A Computational Simulation of the Cognitive Process of Children Knowledge Acquisition and Memory Development

The cognitive mechanisms of knowledge representation, memory establishment, and learning are fundamental issues in understanding the brain. A basic approach to studying these mental processes is to observe and simulate how knowledge is memorized by little children. This paper presents a simulation tool for knowledge acquisition and memory development for young children of two to five years old. The cognitive mechanisms of memory, the mathematical model of concepts and knowledge, and the fundamental elements of internal knowledge representation are explored. The cognitive processes of children’s memory and knowledge development are described based on concept algebra and the object-attribute-relation (OAR) model. The design of the simulation tool for children’s knowledge acquisition and memory development is presented with the graphical representor of memory and the dynamic concept network of knowledge. Applications of the simulation tool are described by case studies on children’s knowledge acquisition about family members, relatives, and transportation. This work is a part of the development of cognitive computers that mimic human knowledge processing and autonomous learning. DOI: 10.4018/jcini.2011040102 18 International Journal of Cognitive Informatics and Natural Intelligence, 5(2), 17-36, April-June 2011 Copyright © 2011, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited. that the average human brain possesses approximately 1011 neurons and each neuron has an average of 103 synaptic connections (Pinel, 1997; Gabrieli, 1998; Sternberg, 1998; Matlin, 1998; Wang, 2009b; Wang & Wang, 2006). The observation on the generally unchanging number of neurons over the life span of an adult leads researchers to believe that information in the brain is stored as relationships between neurons via the creation of synaptic connections (Gabrieli, 1998; Wilson & Keil, 2001; Wang & Wang, 2006). Based on these factors, Wang and his colleagues find that the maximum capacity of human memory, i.e., the possible number of synaptic connections among neurons in the brain, is up to 108,432 bits based on a rigorous mathematical model (Wang et al., 2003). The current size of a desktop computer with dual terabyte drives holds close to 1012 bits of information. When we compare how miniscule the amount of information the desktop computer can hold and that of the human brain, we quickly realize how impressive the brain is. We must also consider the accessibility of that information, how quickly we can sort though the information to recall specific knowledge, and how humans are still much better at understanding patterns than a computer. When all of these observations are taken into account, we not only see that the idea of the computer being better than the brain as ridiculous, but it also demands that the brain be studied so that the current computers may be improved and the future generation of cognitive computers may be developed. All around the globe and throughout history, many people such as Plato, Socrates, and Chuang Tsui have wondered about the cognitive ability of the human mind (Tsui, 400BC; Wang, 2003). This desire for answers led to the development of fields of study such as philosophy, psychology, life science, and knowledge engineering. A new field of enquiry, cognitive informatics, was initiated by Wang and his colleagues in 2002, which establishes a trans-disciplinary study on cognitive science, computer science, information science, cybernetics, and life science (Wang, 2002, 2003, 2007b; Wang et al., 2009). Cognitive informatics investigates natural intelligence, i.e., how the brain acquires, processes, interprets, expresses, and utilizes information, its applications in cognitive computing, and the denotational mathematical means for both natural and computational intelligence (Wang, 2003). It is recognized that studies about human knowledge acquisition, memory development, and internal knowledge representation can be enriched by observations on mechanisms of young children learning and memory development. Findings in this approach may improve the understanding about human memory and knowledge representation. Based on this study, a computational simulation of the cognitive process of children knowledge acquisition and memory development is designed and implemented. The project reported in this paper uses the theories of the formal concept model of memory to model the growing understanding of a small child. A child of eighteen months should have a vocabulary of three to twenty words and be able to comprehend approximately fifty words. A child of twenty-four months should have a vocabulary of approximately two hundred words (Grizzle & Simms, 2005). This project helps to demonstrate the growth and complexity of the growing amount of information a child knows in order to empirically simulate the relational memory theories (Baddeley, 1990; Squire et al., 1993; Wang, 2009b; Hu et al., 2010) and the mathematical model of formal concepts as the basic unit of human knowledge (Wang, 2008a, 2009a, 2009b). This paper presents a simulation tool for knowledge acquisition and memory development particularly for young children between 2 to 5 years old. Related work on the physiological and logical models of memory is reviewed in Section 2. The cognitive processes of children memory and knowledge development are described based on concept algebra in Section 3, where the cognitive mechanisms of memory, the mathematical model of concepts and knowledge, as well as the fundamental elements of internal knowledge representation are explained. The design of International Journal of Cognitive Informatics and Natural Intelligence, 5(2), 17-36, April-June 2011 19 Copyright © 2011, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited. the tool for children knowledge acquisition and memory development simulation is presented in Section 4 with a graphical representor of memory and the dynamic concept network of knowledge. The implementation of the simulation tool is described in Section 5 where a case study of children knowledge acquisition about transportation is presented. 2. BACKGROUND AND RELATED WORK According to the cognitive models of memory (Baddeley, 1990; Pinel, 1997; Gabrieli, 1998; Sternberg, 1998; Matlin, 1998; Wang, 2009b; Wang & Wang, 2006), there are four types of memory known as the sensory buffer memory (SBM), short-term memory (STM), long-term memory (LTM), and sensory buffer memory (SBM). STM contains all the temporal information during mental operation and reasoning. LTM is where all the permanent information and knowledge are stored. This paper focuses on the study on the mechanisms and simulations of LTM, particularly that of children, at the neural, logical, and mathematical levels. The first level of memory modeling is at the neural layer that explains how knowledge is physiologically represented and memorized in the brain. The neural model is a web-like structure created by the neurons and their synaptic connections as shown in Figure 1, where the micro and macro views of memory are illustrated. It is noteworthy that, although it is well understood that the nervous play an important role in the establishment of knowledge in LTM, it is not explained in neuroscience and cognitive science that: a) Why do adults use fewer neurons (300 × 1011) to represent more knowledge in memory than that of children (at the peak of 1000 × 1011) in 8 month-old (Pinel, 1997; Sternberg, 1998)? and b) Why may increased knowledge acquisition in an adult’s brain result in no change of the number of neurons in it? The observation in neurophysiology that the number of neurons is kept stable during life-long growth of knowledge in adult brains is an indirect evidence for supporting the relational cognitive model of information representation in human memory. Based on the relational metaphor that knowledge is represented and memorized by the synaptic connections of neurons, the Object-Attribute-Relation (OAR) model for internal knowledge representation was developed by Wang in 2007. The OAR model (Wang, 2007c) creates a logic level of explanation of human memory where information is stored as a finite set of objects, a finite set of attributes, and the relational connection. The OAR model is illustrated in Figure 2 where O is a set of objects, A is a set of attributes, and r is a set of relations such as r(O, A), Figure 1. The physiological model of memory for knowledge representation 20 International Journal of Cognitive Informatics and Natural Intelligence, 5(2), 17-36, April-June 2011 Copyright © 2011, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited. r(O, O), and r(A, A). The OAR model provides an explanation for internal knowledge representation by creating new relations rather than requiring more neurons. It also provides a rigorous estimation of the maximum capacity of human memory (Wang et al., 2003) as discussed earlier in the introduction section. The highest level of human memory models beyond the physiological and logical levels is the mathematical level. This level can be described by the formal concept model developed by Wang in 2008. This new model adds concepts to the OAR model and dictates that a physiological and logical object can be modeled as a universal mathematical entity known as the formal concept (Wang, 2008a, 2010b). Detailed description of the concept model and concept algebra will be provided in Section 3.2. Related denotational mathematical studies may be referred to (Wang, 2007a, 2008a, 2008b). Although there are many computational simulations on processes of neural network aggregations, there is no model explaining how knowledge is stored within human memory, particularly LTM, in the brain. Currently, the closest project out there is WordNet (Miller et al., 1990; Miller, 1995), which is a linguistic network of words founded upon how they are connected because of their semantic relations in the English language. If we are able to better understand how information is stored and retrieved from the human brain, it will help us to create better ways to store and use the wealth of information available online in the web and the Internet. 3. DESCRIBING CHILDREN MEMORY DEVELOPMENT BY CONCEPT ALGEBRA Investigations into the cognitive models of information and knowledge representation in the brain is perceived to be one of the fundamental research areas that help to unveil the mechanisms of the brain (Wang, 2003, 2009a, 2010a; Wang et al., 2006, 2009, 2010; Tian et al., 2009, in press). The OAR model (Wang, 2007c) describes human memory, particularly LTM, by using the relational metaphor, rather than the traditional container metaphor that used to be adopted in psychology, computing, and information science. The OAR model shows that human memory and knowledge are represented by relations, i.e., connections of synapses between neurons, rather than by the Figure 2. OAR: The logical model of memory and internal knowledge representation International Journal of Cognitive Informatics and Natural Intelligence, 5(2), 17-36, April-June 2011 21 Copyright © 2011, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited. neurons themselves as the traditional container metaphor suggested. The OAR model reveals the biological and physiological foundations of human concept and knowledge formation. On the basis of OAR, the logical and mathematical models of concepts and knowledge may be rigorously derived in the following subsections. 3.1. The Cognitive Mechanisms of Memory The cognitive process of memorization encompasses encoding (knowledge representation), retention (store in LTM), retrieve (knowledge reallocation and LTM search), and decoding (knowledge reformation) as shown in Figure 3 (Wang, 2009b). The sign of a successful memory Figure 3. The cognitive process of memorization Figure 4. The hierarchical relations of concepts and their internal structures 22 International Journal of Cognitive Informatics and Natural Intelligence, 5(2), 17-36, April-June 2011 Copyright © 2011, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited. process in cognitive informatics is that the same information can be correctly recalled or retrieved. Therefore, memorization may need to be repeated for a number of cycles before it is completed. The memorization process is a closed-loop between STM and LTM, where it may be divided into the establishment and reconstruction phases. The establishment phase of memorization is a memory creation process that represents a certain information in the form of a sub-OAR in STM via encoding, and then creates relations with the entire OAR in LTM via retention. The reconstruction phase of memorization is a retrieval process that searches the entire OAR in LTM via content patterns or keywords, and then reconfigures the information in STM via decoding. The tremendous difference of memory magnitudes between human beings and computers demonstrates the efficiency of information representation, storage, and processing in human brains. Computers store data in a direct and unconsumed manner; while the brain stores information by relational neural clusters. The former can be accessed directly by explicit addresses and can be sorted; while the latter may only be retrieved by content-sensitive search and matching among neuron clusters where spatial connections and configurations themselves represent information. Figure 5. Concept graph of knowledge about relatives in memory International Journal of Cognitive Informatics and Natural Intelligence, 5(2), 17-36, April-June 2011 23 Copyright © 2011, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited. 3.2. The Mathematical Model of Concepts and Knowledge A concept is a cognitive unit to identify and/or model a real-world concrete entity and a perceivedworld abstract subject. A concept can be identified by its intension and extension (Smith & Medin, 1981; Murphy, 1993; Codin et al., 1995; Ganter & Wille, 1999; Medin & Shoben, 1988; Wang, 2008a). The intension of a concept is the attributes or properties that a concept connotes, while the extension of a concept is the members or instances that the concept denotes. Based on the formal structure of concepts and their relations, meanings of real-world concrete entities may be represented and semantics of abstract subjects may be embodied. A formal concept C is modeled as a 5-tuple (Wang, 2008a), i.e.: C O A R R R c i o  ( , , , , ) (1) where O is a nonempty set of objects of the concept, O = {o1, o2, ..., om}, A is a nonempty set of attributes, A = {a1, a2, ..., an}, R c ⊆ O × A is a set of internal relations, Ri ⊆ A′ × A is a set of input relations with external concepts. For convenience, R may be simply denoted asR C i = R× where K denotes existing knowledge, andR C o = ×R is a set of output relations. Figure 6. Concept graph developed based on Figure 5 24 International Journal of Cognitive Informatics and Natural Intelligence, 5(2), 17-36, April-June 2011 Copyright © 2011, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited. The most important properties of the formal concept model, as defined in Eq. 1, are the capture of a set of essential attributes as its intension; the classification of a set of instantiation objects as its extension; and the adaptive capability to autonomously interrelate itself to other concepts in existing knowledge. According to Eq. 1, the general schema of concepts can be modeled as shown in Figure 4. On the basis of the formal concept model and the OAR model, human knowledge is a hierarchical concept network interconnected by a set of concept associations R, i.e.: