#XLP #course # Initial Draft There are three things that must be handled in this document: The [[Why Cognitive Foundation]], [[What CF]], and [[How CF]]. ## Why a Track on Cognitive Foundation (CF) in ABC Curriculum? ![[Why Cognitive Foundation#Synposis Why CF]] ## What is in the CF Track? ![[What CF#Synopsis What is the CF Track]] ## How to Learn CF in the age of GAI? ![[How CF#Synopsis]] The immediate opportunity here is that Large Language Models and many late-breaking technologies are enabling a degree of automation that has never been possible before. This is the ultimate situation where paradigm shifts are taking place, and incommensurability is everywhere. Using an abstract model to define a Cognitive Foundation that allows for changes, embraces paradigm shifts as a dynamic knowledge management platform for decentralized agents and agencies will be an idea that could last for a long time to come. ## The Most Powerful Foundation is Invisible Another feature of this CF is that it must be relatively concise, and almost invisible, so that it can fit into application contexts without being intrusive, so that people can truly perceive it power. # Introduction We often perceive our daily experiences as a patchwork of isolated anecdotes, far from universal truths. Each event demands our individual attention, with limited external support or guidance. However, the key to a robust cognitive foundation lies in [[universality]], a concept with two pillars: [[soundness]] and [[completeness]]. This means everyone can confidently rely on the same foundation to think and act, leading to: - **Enhanced regularity in human actions:** Consistent understanding of the world would result in more predictable behavior, fostering cooperation and reducing conflict. - **Knowledge reuse:** By sharing a common cognitive framework, we can readily build upon each other's insights, accelerating societal progress. - **Systematically Reproducible behavior:** Shared patterns of reasoning and decision-making would allow us to learn from past successes and failures, paving the way for more reliable outcomes. In essence, a universal cognitive foundation wouldn't just unify our understanding of the world, it would empower us to act upon it collectively. Imagine a world where collaboration thrives, knowledge flows freely, and the future is shaped not by isolated individuals, but by a chorus of minds resonating on the same fundamental frequency. This is the promise of a truly universal cognitive foundation – a shared bedrock upon which we can build a brighter future, together. # The Cognitive Foundation in ABC Curriculum By bridging the gap between intuition and logic, the Cognitive Foundation (CF) enables human-centered decision-making with modern data-intensive technologies. It understands, like [[Design Thinking]], that good choices emerge via a dynamic, iterative process. CF copes with this dynamic by offering an iterative cycle of language-based knowledge refinement workflow in three-stages with the help of Large Language Models (LLMs): - **Generating customized languages:** LLMs may be used by decision-makers to generate "domain-specific languages" (DSLs), which are intermittent stages of responses that can be progressively adjusted for every decision situation. Each DSL may represent a different domain of behaviors, from spatial-temporal, to operational or even legal/financial. These customized vocabulary accurately represent the subtle distinctions of particular situations, enabling meticulous and incremental investigation. - **Unifying knowledge representation:** CF captures the [[Single-source of Truth]] with a common input format: "[[Logic Model]]". Logic Model is employed universally to help decision-makers craft their Domain-Specific Languages (DSLs). The syntax of [[Logic Model]] is human-readable, yet machine-processable, so it allows for effective human communication and automation. - **Validate representational efficiency:** As users fill content into "[[Logic Model]]", each instance of logic model will be iteratively refined, and associated with operational records regarding how they are fulfilled or failed. These contextualized data provide a reference to help determine the quality of Logic Models and therefore accumulate knowledge over time. Click here to edit [[Cognitive Foundation Workflow.excalidraw]] ![[Cognitive Foundation Workflow.excalidraw.svg|800px]] # Logic Model as the unit of cognitive record While CF provides the "[[Logic Model]]" as an interactive form for direct human input, context-sensitive information may be captured through many data collection and conversion pipelines. For example, once any type of multi-modal input is fed into an LLM-enabled system, as demonstrated by [[Google]]'s [[Gemini]] in December 2023, LLMs can automatically detect contextualized information and generate relevant questions and answers for those who prefer a hands-off approach, by letting cameras see and microphones listen to the contextualized data to make implicit guesses. In a world with LLMs, machines can become cognizant of many types of information that were not conceived to be possible. ![[LogicModel_SampleForm.png]] The working concepts of how to make decisions must still be articulated and based on the cognitive foundation of stakeholders, regardless of how people employ Generative AI technology to generate their solutions. The [[ABC curriculum]]'s CF track enables users to understand the "why" underlying the dynamics and features of current decision-making processes. It also gives them options for different decision-making processes and assists them in navigating even the most difficult problems with logical rigor. # Foundations in Cognitive Processes The Cognitive Foundation series of learning activities will present the working principles behind decision-making in general. It unites theories and methods originally developed in cognitive sciences, theoretical computer science, and linguistic theories, especially the [[Speech Act Theory]]. To establish a strong "Cognitive Foundation" for rational decision-making in the age of generative artificial intelligence, three essential perceptual concepts are introduced: Firstly, the cognizance of the external world can be modeled in terms of evolving [[type|types]] of languages; secondly, the chosen vocabulary (a.k.a. [[Namespace]]) in the working language dictates cognitive performance; and thirdly, it is possible to interactively manipulate these languages in terms using computational instruments. These three concepts defines the [[Cognitive Foundation]] of how ABCers works with Generative AI to cope with real-world affairs: ## Language Engineering with LLM support Envision encountering a perplexing situation that is distinct in its nature, requiring a specialized set of words and structure specifically designed for it. The [[Language-oriented Modeling]] ([[LoM]]) technique tackles this difficulty by using their linguistic expertise to create Domain-Specific Languages (DSLs) that are specifically designed for each situation. Abandon inflexible, predetermined languages. LoM thoroughly examines the context of your query, carefully selecting pertinent "tokens" - which might be words, phrases, or even data kinds - from the extensive collection in pre-trained, foundational Large Language Models. Your DSL is created by dynamically curating this collection, making it a customized language tailored to your unique situation. Consider the process as constructing a Lego castle, where each brick represents not just a word, but every conceivable kind inside a language, including numerical, temporal, or even musical elements. Each distinct data structure and every idiosyncrasy of a programming language might serve as a possible fundamental component. Now, the inquiry becomes really dynamic. LoM utilizes this flexible Domain-Specific Language (DSL) to explore the problem's state space, which is a complex network of possible solutions. However, as contrast to a static labyrinth, this expedition is adaptable. The LoM has the capability to dynamically adjust the size of the DSL, either by expanding or contracting it. Encountering an impasse? The introduction of new tokens and types may expand the language environment. Making progress towards a solution? The Language of Modeling (LoM) has the ability to enhance and improve the Domain-Specific Language (DSL), by focusing specifically on the most favorable and advantageous paths. The efficacy of this dynamic framework relies on a fundamental verity: it accurately reflects human cognition. We enhance our cognitive processes by assimilating new data and eliminating extraneous elements. Similarly, LoM dynamically adjust their Domain-Specific Languages (DSLs) to imitate our innate problem-solving methodology. #### The Theoretical Foundation of Types Type Theory perceives language as a complex structure consisting of interwoven threads of interdependent relationships, rather than a random collection of words. Every word possesses not only a symbolic meaning but also a complex network of structural relationships that contribute to a deeper understanding and existing knowledge. By comprehending these linguistic interconnections and selectively utilizing words from the structure of Type Theory, we can construct sentences that efficiently convey substantial information. Type Theory revolutionizes the way we think about language by treating all linguistic elements, such as words and concepts, as categories of types. This category is not just simple; it represents a significant advancement in our means of communication. Words cease to be mere labels and instead acquire a vital role as fundamental components, each carrying significance through its vast interconnectedness within the system. The training activities in CF guide users to use LLM-powered engines with Type Theory in mind. When users employ LLM tools to effortlessly generate grammatically accurate expressions, users will start to read the generated answers by dissecting the words and phrases into types of tokens. Each token type should be automatically captured in a token dictionary in [[PKC]], so that type-based patterns will be captured systematically, and ready for future reuse. This is also known as the practice of [[Namespace Management]], to be explained later. This shift not only improves communication, but also radically changes intelligence. Language-oriented Modeling surpasses basic processing and encompasses the complex operations of the human mind by incorporating Type Theory into the utilization of LLMs. They skillfully navigate the intricate network of information, producing not only surface replies, but profound insights. They engage in collaborative efforts to comprehend and mutually create significance. The inherent effectiveness of Type Theory lies not only in its ability to condense information, but also in its capacity to enhance it. The students in the ABC Curriculum actively create their own language models by actively participating in LLMs, posing inquiries, employing logical thinking, and working together with their peers. This approach enables individuals to actively participate in the generation of knowledge within a social framework, utilizing a diverse array of content knowledge that encompasses the majority of existing publications. Therefore, understanding Type Theory in the context of language modeling improves the capacity to generate surface-level responses by constructing deep questions that include strategic probing effects for future Q&A sessions. It is recommended that CF embraces Type Theory as the underlying underpinning of cognition. ## Namespace Management: Size Matters (When talking about **Size**, remember to talk about [[Counting]] and [[Accounting]] ) The introduction of LLMs into the realm of decision-making processes throws down a gauntlet of exciting possibilities, but also unveils some intricate challenges. One key hurdle lies in the realm of **[[Namespace Management]]**, or the organization and control of the vast vocabulary employed by these models. Let's delve into the specifics: **Challenges:** - **Fragmentation and Silos:** LLMs often learn from diverse datasets, leading to an accumulation of overlapping or conflicting token definitions across various "namespace silos." This can cause confusion and ambiguity when interpreting model outputs or leveraging information for decision-making. - **Evolving Languages:** LLMs learn and adapt dynamically, incorporating new tokens and potentially altering the meanings of existing ones. This dynamism makes it challenging to maintain long-term consistency and coherence within the knowledge base. - **Transparency and Explanation:** Understanding how LLMs arrive at decisions using complex language models can be opaque. This lack of transparency makes it difficult to assess the reliability and trustworthiness of their outputs, especially in critical decision-making scenarios. **Incorporating Existing LLMs:** Integrating existing LLMs into a knowledge management system requires careful consideration of namespace compatibility. Approaches like mapping, translation, and model distillation can help bridge the gap between different vocabulary sets and ensure consistency. **Dictionaries of Relevant Tokens:** Curating domain-specific dictionaries of relevant tokens can offer a starting point for managing namespaces. These dictionaries can be used to guide LLM training, constrain outputs, and improve the interpretability of results. **Prompt Templates and Strategies:** Effectively framing queries through well-designed prompt templates plays a crucial role in controlling the direction of LLM exploration within the namespace. Strategies like prompt engineering and active learning can be employed to refine prompts and navigate the language model toward desired outcomes. **Namespace Management and Cognitive Foundation:** Central to the "Cognitive Foundation" concept is the idea of a unified, interpretable knowledge base. Effective namespace management forms the bedrock of this foundation, ensuring clear distinctions, consistent meanings, and reliable information flow for robust decision-making. **Intention Alignment and Namespace Management:** Modern LLM training and alignment practices increasingly focus on aligning the model's intent with user's goals. Namespace management plays a pivotal role in this endeavor, as it ensures the model operates within a shared understanding of concepts and avoids misinterpretations based on ambiguous or conflicting vocabulary. **Teaching Namespace Management:** Equipping students with the skills to manage namespaces effectively is crucial for future-proofing their knowledge management and decision-making skills. Teaching methods can include: - **Interactive simulations:** immersing students in simulated LLM environments where they can experiment with different namespace configurations and observe their impact on model outputs. - **Case-study analysis:** exploring real-world examples of successful and unsuccessful namespace management in LLM-driven systems, highlighting best practices and potential pitfalls. - **Project-based learning:** assigning students projects where they design and implement namespace management strategies for specific LLM applications. By fostering a critical understanding of namespace management and equipping students with the necessary skills, we can empower them to harness the full potential of LLMs for reliable knowledge management and informed decision-making in the age of information abundance. ## Power of the Tree: Convergence The ability of Large Language Models (LLMs) to seemingly reason about anything across any domain stems from fascinating cornerstones of linguistics and computer science: **[[Universal Grammar]] (UG)** and **[[Lambda Calculus]] (λ-calculus)**. Let's explore their expressiveness and connection to dynamic language generation and namespace management in the LLM era: **Universal Grammar:** - **Conceptual Framework:** UG posits a set of innate principles and constraints underlying all human languages. Imagine it as a universal scaffolding upon which diverse languages build their specific structures. - **Expressiveness:** UG's power lies in its ability to capture fundamental concepts like subject-verb agreement, recursion, and negation, ensuring basic communicative functionality across languages. - **Relevance to LLMs:** LLMs learn from vast amounts of text data, unconsciously absorbing these universal principles. This enables them to generate sentences that follow grammatical rules, even in novel contexts and domains. **Lambda Calculus:** - **Formal System:** λ-calculus is a mathematical framework for manipulating functions and expressions. Think of it as a powerful Lego set for building and combining building blocks of logic. - **Expressiveness:** λ-calculus boasts immense expressiveness, allowing the representation of any computable function. It's like a universal language for describing any conceivable process or calculation. - **Relevance to LLMs:** LLMs often employ techniques inspired by λ-calculus to internally represent and manipulate the relationships between concepts and words. This enables them to reason about complex relationships and generate text that reflects logical connections. ### Representing Varieties in a Tree of Types A fundamental principle governing a data structure like a tree is that it possesses only a single root. This structural necessity facilitates the classification of a diverse range of behavioral patterns in a convergent manner. All databases utilize a shared root to ensure that the search for specific data content does not encounter any loops during traversal. Nevertheless, the presence of numerous layers of branching/directory structures in a tree might pose challenges when attempting to locate data within a deep tree. Data is often concealed within intricate hierarchical structures, making it arduous to locate the desired information. #### Classifying Logic Models in a Tree of Types A type in type-based programming languages is a fundamental categorization that specifies the characteristics of data values and the permissible operations that can be executed on them. It functions as a schematic or model that guarantees uniformity and security within the code. This concept can also be employed to oversee an individual's collection of personal data. When a group of [[Logic Models]] defines a set of qualities that represent a particular kind, these Logic Models can assist in organizing data content using a classification scheme that aligns with the cognitive abilities of its users. Moreover, Logic Models can be organized in a Tree of Types. This allows a large collection of Logic Models can be organized in some hierarchical structure, and this structure itself can be manipulated using some automated algorithms to refactor. Moreover, the Logic Models themselves can be dynamically associated with many instances of data content, therefore, creating an additional layer of information compression. Based on this data dependency, one may iteratively refine the hierarchical structures of Logic Models, which indirectly changes the navigational paths to identify data elements associated with Logic Models. The actual content and the directory structure of how data is stored can be separately managed by the concrete choice of data storage techniques/methods. Therefore, we will have an additional abstract reference to improve data identification and reorganization without incurring additional storage costs. This method of data content manage is compatible with the idea of [[Content Addressable Scheme]], like [[Git]] and [[IPFS]], where large amounts of data can be referenced without making unnecessary redundant copies. ## A type-based data processing funnel A type-based data filtering funnel optimizes data processing by streamlining the processes involved. #### Precise Categorization and Structuring: Types serve as exact designations for data components, specifying their attributes and connections. Logic Models categorize types into a hierarchical structure known as a Tree of Types, which accurately represents cognitive comprehension. The use of this organized categorization allows for effective sorting and exploration of extensive datasets. #### Focused Data Extraction: Filtering funnels enable the accurate selection of particular data categories or combinations thereof. Only pertinent information is allowed to pass, minimizing computational burden and directing attention towards the crucial components. #### Process of automating the improvement and enhancement of a system using refinement and optimization techniques. [[Logic Models]] can be progressively improved through the analysis of data relationships and usage patterns. This process of dynamic optimization guarantees that the funnel structure remains in line with changing requirements and continues to operate with maximum efficiency. #### Utilizing abstraction to enhance agility and efficiency: Flexibility is enhanced by separating the data content from its physical storage structure using content-addressable methods. Information may be rearranged and accessed without the need to physically move it, which reduces unnecessary costs and enhances efficiency. #### Efficient Processing Operations: Precise type definitions and a hierarchical organization provide focused operations on certain subsets of data. Processing methods can be optimized to operate efficiently with clearly specified data types, minimizing errors and improving efficiency. #### Enhanced storage efficiency through the reduction of redundancy. Content-addressable methods eradicate superfluous data duplications, thereby preserving storage capacity and streamlining administration. Data elements are designated in a distinct manner based on their content, which guarantees both consistency and integrity. #### Improved cooperation and dissemination of information: Shared type systems and logic models facilitate mutual comprehension and communication among teams and systems. This enables the cooperation, transmission of knowledge, and merging of many data sources. Essentially, a type-based data filtering funnel serves as a potent instrument for efficiently and effectively organizing, managing, and processing large quantities of data. It introduces the precision and organization of type systems to the realm of data, enabling a higher degree of flexibility and efficiency in data-driven procedures. # The Speakable and Unspeakable in Logic Model Like John Stewart Bell's famous work "Speakable and Unspeakable in Quantum Mechanics," there are certain events that are difficult to depict accurately. Therefore, it is crucial to determine these events by making several measurements and represent them using probabilistic metrics. The problem continues to exist within the realm of knowledge management. The exact positioning of data may vary as users make modifications to the referential paths that specify the data's location. To ensure data consistency, regardless of the various available paths to access the data, the retrieved data content must always be distinct at all times. An effective approach to accomplish this is by utilizing a data replication infrastructure such as blockchain. Irrespective of the specific technologies used for storing and retrieving data, it is important to establish a consistent set of requirements to define data consistency. This ensures that we have a reliable framework to determine the accuracy of the data. We hereby establish a data storage and retrieval system that efficiently delivers accurate information, provided that it supplies the current data content [[Timeliness|promptly]] accordance with the requirements of the application, ensures [[Accountability|responsibility]] for data modifications, and ensures that changes made to the data content are easily [[Observability|observable]], regardless of the particular technology employed. The timeliness, accountability, and observability conditions can be modeled in a [[Logic Model]] as shown below: ![[Logic Model for Data Correctness]] # The Role of CF in ABC curriculum The significance of cognitive foundation in the ABC curriculum: Constructing a ## Learning Engine that Focuses on Data Envision an educational program where data serves not only as a source of energy, but also as the guiding plan: this encapsulates the fundamental concept of Cognitive Foundation (CF) inside the ABC framework. This course is not only theoretical; it serves as the fundamental basis for structuring and navigating the extensive body of information inside ABC. The following outlines how CF influences the ABC learning experience: **Data-Oriented Navigation:** CF abandons conventional content compartments and embraces a methodical, data-focused strategy. Consider it as a highly structured library where information is categorized into certain "[[Namespace|namespaces]]," and educational paths are ordered in a logical chronological order. This framework, derived from Computational Thinking, enhances the efficiency and focus of investigation. **Visualizing Abstract topics:** Have you ever desired the ability to visually see complex mathematical topics such as algebraic topology? The ambitious visual language effort by CF brings that ambition closer. This language is based on [[Cubical Type Theory]] and [[Lens-like automata]] ([[Lenia]]). Its purpose is to convert intricate concepts from [[Linear Algebra]], cellular automata, and other fields into easily understandable visual representations. Visualize the process of analyzing intricate topological ideas directly in front of you, facilitated by the potency of Sheaf theory and "stalks". **Enabling Data Observability:** Acquiring knowledge from data necessitates its availability and clarity. CF relinquishes the use of unclear educational measurements and adopts the concepts of version control systems like as Docker and Git. Each piece of material is assigned a date and version history, enabling learners to monitor its development and comprehend the rationale for its present state. **Examining hypothetical scenarios using counterfactuals:** Counterfactual thinking highlights the influence of alternative possibilities. Through the process of simulating various outcomes, learners have the opportunity to enhance their ability to make effective decisions, understand cause-and-effect connections, and unleash their creative problem-solving talents. It resembles having an inherent cognitive arena to experiment with ideas and gain knowledge from errors, devoid of repercussions in the physical realm. The CF courses have an interdisciplinary approach, including modules in several fields such as logic, music, visual arts, athletics, psychology, and others. The unifying language of data and counterfactuals facilitates the integration of many domains, enabling learners to establish linkages and discover unforeseen synergies across apparently unrelated subjects. # Design Thinking and CF [[Design Thinking]] and Cognitive Foundation (CF) in the ABC curriculum are more than just partners; they're two sides of the same coin, fueling each other to create a powerful learning engine. Here's how they intertwine: **Empathy Fuels Data-Driven Understanding:** Design Thinking starts with empathy, understanding user needs and perspectives. CF takes this a step further by translating needs into **data-driven insights**. Students learn to analyze user behavior, gather feedback, and interpret data to inform content and learning pathways. This constant feedback loop ensures the curriculum remains relevant and responsive to learners' needs. **Iterative Learning Mirrors Design Prototyping:** Just like Design Thinking uses prototypes to test and refine solutions, CF embraces **iterative learning**. Students actively experiment with content, explore different learning avenues, and analyze their progress. This continuous feedback loop allows them to adapt their learning strategies and personalize their journeys. **Visual Thinking Enhances Mental Frameworks:** Design Thinking relies heavily on visual tools and sketches to communicate ideas and solutions. CF echoes this by developing a **visual language** based on Cubical Type Theory and Lenia-like automata. This language helps students visualize complex concepts, build mental frameworks for understanding, and connect seemingly disparate pieces of information. **Problem-Solving Meets Counterfactuals:** Both Design Thinking and CF emphasize **problem-solving skills**. In CF, this goes a step further with the focus on **counterfactual reasoning**. Students learn to explore "what if" scenarios, considering alternative solutions and analyzing their potential outcomes. This hones their critical thinking skills and prepares them for real-world challenges with multiple variables. **Collaboration Drives Collective Learning:** Design Thinking thrives on collaboration, and CF fosters the same spirit. The curriculum encourages **self-governing networked communities** where students share experiences, learn from each other, and refine content collaboratively. This collective learning environment amplifies the effectiveness of both frameworks. Ultimately, Design Thinking and CF work together to build a dynamic learning engine within the ABC curriculum. Design Thinking provides the human-centered focus and iterative methodology, while CF lays the data-driven foundation and visual language tools. Together, they equip learners with the cognitive skills and mindset to navigate the ever-evolving knowledge landscape and become problem-solvers, not just knowledge consumers. # Identify information sources actively [[Open Source Intelligence]] ([[OSINT]]) is the practice of collecting information from publicly available sources to be used in an intelligence context. In relation to the Cognitive Foundation (CF) and group learning, OSINT can play a significant role in several ways: 1. **Data-Centric Learning**: CF emphasizes the importance of data as the foundation for cognitive processes. OSINT aligns with this by providing a method for gathering real-world data that can be analyzed and used to inform decisions and learning. In a group learning context, students can practice data collection, verification, and analysis using OSINT techniques, which enhances their understanding of how data impacts cognition and decision-making. 2. **Critical Thinking and Analysis**: OSINT requires critical thinking to assess the credibility of sources and the reliability of information. This is in line with the CF's focus on teaching learners to make judgments based on observable and reproducible data. Group learning can benefit from OSINT activities that challenge students to evaluate information critically, a skill that is transferable to many other domains. 3. **Collaborative Learning**: CF encourages self-governing networked communities where students share experiences and learn from each other. OSINT tasks can be collaborative, with group members dividing the work of gathering and analyzing information from different sources. This collective effort can lead to a richer understanding of the subject matter and foster a sense of community. 4. **Counterfactual Reasoning**: CF uses counterfactual reasoning to help learners understand cause-and-effect relationships and explore different outcomes. In OSINT, similar reasoning can be applied when considering the implications of intelligence findings or when planning how to gather intelligence based on different scenarios. Group learning can involve exercises where students use counterfactuals to predict the outcomes of intelligence operations or to understand historical events better. 5. **Real-World Application**: OSINT provides a way for learners to engage with real-world issues and data, making the learning experience more relevant and engaging. By incorporating OSINT into the CF curriculum, learners can apply theoretical knowledge to practical situations, enhancing their problem-solving skills and preparing them for real-world challenges. 6. **Interdisciplinary Approach**: CF courses have an interdisciplinary approach, and OSINT can be a unifying practice that draws on various fields such as logic, psychology, and technology. In group learning, students from different backgrounds can contribute their unique perspectives to the intelligence-gathering process, leading to a more comprehensive understanding of the data. 7. **Observable Data with Time-stamps**: CF emphasizes the importance of observable data with time-stamps for tracking the evolution of information. OSINT activities can teach learners how to document their findings with time-stamps, creating a verifiable trail of data that can be analyzed over time. In summary, OSINT relates to the Cognitive Foundation by providing practical, real-world data that can be used to enhance cognitive processes, critical thinking, and collaborative learning. It supports the CF's data-centric approach and can be integrated into group learning to foster a dynamic and engaging educational experience. # Influence of Linguistic Knowledge in CF The knowledge about [[Syntax]] and [[Rhetoric]] within the context of the Cognitive Foundation (CF) plays a significant role in structuring and revealing hidden relations and structural patterns. Here's how: 1. **Syntax in Cognitive Foundation:** - **Namespace Management:** Syntax, the set of rules for constructing sentences in a language, is analogous to the systematic approach CF takes in establishing namespaces. By understanding the syntax of data organization, learners can structure information in a way that reveals patterns and relationships that might not be immediately apparent. - **Data-Centric Methodology:** Just as syntax provides a structure for language, CF uses a data-centric methodology to structure cognitive processes. This involves organizing data in a logical and hierarchical manner, similar to how sentences are structured to convey clear and coherent meaning. - **Visual Language Development:** The development of a visual language based on Cubical Type Theory and Lenia-like automata within CF is akin to creating a new syntax for representing complex concepts. This visual syntax helps in making abstract ideas more tangible and discernible, thus revealing hidden structures. 2. **Rhetoric in Cognitive Foundation:** - **Persuasive Communication of Data:** Rhetoric, the art of effective or persuasive speaking or writing, is reflected in CF's emphasis on translating data into compelling narratives. By applying rhetorical techniques, learners can present data in a way that highlights underlying patterns and relationships, making them more evident to the audience. - **Counterfactual Reasoning:** Rhetoric often involves arguing for a particular viewpoint by presenting alternative scenarios or possibilities. Similarly, CF's use of counterfactual reasoning allows learners to explore different outcomes and understand the structural patterns that lead to various scenarios. - **Interdisciplinary Integration:** Rhetoric is about connecting with diverse audiences, which requires an understanding of different fields and contexts. CF's interdisciplinary approach, which includes logic, music, visual arts, and more, relies on rhetorical skills to integrate and relate concepts across these domains, revealing deeper connections. 3. **Synergy of Syntax and Rhetoric in CF:** - **Enhanced Cognitive Capacity:** The synergy of syntax and rhetoric in CF enhances cognitive capacity by enabling learners to structure their thoughts (syntax) and communicate them effectively (rhetoric). This dual focus helps in uncovering and understanding hidden relations and structural patterns in data. - **Iterative Learning and Prototyping:** CF's iterative learning process mirrors the drafting and revising stages in writing, where syntax and rhetoric are refined to clarify and strengthen the message. This iterative process in CF helps learners to refine their understanding of data and its patterns. - **Collaborative Learning:** In collaborative learning environments, the use of syntax and rhetoric is crucial for effective communication and knowledge sharing. By structuring information coherently (syntax) and presenting it persuasively (rhetoric), learners can work together to uncover and understand complex patterns. In conclusion, the knowledge of syntax and rhetoric is integral to the Cognitive Foundation's approach to education. It influences the structuring of data and the articulation of insights, which in turn facilitates the revelation of hidden relations and structural patterns. By applying principles of syntax and rhetoric, CF equips learners with the tools to navigate and make sense of complex information landscapes. # Logic Model applied to Case Studies Try to use Logic Models to represent, record, and compare the outcomes of their problem is the observable way to enable people to become effective decision-makers with a strong Cognitive Foundation: **1. Experiment with Dynamic Language Construction:** - **Interactive LLM exploration:** Let students engage with LLMs, asking diverse questions and observing how the generated language adapts. This hands-on experience demystifies LLM flexibility and showcases its potential for crafting unique solutions. - **"Logic Model" workshops:** Train students in constructing and manipulating "Logic Models," a common foundational language that represents knowledge and relationships. This empowers them to think like LLMs, organizing information and building adaptable solutions. - **Real-world application projects:** Challenge students to tackle complex, multi-faceted real-world problems using LLMs guided by "Logic Models." This bridges the gap between theory and practice, demonstrating the value of dynamic language construction in real-world decision-making. **2. Know the Theoretical Foundation:** - **Universal Grammar and Lambda Calculus:** Introduce the core principles of UG and λ-calculus, highlighting their role in LLM reasoning and language generation. This equips students with a deeper understanding of how LLMs process information and make decisions. - **Tree-based Dependency Structures:** Train students in analyzing sentences through dependency structures, identifying relationships between words and extracting meaning. This skill translates to better comprehension of information and improved critical thinking for informed decision-making. - **Interdisciplinary Approach:** Encourage students to combine knowledge from linguistics, computer science, cognitive science, and other relevant fields. This broadens their perspective and enables them to approach problems from multiple angles, leading to more holistic and informed decisions. **3. Develop Continuous Learning:** - **Encourage experimentation and exploration:** Foster a culture of curiosity and openness to new information. Guide students to actively engage with emerging LLM advancements and explore their potential applications in various contexts. - **Provide learning resources and support:** Offer access to relevant materials, workshops, and mentorship programs to keep students updated on the evolving landscape of LLMs and Cognitive Foundation concepts. - **Promote collaboration and knowledge sharing:** Create opportunities for students to connect with peers, discuss challenges, and share their learnings. This collaborative environment fosters continuous learning and strengthens the overall understanding of Cognitive Foundation principles. By implementing these strategies, you can empower individuals to become effective decision-makers with a strong Cognitive Foundation. They will be equipped to navigate the ever-changing information landscape, think critically, generate creative solutions, and confidently make informed choices in a world powered by LLMs. Remember, the journey to a strong Cognitive Foundation is continuous. By promoting a culture of learning, exploration, and collaboration, you can cultivate a generation of decision-makers who can thrive in the dynamic world of information and artificial intelligence. # Content Knowledge and Practical Concerns Having [[Large Language Model]] in mind, to best organize content in ways that help learners best explore information represented in a universal curriculum, we focus on three core subjects: Category Theory, Quantum Mechanics, and Music. These disciplines exemplify the application of additive and composable structures that can encapsulate complex information systems. The "ABC Curriculum" is designed to instill a cognitive habit in learners, enabling them to see and utilize these universally relevant structures. Alongside these core subjects, we position Large Language Models and Note-taking with tools like ([[PKC]]) and [[Git]] as personalized assets and habits that enrich the curriculum. 1. **Category Theory**: This field abstracts the concept of information carriers into "[[morphism|morphisms]]," sophisticated terms for "functions." It offers a high-level understanding of how different mathematical structures relate and transform, emphasizing a universal mapping and transformation principle that is applicable across various domains. Learning category theory with a Lens of pragmatism, knowing [[Linear Algebra]] well (see [[Pixel Array Method]] and [[@SevenSketchesCompositionality2018|Seven Sketches in Compositionality: An Invitation to Applied Category Theory]]) can help you better see the overall picture. 2. **Quantum Mechanics**: Utilizing linear algebra or Hilbert Spaces, Quantum Mechanics formats its generalized information carriers in a way that allows for the depiction of quantum states and their evolution. This representation method highlights the manipulation of information at the quantum level, demonstrating the power of vector spaces and linear operators. Why we must introduce mechanics in CF can be partially explained [[@FromStoryOfYourLifeToControlTheory|From Story of Your Life to Control Theory (in Chinese with English Translation)]]. Otherwise, one can refer to [[Steven Brunton]]'s [[@PhysicsInformedMachine2024|Physics Informed Machine Learning: High Level Overview of AI and ML in Science and Engineering]]. 3. **Music**: Music itself can be understood as a form of [[multispectral data representation]]. Rather than wavelengths, it uses time, duration, and intensity to encode complex information. This demonstrates the principles of temporal additive structures for organizing time-series data. **Personalized Asset - Large Language Models**: As a personalized asset, Large Language Models, such as the GPT series, conceptualize information in the form of hash values or "tokens," which are represented as "embeddings" or vectors. This illustrates the use of vector spaces for capturing and processing linguistic data, emphasizing semantic relationships and offering a customizable tool for exploring linguistic and semantic structures. **Personal Habit - Note-taking with PKC and Git**: The practice of note-taking, especially using digital tools like [[PKC]] (initially we will employ [[Obsidian]]) and version control systems like Git, is recommended as a personal habit within the ABC Curriculum. This habit supports the digital documentation and organization of knowledge in an additive and composable manner. It mirrors the curriculum's core principles by enabling the incremental construction and linkage of information, fostering a personal knowledge base that evolves over time. The "ABC Curriculum" thus combines these three main subjects with the personalized asset of Large Language Models and the personal habit of digital note-taking to offer a comprehensive educational framework. This framework aims to cultivate an appreciation for universal structures that are simple yet capable of accommodating vast complexities, encouraging learners to adapt and apply these principles across a wide range of contexts. # Conclusion: Foundation in Holy-Trinity CF is not a single course, but rather a collection of courses and learning activities that use a pedagogical method to investigate truth using data. This curriculum equips learners with the essential aptitudes and mindset required to thrive in a data-driven society. Within this context, the abundance of information is vast, subject to frequent updates, and may be obtained via the use of logical reasoning, visualization, and exploration. # The notion of spacetime in Cognitive Foundation In [[ABC curriculum]], due to its data-centric content organization approach, cognitive foundation is defined in terms of [[Namespace Management]] for content [[space]], and [[precedence order]] for [[time]], that is grounded in the [[Computational Thinking]] part of [[ABC curriculum]]. The notion of spacetime idea in [[ABC curriculum]] will then be encoded in the nomenclature that follows [[Cartesian Cubical Computational Type Theory]], also to be elaborated in the context of [[Computational Thinking]]. Starting in this article, we will call Cognitive Foundation, [[CF]]. ## The User Interface of Cognitive Foundation One idea of designing the curriculum is to create a visual language that is going to be used across the entire [[ABC curriculum]], while grounding this language in the formalism of [[Cubical Type Theory]] and [[Lens-like Automata]] or [[Lenia]]. In this language, the notion of [[Linear Algebra]], [[cellular automata]] or spatial and temporal implications of number/logical cell arrangements, and the continuous cellular automata ideas could all be encoded in a common data visualization platform that is tightly integrated with the formalism. Therefore, one could also argue that we are grounding a cognitive foundation with this new language. The key insight is that by using [[Sheaf]], [[stalk]], and other simple relational representation mechanism in a spatial and temporal (dynamical) animation, we are relating a visual experience that could strongly suggests the insights of algebraic topology in ways that usually requires gifted students who naturally have this tendency to reason about things in this geographically informed structure. Now, we could help build the mental scaffolding for them. Most importantly, the set of vocabulary in [[Type Theory]] is by definition a namespace, and we can use [[LLM]] technologies to help us manage the namespace for building this system. ### Parenthesis in Lisp/Lambda Calculus A few days ago, I wrote in [[ProjectKnowledgeTemplate]] about the notion of Lisp Parenthesis, it is transcluded below: ![[ProjectKnowledgeTemplate#Directory Structure as Parenthesis in Lisp]] Leveraging the directory structure in file systems to denote hierarchical data set is rather common. However, I plan to wire this up with [[Lenia]]. Think about each cell is one node, or one folder, and it could keep expand itself to be having more sub nodes, a structure that can be captured by [[Neo4j]]. This experience can be further improved if one carefully study the way [[VS Code]] integrates all kinds of plug-ins, and specifically its management of process and file attachment with its user interfaces. See [[@NginxMasteryLocalDNS2022|Nginx Mastery | Static Files | Multiple Domain | Local DNS configuration]] for more inspiration. One should realize that the VS Code environment is already a very functional cognitive platform for managing almost all kinds of data and all kinds of dynamically configurable user interfaces through its plug-in installation mechanism. We just want to do it over the web, which VS Code also have done a significant portion of that. # The Data Plane aspect of Cognitive Foundation In [[CF]], the main concern is whether certain type of data is accessible or not. This tremendously differs from the tradition that we are not talking about whether one has taken certain courses or acquired some vocabulary in a course, we are talking about whether you can have access to certain type of data, and what are the time-stamps of those data set. This is the data-centric approach to Cognitive Foundation. Therefore, the performance and the historical evidence for certain data is available, or have been exposed to certain person/organizations, becomes the main concern. This makes everything [[Observability|observable]]. ### Observable data with Time-stamps [[CF]] qualifies observable content by tagging data with time-stamps. Data that are submitted to be a part of observable data assets must be bound with a [[SBT]] and relevant timestamps. Content that are time sensitive in nature could also be shown in time-based visualization software such as [[Grafana]] or [[Prometheus]]. Other dimensional content, such as spatial locations, or personal identities, if available, should also be packaged in a way that can be analyzed and organized with some data query software, such as [[Neo4j]]. The most important thing about data is that data must be qualified with timestamps, and version controlled numbers. This can reference the way Docker, Git, and Nix manages version controlled data. ### Lowering the cost of data acquisition by design The focus of [[CF]] in [[ABC curriculum]] is to establish a common data collecting foundation that helps individuals and organizations to practice the habit of collecting data. This is the foundational skills to be taught in [[ABC curriculum]]. By offering turn-key solutions, such as [[PKC]], and pre-scribed methods and tools to help people collecting data of their own interests, [[CF]] serves a purpose in helping people to acquire evidence about an area of interest that they can judge for themselves about what is true, and what can be questionable. This is the foundation to make judgement based on observable and reproducible data collection practice. ## Counterfactuals helps formulate Cognitive Foundation [[Counterfactual|Counterfactuals]] play a crucial role in the formation of cognitive foundations by helping individuals understand cause-and-effect relationships, make sense of the world, and learn from their experiences. Counterfactual thinking involves mentally simulating alternative scenarios or outcomes that could have happened but did not. It allows individuals to imagine different possibilities and evaluate the consequences of various actions or events. By considering what might have been, people can better understand the causal factors that led to a particular outcome. Counterfactuals help to shape cognitive foundations by providing a framework for learning from past experiences. When people reflect on counterfactual alternatives, they can identify mistakes, missed opportunities, or better choices that could have led to a more desirable outcome. This process allows individuals to adjust their mental models and improve decision-making in future situations. Additionally, counterfactual reasoning helps individuals understand causality and develop a sense of agency. By imagining different scenarios and outcomes, people can discern the factors that contribute to certain events and recognize the role of their own actions or decisions in shaping those outcomes. Counterfactuals also contribute to cognitive development by fostering creativity and problem-solving skills. When individuals engage in counterfactual thinking, they explore uncharted possibilities and generate new ideas or solutions. This imaginative process enhances cognitive flexibility and promotes innovative thinking. In summary, counterfactuals are essential in the formation of cognitive foundations as they enable individuals to understand cause-and-effect relationships, learn from past experiences, develop a sense of agency, and foster creativity and problem-solving abilities. ## Links to Machine Learning [[David Shapiro]] wrote a book on [[Natural Language Cognitive Architecture]], it provides a wealth of great ideas. ## Learnable Content of Cognitive Foundation Here is a list of content knowledge related to CF courses: 1. Logic and Belief System: This category focuses on the understanding of symbolic representations, [[Logic|logical inference]], and beliefs, practices, and their implications on individuals and societies. It includes knowledge about different logical symbol systems, religions, philosophical traditions, rituals, ethics, and moral values. 2. Organizational Cognitive Capacity: This category pertains to the cognitive abilities necessary for effective organization and management. It encompasses knowledge about decision-making processes, problem-solving strategies, leadership styles, communication techniques, teamwork dynamics, and organizational development. 3. Music: The cognitive foundation in music involves understanding musical concepts such as rhythm, melody, harmony, pitch, tempo, timbre, and form. It also includes knowledge about different genres, styles, composers' works throughout history, and music theory principles like notation and scales. 4. Visual Arts: This category involves knowledge about various visual art forms like painting, sculpture, photography, architecture, etc. It encompasses understanding artistic elements such as color theory, composition principles (balance/proportion), art history movements/styles (Impressionism/Renaissance), and influential artists' works. 5. Physical Health/Sports: The cognitive foundation in physical health/sports includes knowledge about human anatomy and physiology relevant to physical activity. It also entails an understanding of sports rules/strategies/tactics (e.g., football or basketball), training principles (strength/conditioning), and nutrition's impact on performance/recovery. 6. Psychology and Mental Disciplines: This category encompasses knowledge about human behavior/mind processes through psychology principles/theories (e.g., learning/memory). It involves understanding cognitive processes (attention/perception) emotions/motivation influence behaviors; mental disciplines like meditation or mindfulness; therapeutic approaches/modalities like psychotherapy or cognitive-behavioral therapy. These summaries provide a general overview of the cognitive foundation in each category, highlighting the core knowledge areas relevant to each field. # Conclusion The notion of Cognitive Foundation (CF) is a crucial component in the domain of Design Thinking and the wider context of cognitive interpretation in data-driven contexts. Written by Ben Koo, CF is a conceptual framework that highlights the importance of data as the foundation of cognitive processes, for both people and organizations. It is closely connected to the ideas of Computational Type Theory, which offers a systematic method for identifying representable things and classifying computable judgments. Within the ABC curriculum, CF is distinguished by its own method of organizing content space via namespace management and creating temporal precedence order, both of which are firmly based on Computational Thinking. The curriculum utilizes a data-focused organizing approach, explaining the idea of spacetime using the terminology of Cartesian Cubical Computational Type Theory. The user interface of CF is designed to be a visual language that covers the whole ABC curriculum. It is based on the formalism of Cubical Type Theory and Lenia-like automata. This language seeks to integrate ideas from Linear Algebra, cellular automata, and continuous cellular automata into a cohesive data visualization platform. The program utilizes Sheaf theory and stalks to impart ideas in algebraic topology via visual experiences, thereby enabling students to develop mental scaffolding. The Data Plane element of CF prioritizes the availability of data categories, deviating from conventional educational measurements. The text emphasizes the significance of data observability, which involves adding time-stamps to content and ensuring that data is version-controlled. This approach is influenced by the management approaches used in Docker, Git, and Nix. Counterfactual reasoning is crucial for the development of CF, since it allows humans to investigate cause-and-effect connections and gain knowledge from hypothetical situations. Through the process of mentally simulating several potential results, people may improve their ability to make decisions, deepen their comprehension of cause and effect relationships, and cultivate their creativity and problem-solving capabilities. CF is a comprehensive framework that integrates logic and belief systems, organizational cognitive capacity, music, visual arts, physical health/sports, psychology, and mental disciplines. This is a detailed manual that explains the fundamental cognitive foundations of different areas, with a focus on the use of facts, counterfactuals, and visual language in influencing cognitive capacities and promoting learning. # References ```dataview Table title as Title, authors as Authors where contains(subject, "Cognitive Foundation") or contains(subject, "Collective Intelligence") ```