combination of substructures. Each (sub)structure is described by the nodes, the labels and the variables in its terminal nodes. Such variables can be unified seamlessly with either another substructure or another variable. In general, ADDs can be represented compactly through a recursive definition due to the presence of isomorphic sub-graphs. At the same manner, a structure can be defined recursively. The figure 2 shows an example.
Fig. 2. Each structure can be defined recursively as composed by its substructures. A structure can be decomposed into a collection of substructures. Each substructure can be defined separately, and the original structure can be defined as a combination of substructures. Each (sub)structure is described by the nodes, the labels and the variables in its terminal nodes. Such variables can be unified seamlessly with either another substructure or another variable. In general, ADDs can be represented compactly through a recursive definition due to the presence of isomorphic sub-graphs. At the same manner, a structure can be defined recursively. The figure 2 shows an example.
Fig. 1. The decomposition of an ADD in the corresponding structure-vector pair (5, v). which is made up by nodes, arcs, and labels, and v is the vector containing the values in terminal nodes of the ADD. Let’s consider the ADD described in the previous section. Figure 1 shows its decomposition in the structure-vector pair Terminal nodes are substituted with variables, and the ADD is transformed int« its structure. Each element of the vector v is a couple made up by a prope! variable inserted into the i-th leaf node of the structure, and a probability value that was stored originally into the i-th leaf node.
Fig. 1. The decomposition of an ADD in the corresponding structure-vector pair (5, v). which is made up by nodes, arcs, and labels, and v is the vector containing the values in terminal nodes of the ADD. Let’s consider the ADD described in the previous section. Figure 1 shows its decomposition in the structure-vector pair Terminal nodes are substituted with variables, and the ADD is transformed int« its structure. Each element of the vector v is a couple made up by a prope! variable inserted into the i-th leaf node of the structure, and a probability value that was stored originally into the i-th leaf node.
Fig. 3. The MetaADD corresponding to the ADD introduced in the figure 1. implementation of an operator op applied to MADDs can be derived by the cor- responding operator defined for ADDs. Given three ADDs, add,, addz, and adds, and their corresponding MADDs madd, madd2, and madds3, then add, op addz = adds = madd, op maddz = madds3.
Fig. 3. The MetaADD corresponding to the ADD introduced in the figure 1. implementation of an operator op applied to MADDs can be derived by the cor- responding operator defined for ADDs. Given three ADDs, add,, addz, and adds, and their corresponding MADDs madd, madd2, and madds3, then add, op addz = adds = madd, op maddz = madds3.
Fig. 5. The decomposition of a MADD structure into the pair (17S, v), and the cor- responding MMADD 5). We called such computational entity meta-structure MS. It has neither values nor labels: all its elements are variables. MS is coupled with a corresponding vector v, which contains variable-label couples (see Figure 5). The definition of
Fig. 5. The decomposition of a MADD structure into the pair (17S, v), and the cor- responding MMADD 5). We called such computational entity meta-structure MS. It has neither values nor labels: all its elements are variables. MS is coupled with a corresponding vector v, which contains variable-label couples (see Figure 5). The definition of
Fig. 4. Two MADDs are added, producing a third MADD. Results are computed according to the formulas described inside the box.
Fig. 4. Two MADDs are added, producing a third MADD. Results are computed according to the formulas described inside the box.
Table 1. The distribution of CiTO properties selected by the users. CiTO property by all 5 users, while for 23 citations the humans selected at most two properties. These results are summarised in Table 2, together with the list of selected properties. In that table, we indicate how many citations of the dataset users agreed, and the number of properties selected by the users.
Table 1. The distribution of CiTO properties selected by the users. CiTO property by all 5 users, while for 23 citations the humans selected at most two properties. These results are summarised in Table 2, together with the list of selected properties. In that table, we indicate how many citations of the dataset users agreed, and the number of properties selected by the users.
Fig. 1: A process interpretation of Peirce’s hierarchy of sign aspects, introduced in [5]. Horizontal lines are used to designate interaction events between representations of the input from different perspectives (cf. sign aspects). The input of the process is associated with the qualisign position
Fig. 1: A process interpretation of Peirce’s hierarchy of sign aspects, introduced in [5]. Horizontal lines are used to designate interaction events between representations of the input from different perspectives (cf. sign aspects). The input of the process is associated with the qualisign position
Fig. 2: (a) A hierarchical representation of information involved in an interaction be- tween a pair of qualities, qg and q,. A pair of integers is used to designate categorical information involved in qz and q; (in this order). (b) The process model of cognitive activity. Horizontal lines are used to designate interaction events between different in- put representations. The types of interpretation used are displayed on the right-hand side in italics
Fig. 2: (a) A hierarchical representation of information involved in an interaction be- tween a pair of qualities, qg and q,. A pair of integers is used to designate categorical information involved in qz and q; (in this order). (b) The process model of cognitive activity. Horizontal lines are used to designate interaction events between different in- put representations. The types of interpretation used are displayed on the right-hand side in italics
Fig. 4: Finite state transition machine diagram for syllogisms
Fig. 4: Finite state transition machine diagram for syllogisms
Acknowledgements. This study was supported by MEXT-Supported Program for the Strate- gic Research Foundation at Private Universities (2012-2014) and Grant-in-Aid for JSPS Fellows (25-2291).
Acknowledgements. This study was supported by MEXT-Supported Program for the Strate- gic Research Foundation at Private Universities (2012-2014) and Grant-in-Aid for JSPS Fellows (25-2291).

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Although human perception is geometrically constrained, not all geometric relations are equally prominent and not all geometric relations are used in everyday settings in human perception. Further, some geometric relations are systematically transformed. In this study we describe a robust geometric framework expressing spatial relations but including some strong and systematic non-geometric extensions that operate in human perception. We generally adopt the view that spatial cognition centers on qualitative spatial relations, including geometrical and topological but also functional ones (Coventry and Garrod, 2004, Gärdenfors, 2014, Mani and Pustejovsky, 2012). The topological and geometrical principles of qualitative spatial reasoning have been formalized using the framework of the Region Connection Calculus (RCC; Cohn et al., 1997), complemented with convexity and distance and orientation primitives. In work in progress, we extend this framework to include functional relations (Coventry and Garrod, 2004, Vandeloise, 1991). The central functional relations are identified as locational control and support, as they enable us to characterize a wide range of further relations, including interlocking, containment, functional enclosure and telicity.

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Spatial Problem Solving and Cognition
Ana-Maria Olteteanu, Ana-Maria Olteteanu

Representations in mind and world , 2018

A spatial problem is (1) a question about a given spatial configuration (of arbitrary physical entities) that needs to be answered (e.g. is there wine in the glass?) or (2) the challenge to construct a spatial configuration with certain properties from a given spatial configuration (e.g. add two matchsticks to the given configuration to obtain four squares) (Bertel, 2010). By spatial configurations we mean arrangements of entities in 1-, 2-, or 3-dimensional physical space, where physical space is commonsensically observable Euclidean space and motion, rather than relativistic space-time. Physical space is contrasted here to abstract space of arbitrary dimensionality. Physical space affords certain actions, like (i) rotation (circular motion of objects around a given location); (ii) motion from one location to another; (iii) deformation of objects; (iv) separation of objects into parts; (v) aggregation of objects; and (vi) combinations, i.e. rotation around a changing location. A special feature of commonsense physical space (CPS) is that operations such as motion are severely constrained and comply with rigid rules we cannot change whereas in abstract spaces we are free to make up arbitrary rules about which operations are possible and which are not. For example, in abstract representations of space (AbsRS) we could allow a 'jump' operation that moves an entity directly from one location to a remote location (as in some board games). In CPS this is not possible: objects always first move to neighboring locations and then to a neighbor of that location, etc., before they can reach a remote location 1. This has implications on the trajectories (including the time course) of motion. As a second example, in abstract space we could come up with an operation that allows an entity to be in two places at the same time. In CPS this is not possible because of the nature of physical space and matter. This has implications on unique identity, presence in a space, containment within it and access to it. In abstract space, the types of operations possible are defined by the agent conceiving the abstract space, while in CPS they depend on the nature of physical space itself. The types of actions that can be performed in CPS define the characteristic structure of physical space (Freksa, 1997) that is exploited by Euclidean geometry and vice versa (Euclid, 300 BC/1956). In this chapter, we discuss (1) how cognitive agents such as humans, other animals, or robots can use concrete CPS and AbsRS for solving spatial problems and (2) what are the relative merits of both approaches. We describe how the approaches can be combined. We look at the roles of spatial configurations and of cognitive agents in the process of spatial problem solving from a cognitive architecture perspective. In particular, we discuss (a) the role of the structures of space and time; (b) the role of conceptualizations 1 This holds for arbitrary granularities of neighborhoods.

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Acquiring, representing and processing spatial relations
Marinos Kavouras

Sixth International Symposium on Spatial Data …, 1994

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Representation Elements of Spatial Thinking
FR FIANTIKA

FR Fiantika, 2017

Abstract.This paper aims to add a reference in revealing spatial thinking. There several definitions of spatial thinking but it is not easy to defining it. We can start to discuss theconcept, its basic a forming representation. Initially, the five sense catch the natural phenomenon and forward it to memory for processing. Abstraction plays a role in processing information into a concept. There are two types of representation, namely internal representation and external representation. The internal representation is also known as mental representation; this representation is in the human mind. The external representation may include images, auditory and kinesthetic which can be used to describe, explain and communicate the structure, operation, thefunction of the object as well as relationships. There are two main elements, representations properties and object relationships. These elements play a role in forming a representation.

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Spatial reasoning as verbal reasoning
Leandra Bucher

We introduce an approach for how spatial reasoning can be conceived as verbal reasoning. We describe a theory of how humans construct a mental representation given onedimensional spatial relations. In this construction process objects are inserted in a dynamic structure called a "queue" which provides an implicit direction. The spatial interpretation of this direction can be chosen freely. This implies that choices in the process of constructing a mental representation influence the result of deductive spatial reasoning. To derive the precise rules for the construction process we employ the assumption that humans try to minimize their cognitive effort, and a cost measure is introduced to judge the efficiency of the construction process. From this we deduce how the queue should be constructed. We discuss empirical evidence for this approach as well as a computational implementation of the construction process.

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Basic Issues in Spatial Representation
Roberto Casati

2014

Spatial representation has in the last decade become a major focus of research in cognitive science and related areas. This includes philosophy as well as psychology, brain science, linguistics, those branches of computer science involved in the construction of machines capable of autonomous interaction with the environment. A fil rouge connects the efforts made by researchers from all of these areas under the rubric of spatial representation. Overall, however, there is also some ambiguity as to what “representation” really means in this regard. Two main options are:

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