Dịch đoạn văn sau sang tiếng việt trừ những từ ngữ chuyên ngành như trong kỹ thuật, lập trình, học máy,..., giữ nguyên định dạng và không đề cập thêm gì hết

They provide a framework for understanding how the mind works and how we interact with the world around us. By using computational models, we can gain a deeper understanding of these processes and contribute to the advancement of cognitive science.



### Exercises



#### Exercise 1

Consider a simple categorization task. Describe how a computational model could be used to predict the categorization behavior of a subject.



#### Exercise 2

Discuss the role of causality in cognitive processes. Provide examples of how causality can influence cognitive processes.



#### Exercise 3

Describe a computational model that could be used to study the relationship between causality and categorization. Discuss the strengths and limitations of this model.



#### Exercise 4

Consider a real-world scenario where categorization plays a crucial role. Discuss how a computational model could be used to study this scenario.



#### Exercise 5

Discuss the importance of computational models in the study of cognitive science. Provide examples of how these models have contributed to our understanding of cognitive processes.



## Chapter 7: Causal Induction



### Introduction



Causal induction, the process of inferring cause and effect relationships from observed events, is a fundamental aspect of human cognition. It allows us to make sense of the world around us, predict future events, and make informed decisions. This chapter delves into the computational aspects of causal induction, exploring how we can model and understand this complex cognitive process.



The chapter begins by introducing the concept of causal induction and its importance in cognitive science. It then moves on to discuss various computational models of causal induction, including probabilistic models, Bayesian networks, and causal graphical models. These models provide a mathematical framework for understanding how humans infer causal relationships and how these inferences can be computationally simulated.



We will also explore the role of learning in causal induction. How do we update our causal beliefs in light of new evidence? How do we balance the need for simplicity and accuracy in our causal models? These questions are addressed through the lens of machine learning and artificial intelligence, providing insights into the computational underpinnings of causal learning.



Finally, the chapter concludes with a discussion on the implications of computational causal induction for cognitive science and artificial intelligence. It explores how understanding causal induction can inform the design of intelligent systems and contribute to our understanding of human cognition.



Throughout this chapter, we will be using mathematical notation to describe these concepts. For instance, we might represent a causal relationship as `$y = f(x)$`, where `$y$` is the effect, `$x$` is the cause, and `$f$` is the function that describes the relationship. We will also use equations to describe the process of updating our beliefs in light of new evidence, such as `$$

\Delta w = ...

$$`, where `$\Delta w$` represents the change in our beliefs.



In summary, this chapter provides a comprehensive overview of computational causal induction, exploring its theoretical foundations, computational models, and implications for cognitive science and artificial intelligence. By the end of this chapter, you should have a solid understanding of how we can use computational methods to model and understand the complex process of causal induction.



### Section: 7.1 Mechanisms of causal induction



Causal induction is a complex cognitive process that involves several mechanisms. These mechanisms allow us to infer cause and effect relationships from observed events, and they play a crucial role in our ability to understand and interact with the world around us.



#### 7.1.1 Temporal Cues



One of the primary mechanisms of causal induction is the use of temporal cues. As mentioned in the previous chapter, humans are predisposed to understand cause and effect, making inferences bi-directionally. When observing an event, people assume that things preceding the event cause it, and things following the event are effects of it. This is often represented in computational models as `$y = f(x)$`, where `$y$` is the effect, `$x$` is the cause, and `$f$` is the function that describes the relationship.



#### 7.1.2 Spatial Relationships and Coincidence of Movement



Another mechanism of causal induction involves spatial relationships and the coincidence of movement. If objects move together (or one object seems to initiate the movement of another), causality is inferred from that relationship. This mechanism is often used in conjunction with temporal cues to infer cause and effect relationships.



#### 7.1.3 Learning and Updating Beliefs



Learning and updating beliefs in light of new evidence is another crucial mechanism of causal induction. This process can be represented mathematically as `$$

\Delta w = \alpha (y - \hat{y})

$$`, where `$\Delta w$` represents the change in our beliefs, `$\alpha$` is the learning rate, `$y$` is the actual outcome, and `$\hat{y}$` is the predicted outcome. This equation is derived from the Rescorla-Wagner model, a well-known model in classical conditioning.



#### 7.1.4 Conforming New Information to Old Information



Finally, humans have a tendency to conform new information to old information, a mechanism that Friedrich Nietzsche referred to as an inverted causal experience. This suggests that cause must be attributed to effect "a posteriori" to understand the causal connection between agent and act. This mechanism is particularly important in situations where the cause and effect are not immediately apparent, and it requires a deeper understanding of the underlying mechanisms of causality.



In the following sections, we will delve deeper into these mechanisms and explore how they can be modeled computationally. We will also discuss how these mechanisms interact with each other and how they contribute to our understanding of causal induction.



### Section: 7.2 Experimental studies in causal induction



Experimental studies in causal induction have provided valuable insights into the cognitive processes underlying our ability to infer cause and effect relationships. These studies often involve manipulating variables in controlled settings and observing the effects on participants' causal judgments.



#### 7.2.1 Cultural Differences in Causal Induction



As discussed in the previous context, cultural differences play a significant role in causal induction. For instance, Yan and Gaier's study on causal attributions of college success and failure revealed that American students were more likely to attribute academic achievement to ability, whereas Asian students did not show this pattern. This suggests that cultural background can influence how we perceive and interpret causal relationships.



Another study involving participants from the UK, China, and Hong Kong showed that members of individualist or collectivist cultures may make different attributions of the origins and motivations of movement on a small scale among animated objects. This further underscores the role of cultural context in shaping our causal inferences.



#### 7.2.2 Experimental Manipulation of Temporal and Spatial Cues



Experimental studies have also manipulated temporal and spatial cues to investigate their role in causal induction. For example, researchers have found that when the temporal order of events is manipulated, participants' causal judgments change accordingly. This supports the idea that we use temporal cues as a primary mechanism for inferring cause and effect.



Similarly, experiments involving the manipulation of spatial relationships and coincidence of movement have shown that these cues also play a crucial role in causal induction. When objects move together or one object seems to initiate the movement of another, participants infer a causal relationship.



#### 7.2.3 Learning and Updating Beliefs



Experimental studies have also investigated the process of learning and updating beliefs in causal induction. For instance, researchers have used the Rescorla-Wagner model to study how we update our beliefs in light of new evidence. These studies have shown that when the actual outcome differs from the predicted outcome, we adjust our beliefs accordingly, as represented by the equation `$$

\Delta w = \alpha (y - \hat{y})

$$`.



#### 7.2.4 Conforming New Information to Old Information



Finally, experimental studies have explored the tendency to conform new information to old information in causal induction. This mechanism, referred to as an inverted causal experience by Friedrich Nietzsche, suggests that we often interpret new information in a way that fits with our existing beliefs and understanding of the world. This can lead to confirmation bias, where we selectively interpret and remember information that confirms our preexisting beliefs.



In conclusion, experimental studies in causal induction have provided valuable insights into the cognitive processes underlying our ability to infer cause and effect relationships. These studies highlight the complexity of causal induction and the many factors that influence it, including cultural background, temporal and spatial cues, and our existing beliefs and understanding of the world.



### Section: 7.3 Bayesian models of causal induction



Bayesian models of causal induction provide a mathematical framework for understanding how people infer causal relationships from observed data. These models are based on Bayes' theorem, a fundamental principle in probability theory and statistics that describes how to update the probability of a hypothesis based on evidence.



#### 7.3.1 Bayes' Theorem and Causal Induction



Bayes' theorem can be formally stated as follows:



$$

P(H|E) = \frac{P(E|H) \cdot P(H)}{P(E)}

$$



where $P(H|E)$ is the posterior probability of hypothesis $H$ given evidence $E$, $P(E|H)$ is the likelihood of evidence $E$ given hypothesis $H$, $P(H)$ is the prior probability of hypothesis $H$, and $P(E)$ is the total probability of evidence $E$.



In the context of causal induction, the hypothesis $H$ typically represents a potential causal relationship, and the evidence $E$ represents observed data. The prior probability $P(H)$ represents our initial belief about the likelihood of the causal relationship before observing the data, and the posterior probability $P(H|E)$ represents our updated belief after observing the data.



#### 7.3.2 Bayesian Models of Causal Learning



Bayesian models of causal learning use Bayes' theorem to update beliefs about causal relationships based on observed data. These models assume that people have prior beliefs about the likelihood of different causal structures, and that they update these beliefs in a Bayesian manner when they observe new data.



For example, consider a situation where a person is trying to determine whether smoking causes lung cancer. The person might start with a prior belief that smoking does cause lung cancer, based on previous knowledge and experience. Then, the person might observe new data, such as the results of a scientific study showing a correlation between smoking and lung cancer. The person would then use Bayes' theorem to update their belief about the causal relationship based on this new evidence.



#### 7.3.3 Strengths and Limitations of Bayesian Models



Bayesian models of causal induction have several strengths. They provide a formal, mathematical framework for understanding causal induction, and they can explain a wide range of empirical findings in the literature. They also have a strong theoretical foundation, as they are based on well-established principles of probability theory and statistics.



However, Bayesian models also have limitations. They often require strong assumptions about the prior probabilities of different causal structures, and these assumptions can be difficult to justify in practice. Furthermore, Bayesian models can be computationally intensive, especially for complex causal structures with many variables.



Despite these limitations, Bayesian models have made significant contributions to our understanding of causal induction, and they continue to be a topic of active research in computational cognitive science.



### Conclusion



In this chapter, we have delved into the fascinating world of causal induction, a key component of computational cognitive science. We have explored how causal induction allows us to make sense of the world around us, by identifying cause and effect relationships and using these to predict future events. This process is fundamental to our ability to learn, adapt, and survive in an ever-changing environment.



We have also examined the various models and theories that have been proposed to explain causal induction, from the simple associative learning models to the more complex Bayesian models. Each of these models offers a unique perspective on how we form and update our causal beliefs, and they all contribute to our understanding of this complex cognitive process.



However, despite the progress that has been made in this field, there are still many unanswered questions. For instance, how do we integrate multiple sources of evidence when forming causal beliefs? How do we deal with uncertainty and ambiguity? And how does causal induction interact with other cognitive processes, such as memory and attention? These are just a few of the exciting challenges that lie ahead in the study of causal induction.



### Exercises



#### Exercise 1

Explain the difference between associative learning models and Bayesian models of causal induction. What are the strengths and weaknesses of each approach?



#### Exercise 2

Describe a real-world situation where causal induction might be used. How would the different models of causal induction explain the formation and updating of causal beliefs in this situation?



#### Exercise 3

Discuss the role of uncertainty in causal induction. How do the different models of causal induction deal with uncertainty?



#### Exercise 4

Explain how causal induction might interact with other cognitive processes, such as memory and attention. Provide examples to support your explanation.



#### Exercise 5

Propose a research question related to causal induction that has not yet been fully explored. How might you go about investigating this question?



## Chapter: Chapter 8: Theories



### Introduction



Theories form the backbone of any scientific discipline, and computational cognitive science is no exception. This chapter, "Theories," delves into the fundamental theories that underpin computational cognitive science, providing a comprehensive understanding of the conceptual frameworks that guide research and application in this field.



Theories in computational cognitive science are not just abstract ideas; they are mathematical and computational models that describe and predict cognitive processes. These theories provide a formalized representation of how cognitive processes work, allowing us to make precise predictions and develop effective interventions.



In this chapter, we will explore the key theories that have shaped computational cognitive science, from early theories that laid the groundwork for the field to contemporary theories that are pushing the boundaries of our understanding. We will examine the assumptions, strengths, and limitations of these theories, and discuss how they have been applied in practice.



We will also delve into the process of theory development in computational cognitive science. This includes the role of empirical data in shaping theories, the use of computational modeling to test and refine theories, and the ongoing evolution of theories in response to new findings and technological advances.



By the end of this chapter, you will have a solid understanding of the theoretical foundations of computational cognitive science. You will be equipped with the knowledge to critically evaluate theories, understand their implications for research and practice, and contribute to the ongoing development of new theories in the field.



Remember, theories are not static; they evolve as our understanding deepens and new data emerges. As such, this chapter is not just a snapshot of current theories in computational cognitive science, but a guide to the dynamic, evolving landscape of theoretical understanding in this exciting field.



### Section: 8.1 Role of theories in cognitive science



Theories play a pivotal role in cognitive science, serving as the conceptual frameworks that guide our understanding of cognitive processes. They provide a structured way to organize and interpret empirical findings, and offer a basis for generating hypotheses and predictions that can be tested through research. 



In the context of computational cognitive science, theories are often expressed as mathematical or computational models. These models provide a formalized representation of cognitive processes, allowing for precise predictions and the development of effective interventions. 



#### 8.1.1 Theories and Schemas



One of the key theories in cognitive science is the concept of schemas. As discussed in the previous chapter, schemas are pre-established methods of organizing and perceiving the world. They provide a basic scaffolding that allows humans to make assumptions about a social structure without remembering every detail individually. This preserves neural resources, allowing for representation of larger structures. 



In computational cognitive science, schemas can be modeled as networks, with nodes representing individuals or groups, and edges representing relationships or interactions. These network models can be used to simulate and predict social dynamics, and to understand the cognitive processes underlying social perception and behavior.



#### 8.1.2 Theories and Systematic Errors



Theories also play a crucial role in understanding systematic errors in cognitive processes. For instance, schemas, while efficient, can lead to systematic errors in network perception. These errors can be modeled and predicted using theories in computational cognitive science, providing valuable insights into the cognitive biases that shape our perception of social structures.



#### 8.1.3 Theories and Learning Networks



Theories in cognitive science also shed light on how individuals learn and adapt to new networks. Behavioral research suggests that individuals are better at learning networks that group members by positive relations (e.g. "liking") and divide groups by negative relations (e.g. "disliking"). This can be explained by theories that posit that our cognitive systems are optimized for processing information that is consistent with our existing schemas.



In conclusion, theories in cognitive science serve as the bedrock upon which our understanding of cognitive processes is built. They provide the conceptual frameworks that guide our research, shape our interpretations of empirical findings, and inform our development of interventions. As our understanding of cognitive processes deepens and new data emerges, these theories continue to evolve, driving the ongoing advancement of cognitive science.



### Section: 8.2 Theory construction and evaluation



The construction and evaluation of theories are integral parts of the scientific process in cognitive science. Theories are not merely abstract ideas; they are structured, testable explanations of observed phenomena. They are built on empirical evidence and are continually refined as new data becomes available. 



#### 8.2.1 Theory Construction



The construction of a theory in computational cognitive science often begins with the identification of a cognitive phenomenon that needs explanation. This could be a pattern of behavior, a cognitive bias, or a neural process. The next step is to formulate a hypothesis that explains this phenomenon. This hypothesis is then formalized into a mathematical or computational model.



For instance, the concept of schemas, as discussed in the previous section, was initially a theoretical construct used to explain how humans organize and perceive the world. This theory was then formalized into a network model, with nodes representing individuals or groups, and edges representing relationships or interactions.



The construction of a theory also involves making predictions based on the model. These predictions are then tested empirically. If the predictions are confirmed, the theory is supported. If not, the theory may need to be revised or discarded.



#### 8.2.2 Theory Evaluation



The evaluation of a theory in computational cognitive science involves assessing its explanatory power, its predictive accuracy, and its falsifiability.



- **Explanatory Power**: A good theory should be able to explain a wide range of phenomena. For instance, the schema theory can explain not only how we perceive social structures, but also how we make systematic errors in network perception.



- **Predictive Accuracy**: A theory's predictions should be accurate. The predictions made by a theory can be tested empirically. If the predictions are consistently confirmed, this supports the theory. If not, the theory may need to be revised.



- **Falsifiability**: A theory should be falsifiable. This means that it should be possible to conceive of an observation that would disprove the theory. If a theory is not falsifiable, it is not considered scientific.



In addition to these criteria, a good theory should also be parsimonious, meaning that it should explain the phenomena with the fewest possible assumptions and variables.



#### 8.2.3 Theory Revision



Theories are not static; they evolve over time as new data becomes available. If a theory's predictions are not confirmed, or if new phenomena are discovered that the theory cannot explain, the theory may need to be revised. This process of revision is an essential part of the scientific process, allowing theories to become more accurate and comprehensive over time.



In conclusion, the construction and evaluation of theories are crucial processes in computational cognitive science. They allow us to develop structured, testable explanations of cognitive phenomena, and to refine these explanations as new data becomes available.



### Section: 8.3 Neural network theories



Neural network theories are a cornerstone of computational cognitive science. These theories propose that cognitive processes can be understood as the emergent properties of interconnected networks of simple units. The units, often referred to as "neurons" or "nodes", are typically simple processors that receive input, perform a computation, and produce an output. The connections between these units, or "edges", represent the flow of information within the network.



#### 8.3a Connectionist models



Connectionist models, also known as parallel distributed processing (PDP) models, are a type of neural network theory that emphasizes the distributed nature of information processing in the brain. These models propose that cognitive processes emerge from the simultaneous processing of information across many interconnected units.



In a connectionist model, each unit typically computes a weighted sum of its inputs and applies a non-linear function to produce its output. The weights on the connections between units are adjusted through a learning process, often using a method known as backpropagation. This learning process allows the network to adapt its behavior based on the input it receives, making it capable of learning complex patterns and behaviors.



Connectionist models have been used to explain a wide range of cognitive phenomena, including perception, memory, language, and decision-making. For instance, the concept of schemas, as discussed in the previous section, can be modeled as a network of interconnected units, with each unit representing a concept or category, and the connections representing relationships or associations between these concepts.



However, connectionist models also face several criticisms. One criticism is that they often fail to capture the symbolic nature of human cognition. For instance, while connectionist models can learn to recognize patterns, they often struggle with tasks that require symbolic reasoning or the manipulation of abstract concepts. This has led to the development of hybrid models that combine connectionist and symbolic approaches, in an attempt to better capture the mechanisms of the human mind.



Another criticism is that connectionist models often require large amounts of data and computational resources to learn effectively. This contrasts with human cognition, which is often capable of learning from a small number of examples. This discrepancy has led some researchers to question the plausibility of connectionist models as cognitive models.



Despite these criticisms, connectionist models remain a powerful tool in computational cognitive science. They provide a flexible framework for modeling cognitive processes, and their ability to learn from data makes them a valuable tool for understanding the mechanisms of human cognition.



#### 8.3b Symbolic models



Symbolic models, also known as rule-based models, are another type of neural network theory that emphasizes the symbolic nature of human cognition. These models propose that cognitive processes can be understood as the manipulation of symbols according to a set of rules.



In a symbolic model, each unit, or "symbol", represents a concept or category, and the connections between these symbols represent relationships or associations between these concepts. The rules that govern the manipulation of these symbols can be thought of as the "program" that the cognitive system follows to process information.



Symbolic models have been used to explain a wide range of cognitive phenomena, including problem-solving, reasoning, and language comprehension. For instance, the concept of a "mental lexicon", as discussed in the previous section, can be modeled as a network of interconnected symbols, with each symbol representing a word or phrase, and the connections representing semantic or syntactic relationships between these words.



However, symbolic models also face several criticisms. One criticism is that they often fail to capture the distributed nature of information processing in the brain. For instance, while symbolic models can explain how we manipulate symbols to solve problems or understand language, they often struggle with tasks that require parallel processing of information, such as perception or motor control.



Another criticism is that symbolic models often rely on explicit rules, which may not accurately reflect the implicit, probabilistic nature of many cognitive processes. For instance, while we can use rules to describe the grammar of a language, these rules often fail to capture the probabilistic nature of language use, where the meaning of a word or phrase can depend on its context.



Despite these criticisms, symbolic models have made significant contributions to our understanding of cognitive processes. They provide a framework for understanding how we manipulate symbols to solve problems, reason, and understand language