diff --git a/leerdoelen/blooms-taxonomy.md b/leerdoelen/blooms-taxonomy.md new file mode 100644 index 00000000..7d711caa --- /dev/null +++ b/leerdoelen/blooms-taxonomy.md @@ -0,0 +1,55 @@ +## Bloom's Taxonomy + +For the analysis of these *leerdoelen*, I use *Bloom's Taxonomy* (Bloom, Benjamin Samuel. *Taxonomy Of Educational Objectives: The Classification of Educational Goals*, 1961). According to this taxonomy, educational goals can be categorized into six levels: knowledge, comprehension, application, analysis, synthesis, and evaluation. + +*Knowledge* +The first level, knowledge, is meant to remember the relevant knowledge and to retrieve this from long-term memory. A student determines the meaning of key concepts and how they relate to each other. The student should remember and reproduce the learned information, concepts or procedures. The student recognizes and/or remembers information, without direct comprehension of the concept's meaning or its applications. Without the ability to remember key concepts, it is impossible to understand or apply information afterwards. Recognizing and recalling are central. + +*Comprehension* +Second, understanding or comprehension of information focuses on the construction of a cognitive model in which the meaning of information is constructed. The student is able to formulate and explain the concepts in his own words, come up with own examples, can distinguish counter-examples, and can recognize causal relations. At this level, the student gains insight to connect new information with knowledge he already has. This includes interpretation, exemplification, classification, summarization, inference, comparison and explanation. + +*Application* +The level of application concerns application of abstract concepts, procedures or principles in concrete, new situations. This requires the understanding of the concept as well as the ability to choose which knowledge is relevant and how it is useful for a specific case. Application corresponds with “transformation”: the transfer of learning from one context to another. Central parts are execution and implementation. + +*Analysis* +The analyze-level consists of the distinction of information in separated parts, the research of relations between the parts and the understanding of the underlying structures. The student learns to distinguish the parts and discovers how the parts function together as a whole. This is pattern analysis: breaking down complex information into manageable units to uncover hidden relationships. + +*Synthesis* +The next level is the one of evaluation. The student weighs alternatives against one another using explicit criteria and standards. This means that one does not merely observe or analyze, but also judges the quality, validity, or applicability of those alternatives. This engages meta-cognitive skills, in which the student reflects on their own thought processes and, on that basis, forms a defensible judgment. + +*Creation* +Last but not least, at the level of creation the student combines elements and insights from earlier levels to construct something entirely new. This may involve formulating new hypotheses from multiple sources, producing an original design, or developing an innovative argument. This level brings together both convergent and divergent thinking processes: synthesizing various ideas and generating new possibilities. + + +### Taxonomy per leerdoel +The following tabular provides an overview of the *Leerdoelen* related to Bloom's taxonomy. + +| **Bloom's Taxonomy** | LD 1 | LD 2 | LD 3 | LD 4 | +|----------------------|------|------|------|------| +| Knowledge | + | + | + | - | +| Comprehension | + | + | + | - | +| Application | - | - | + | + | +| Analysis | - | + | - | - | +| Synthesis | - | + | - | + | +| Creation | - | - | - | - | + +The first *leerdoel*, regarding an overview of logical methods used in AI, is at the level of knowledge and comprehension. First, a broad overview directly requires recall and recognition of various logical methods. It presupposes that students must retrieve stored information about different logical systems and approaches. In addition, to construct an overview, students must not only know what each method is, but also understand how they differ and relate to each other, which is an act of conceptual integration. It requires recognizing categories and explaining features, which are comprehension-level tasks. + +On the other hand, the first *leerdoel* is not at the level of application, since this objective does not ask students to use the methods to solve problems or apply them to new contexts. It remains at the level of knowing about methods rather than doing something with them. Moreover, the analysis level is absent, because there is no requirement to break down the logical methods or examine their internal structure. The learning goal is synthetic rather than analytic. Either synthesis and creation are not present. Indeed, the overview is descriptive rather than judgmental. Students are not asked to compare or evaluate methods on the basis of criteria. And students are not expected to construct new methods or ideas. + +The second *leerdoel*, regarding the understanding how and why logical methods work, focuses on the knowledge, comprehension, analysis and synthesis level. To begin with, understanding presupposes prior factual knowledge of the methods in question. Students must have access to information about the mechanics and assumptions of various techniques. Second, the keyword "begrijpen" indicates the comprehension level directly. Students are being asked to form logical models of why methods work, involving interpretation and explanation in their own terms. Moreover, this learning goal is at the level of analysis, because to understand how and why a method works and what its limitations are requires dissecting its logical structure. This is analytical: examining mechanisms, assumptions, and possible failure modes. Last but not least, the synthesis level is visible in the fact that discussing limitations inherently involves evaluating the method against some standard (e.g., generalization, consistency, completeness). This introduces an evaluative judgment, aligned with synthesis in Bloom's taxonomy. + +However, the second *leerdoel* doesn't focus on the level of application and creation. While understanding is a precondition for application, this goal stops short of asking students to actually apply logical methods to new problems. Secondly, although students reflect on how methods work, they are not expected to construct alternatives or develop new models. + +The third *leerdoel*, regarding applying logical methods in domains of AI, calls for a knowledge, comprehension and application level. Firstly, to apply a method, one must first know what it is: its steps, definitions, and assumptions. This background knowledge is required for further steps of understanding. Next to that, application requires understanding both the method itself and the context in which it is to be applied. This presupposes the ability to interpret both. As a result, the level of application is the central intent of the learning goal: to take abstract methods and use them in new, concrete cases. + +The third *leerdoel* misses the levels of analysis, synthesis and creation. There is no explicit call to decompose problems or methods into parts, nor to identify logical inter-dependencies. Therefore, analysis is not necessary. Furthermore, students are not asked to weigh alternatives or make normative judgments. The focus is on execution, not evaluation. Besides, the goal does not require developing new approaches or original extensions. The use is within established methods and known contexts. + +The fourth and final *leerdoel*, regarding skills to evaluate inferences, focuses on the application and synthesis level of Bloom's taxonomy. Firstly, students should use logical tools to assess inference quality. This is a functional task: applying rules to cases. Secondly, the core activity here is evaluation: students are asked to judge the validity of inferences, which entails applying criteria and making determinations. + +By contract, the levels of knowledge, comprehension, analysis and creation are not central in this fourth *leerdoel*. This learning goal frames logic as a skill. It focuses on procedural fluency, not declarative memory. While comprehension likely plays a role, it is not the most prominent part of the learning goal. Finally, no requirement to formulate new arguments, design logical systems, or invent inference strategies. The activity is assessive, not generative. + +In conclusion, most *leerdoelen* concern the level of knowledge and comprehension. Some are either at the level of application or analysis or synthesis. However, none of the learning goals focus on the creation level. Though this learning could be visible in the chapters, it is not prominent in the learning goals. + + +--- \ No newline at end of file diff --git a/leerdoelen/index.md b/leerdoelen/index.md new file mode 100644 index 00000000..8eac89ed --- /dev/null +++ b/leerdoelen/index.md @@ -0,0 +1,26 @@ +# Leerdoelen analysis + +**Logical Methods** +*Stage, Logische methoden voor KI* +*Filosofie, Universiteit Utrecht* +**Annefleur de Haan (s7328893)** +*Version 16 June 2025* + +--- + +## Table of contents + +1. [Leerdoelen](#leerdoelen) +2. [Bloom's Taxonomy](#blooms-taxonomy) +3. [Chapter 1: Logic and AI](#logic-and-ai) +4. [Chapter 2: Valid inference](#valid-inference) +5. [Plan for chapters](#plan-chapters) + + +--- +As a part of my research internship for the book project *Logical methods*, I analyse the *leerdoelen* of the course *Logische methoden voor KI* and how they fit with the first and second chapter of [Logical Methods](https://logicalmethods.ai). This *leerdoelen* analysis provides insights in the structure of the course and of *Logical methods*. Moreover, due to the analysis, it is some points for improvement can be concluded. + +To analyze the *leerdoelen*, I first explain some details about the taxonomy of Bloom. Then, I show how Bloom's taxonomy relate to the *leerdoelen*. Finally, I describe how the *leerdoelen* are present in the first two chapters of the book and what improvements can be made to the chapters to realize a more solid foundation of the *leerdoelen*. + +This document is still in development, since I plan to analyze the *leerdoelen* for the third chapter and forward as well. In addition, the structure of the analysis provides a framework for the analysis of the following chapters. + diff --git a/leerdoelen/leerdoelen.md b/leerdoelen/leerdoelen.md new file mode 100644 index 00000000..ef6c0203 --- /dev/null +++ b/leerdoelen/leerdoelen.md @@ -0,0 +1,29 @@ +## Leerdoelen + +In this document, I analyse the *leerdoelen* of the course *Logische methoden voor KI* and how they fit with the first chapter of [Logical Methods](https://logicalmethods.ai). + +According to the *Cursusbeschrijving*, the *leerdoelen* are: + +1. Een breed overzicht krijgen van de logische methoden die worden gebruikt in AI-onderzoek. +2. Begrijpen hoe en waarom deze methoden werken en wat hun beperkingen zijn. +3. Leren hoe je deze methoden kunt toepassen in specifieke probleemgebieden binnen AI. +4. Algemene logische vaardigheden verwerven om inferenties te evalueren. + +### Leerdoelen per onderwerp + +| **Leerdoel** | LD 1 | LD 2 | LD 3 | LD 4 | +|-----------------------|------|------|------|------| +| 1. Logic and AI | + | + | + | - | +| 2. Valid inference | - | + | - | + | +| 3. Formal languages | | | | | +| 4. Boolean algebra | | | | | +| 5. Boolean satisfiability | | | | | +| 6. Logical conditionals | | | | | +| 7. Logical proofs | | | | | +| 8. FOL | | | | | +| 9. FOL inference | | | | | +| 10. Many-valued logics | | | | | +| 11. Logic and probability | | | | | +| 12. Logic-based learning | | | | | + +--- diff --git a/leerdoelen/logic-and-ai.md b/leerdoelen/logic-and-ai.md new file mode 100644 index 00000000..7f405afa --- /dev/null +++ b/leerdoelen/logic-and-ai.md @@ -0,0 +1,89 @@ +# Leerdoelen analysis + +**Logical Methods** +*Stage, Logische methoden voor KI* +*Filosofie, Universiteit Utrecht* +**Annefleur de Haan (s7328893)** +*Version 16 June 2025* + +--- + +## Table of contents + +1. [Leerdoelen](#leerdoelen) +2. [Bloom's Taxonomy](#blooms-taxonomy) +3. [Chapter 1: Logic and AI](#chapter-1-logic-and-ai) +4. [Chapter 2: Valid inference](#chapter-2-valid-inference) + + +--- + +## Chapter 1: Logic and AI + +In the first chapter of *Logical methods*, [Logic and AI](https://logicalmethods.ai/textbook/logic-and-ai/), students are introduced with some important concepts in logic, such as premises and conclusions, and in AI, like symbolic AI and some tools. + +### Textbook *leerdoelen* and Bloom's taxonomy + +In the first chapter, the first, second and third *leerdoel* are introduced. + +*Leerdoel 1* +To begin with, the learning goal to gain a broad overview of the logical methods used in AI research is directly fulfilled by the entire structure of the chapter. The chapter introduces foundational concepts such as inference, validity, deductive and inductive logic, and logical systems (syntax, semantics, proof theory). It systematically explains different logical systems (e.g., propositional logic, predicate logic, modal logic) and their philosophical basis. The three-fold role of logic in AI (foundational, methodological, and instrumental) provides a framing schema for understanding the breadth of applications across the discipline. This corresponds to the cognitive level of knowledge and comprehension: acquiring and classifying concepts, understanding relationships between systems, and forming a structured overview of logical methodologies. + +*Leerdoel 2* +The learning goal to understand how and why these methods work and what their limitations are, is addressed with both conceptual depth and critical analysis throughout the chapter. In the section on validity, the distinction between deductive and inductive inference is not only stated but also motivated with examples, showing why deductive validity is “all or nothing”, whereas inductive validity admits degrees. This deepens understanding of how the methods function. +The examples of fallacious reasoning (e.g., “denying the antecedent”) illustrate where logic fails and hence reveal methodological limitations. +The section on logical systems explains their internal architecture (syntax, semantics, proof theory), showing how logical inference is formalized. Crucially, the foundational discussion (Gödel’s incompleteness theorem and Turing’s undecidability result) addresses theoretical boundaries of what logic can and cannot achieve within AI. These are limiting results. This corresponds to Bloom’s level of comprehension and analysis. The chapter encourages students not only to describe logical methods, but also to reason about their functioning and limitations. + +*Leerdoel 3* +The learning goal to learn how to apply these methods in specific problem domains within AI, is met primarily through the chapter’s contextualization of logic within concrete AI applications. For example, “Logic as Methodology” explains the role of logic in symbolic AI, including examples such as expert systems and knowledge representation. These are direct illustrations of logical methods applied to real-world AI tasks. Furthermore, “Logic as a Tool” provides further application contexts. Here, the link between logical formalism and practical computational function is emphasized. Moreover, the chapter distinguishes symbolic versus subsymbolic AI, explaining where logical methods remain operationally relevant, in hybrid AI systems, and in interpreting neural systems through logical approximations. By presenting logic as instrumentally relevant, the chapter shows how logical methods are selectively deployed to solve specific problem domains, such as formal verification, rule-based decision-making, and transparent AI modeling. This satisfies Bloom’s application level: the student is shown how to use abstract logical structures in domain-specific scenarios. + +### Exercises + +I analyse [the exercises](https://logicalmethods.ai/exercises/logic-and-ai/) of the first chapter related to the *leerdoelen* and Bloom's taxonomy. + +| Bloom's taxonomy | Ex. 1 | Ex. 2 | Ex. 3 | Ex. 4 | Ex. 5 | Ex. 6 | Ex. 7 | Ex. 8 | Ex. 9 | +|------------------|-------|-------|-------|-------|-------|-------|-------|-------|-------| +| Remembering | + | + | + | + | + | + | + | - | +/- | +| Understanding | + | + | + | + | + | + | + | + | +/- | +| Applying | - | - | - | + | + | + | + | - | +/- | +| Analyzing | - | - | - | - | - | - | - | + | +/- | +| Evaluating | - | - | - | - | - | - | - | + | +/- | +| Creating | - | - | - | - | - | - | - | + | +/- | + +#### Exercise 1. Test your knowledge + +This is a multiple choice question via which students can check their basic understanding of the chapter. Not all important concepts are asked, but some of the important are. This exercise provides a general insight for the students whether he remembers the concepts correctly. Students must recognize and reproduce the core definitions. The answers are findable in the text, but formulated in different ways in the exercise. Since this exercise is focused on reproduction and recalling of information, it is at the first level of Bloom's taxonomy: remembering. + +Moreover, the exercise is at the understanding level in the sense that students should check whether a proposed description matches that concept. They distinguish the correct from the incorrect formulations. + +#### Exercise 2. Definitions + +This exercise should be described later, when it is determined of which concepts the students should provide a definition. However, the exercise is at the level of remembering and understanding. + +#### Exercise 3. Examples of indicators + +This exercise focuses as well on the first and second level: remembering and understanding. because indicators are used as general concepts that structure the logical methods. Giving examples of the indicators concerns the comprehension of the student about the difference between the premise and inference. Students supply additional premise‐indicator and inference‐indicator words. They need to recall typical indicator vocabulary and show they understand why each word signals a premise or a conclusion. This draws on basic comprehension of indicator function plus simple retrieval. + +#### Exercise 4. Recognizing indicators + +The exercise demands students to recognize the inference indicators and categorize them, given a paragraph. This requires breaking the text into its argumentative components and classifying terms by function. Because the used inference indicators are simple, this is a very basic question. This means that students should remember what indicators are, understand how they work and finally apply this to the sentences of the paragraph to call the indicators correctly. Although not very prominent, the application level fits this question as well. + +#### Exercise 5. Inferences + +Each problem presents a mini‐scenario containing an argument. Students must parse out all premises and pinpoint the conclusion. That is essentially a decomposition task: isolate statements, recognize their roles, and reconstruct the argument’s structure. Therefore, students should remember how an inference is built, they should comprehend the different functions of premises and the conclusion, and they should apply this knowledge to the paragraphs to determine the premises and conclusions. + +#### Exercise 6. Symbolic or subsymbolic + +Descriptions of various AI systems are given. For each one, students decide whether it is symbolic or subsymbolic and justify that choice by referring to defining characteristics. They must understand each description to extract the basic mechanism (rules vs. statistical/probabilistic model) and then decide whether that mechanism matches one category or the other. Thus, this exercise concerns four levels: mostly remembering and understanding what symbolic and subsymbolic systems are, and applying this information to new examples. + +#### Exercise 7. Thinking, fast and slow + +Students generate entirely new examples of System 1 (fast, intuitive) and System 2 (slow, deliberate) thinking. By inventing new examples and explaining why each qualifies, they apply their conceptual knowledge of the distinction between the two forms. Therefore, this exercise is at the level of remembering the definitions of the two systems, understanding their differences and applying this knowledge to new examples. + +#### Exercise 8. Research + +These open‐ended questions require independent literature review, critical comparison of sources, and synthesis of a coherent answer. Therefore this exercise is mostly focused on understanding, analyzing, evaluating and maybe creating. + +#### Exercise 9. Discussion + +The discussion-question can be considered as a combination of multiple levels, depending on in what depth the questions are discussed. diff --git a/leerdoelen/plan-chapters.md b/leerdoelen/plan-chapters.md new file mode 100644 index 00000000..a7dc91d0 --- /dev/null +++ b/leerdoelen/plan-chapters.md @@ -0,0 +1,68 @@ +# Plan for chapters + +## Plan for Chapter 1: Logic and AI + +During the lecture(s) an introduction to the course is provided and all important concepts of the chapter are discussed. Students should study the textbook at home and prepare the workgroups by making some exercises. + +### Self study + +1. Read textbook, chapter 1, *Logic and AI*, and do the following exercises: +2. Exercise 1, *Test your knowledge*: these are multiple choice questions to test whether the student understands some key concepts. +3. Exercise 3, *Examples of indicators*: students should come up with own examples of indicators. +4. Exercise 4, *Recognizing indicators*: students should recognize the indicators. +5. Exercise 5, *Inferences*: students determine the premises and conclusion of an inference. +6. All multiple choice questions “test your knowledge” of the quizzes section. + +### Workgroup + +**Central leerdoel**: Een breed overzicht krijgen van de logische methoden die worden gebruikt in AI-onderzoek. + +1. Are there any questions about the textbook chapter, the lecture or made exercises? +2. Short explanation of inferences, indicators, symbolic versus subsymbolic, system 1 and 2, and other concepts if necessary. +3. Discussion of the following exercises: + - Exercise 6, *Symbolic or subsymbolic*: let the students discuss the cases in groups. Then, discuss the correct answers classical. + - Exercise 7, *Thinking, fast and slow*: let the students discuss examples in groups. Then, let each group present their examples and discuss together whether the examples are correct. + - Exercise 9, *Discussion*: first in groups and then together. +4. Time for more questions + +### Second self study + +After the workgroup student should do: + +1. Exercise 7, *Research* +2. All multiple choice questions of self study in quizzes section + + +## Plan for Chapter 2: Valid inference + +## Plan for this chapter + +During the lecture(s) an introduction to the course is provided and all important concepts of the chapter are discussed. Students should study the textbook at home and prepare the workgroups by making some exercises. + +### Self study + +1. Read textbook, chapter 2, *Valid inferences*, and do the following exercises: +2. All multiple choice “test your knowledge” questions. +3. Exercise 1, *Deduction and induction*: students should come up with own examples of deductive and inductive inferences. +4. Exercise 4, *Semantic tools*: students should remember the semantic tools discussed in the chapter. +5. Exercise 5, *Inferences*: students determine the premises and conclusion of an inference. + +### Workgroup + +**Central goal**: application and analysis of inferences and validity. + +1. Are there any questions about the textbook chapter, the lecture or made exercises? +2. Short explanation of inferences, validity, induction, deduction and semantics +3. Discussion of the following exercises: + - Exercise 2, *Monotonicity*: let the students discuss the cases in groups. Then, discuss the correct answers classical. + - Exercise 4, *Malfunctioning*: let the students discuss the cases in groups. Then, discuss in class. + - Exercise 8, *Discussion*: first in groups and then together. + - Time for more questions + +### Second self study + +Students should do some more work after the workgroup. + +1. Exercise 3, *Validity* +2. Exercise 7, *Research* +3. All multiple choice questions for self study diff --git a/leerdoelen/valid-inference.md b/leerdoelen/valid-inference.md new file mode 100644 index 00000000..8e43764d --- /dev/null +++ b/leerdoelen/valid-inference.md @@ -0,0 +1,103 @@ +# Leerdoelen analysis + +**Logical Methods** +*Stage, Logische methoden voor KI* +*Filosofie, Universiteit Utrecht* +**Annefleur de Haan (s7328893)** +*Version 16 June 2025* + +--- + +## Table of contents + +1. [Leerdoelen](#leerdoelen) +2. [Bloom's Taxonomy](#blooms-taxonomy) +3. [Chapter 1: Logic and AI](#chapter-1-logic-and-ai) +4. [Chapter 2: Valid inference](#chapter-2-valid-inference) + + +--- +## Chapter 2: Valid inference + +In the second chapter of the textbook, [Valid inferences](https://logicalmethods.ai/textbook/valid-inference/), students are introduced with validity of inferences. + +## Textbook *leerdoelen* + +In this chapter of the textbook, the second and fourth *leerdoel* are emphasized. The first and third aren't. + +*Leerdoel 2* +To begin with the second *leerdoel*, students learn how the logical methods function and briefly what their limitations are. For instance, they need to understand what deductive and inductive validity entails, how valid inference are distinguishable from invalid inferences, and what semantics is used for valid inferences. In addition, the limitations of deduction and induction are briefly discussed, e.g., limited applicability to everyday reasoning. However, it might be good to provide a clearer explanation of the reasons why induction and deduction are useful and what their function exactly is in AI. + +*Leerdoel 4* +The other *leerdoel* that is prominent in this chapter is the last *leerdoel* concerning the general logical skills to evaluate inferences. The student learn to recognize the differences between deductive (in)valid and inductive (in)valid inferences. Secondly, the chapter introduces the formal notation and discusses how the logical form of an inference can be evaluated. Finally, the semantic models show how truth-preservation is tested and used. On the other hand, the sections about semantic methods could be expanded to falsification. The section on semantic models currently focuses primarily on confirming validity. It would be beneficial to add an explicit discussion of how the models can also be used to demonstrate invalidity, for example by constituting a countermodel in which the premises are true but the conclusion is false. + +*Leerdoel 1* +This textbook chapter doesn't provide a systematic explanation of the `probleemgebieden' in AI. Therefore, the first *leerdoel* doesn't fit the chapter. + +*Leerdoel 3* +Since the chapter contains of the fundamental, philosophical parts of logic, it doesn't provide a broad overview of how the logical methods are applied in AI studies (*leerdoel* 3). If there is more attention for the connection between logical methods and AI, this *leerdoel* could be more prominent. + +## Textbook Bloom's taxonomy + +Bloom's taxonomy can be applied to this chapter. + +*Knowledge* +To begin with the level of remembering, students need to memorize different concepts. First, students should remember the definition of an inference, which is discussed in the previous chapter. In addition, they learn new concepts, such as validity, symbols used in the models, deduction and induction. + +*Comprehension* +The second level of Bloom's taxonomy, focused on understanding, is important in this chapter, since students should understand the difference between valid and invalid, between deduction and induction, and other abstract concepts. + +*Application* +Due to the examples in the textbook, students see how the concepts are applied to different cases. However, it is not asked to apply concepts by themselves (this is more like the exercises). + +*Analysis, synthesis and creation* +The levels of analyzing, evaluating and creating are not prominent in the chapter. The main focus of the chapter is remembering and understanding. + +## Exercises + +I analyze the exercises of the [second chapter](https://logicalmethods.ai/exercises/valid-inference/) related to the *leerdoelen* and Bloom's taxonomy. Every exercise demands knowledge and comprehension. Most exercises' aims are on the level of analysis as well. However, the level of application lacks in this chapter, which might be beneficial for additional exercises. + +| **Bloom's Taxonomy** | **Ex. 1** | **Ex. 2** | **Ex. 3** | **Ex. 4** | **Ex. 5** | **Ex. 6** | **Ex. 7** | **Ex. 8** | +|----------------------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------| +| Remembering | + | + | + | + | + | + | ± | + | +| Understanding | + | + | + | + | + | + | ± | + | +| Applying | + | -- | -- | + | + | -- | ± | -- | +| Analyzing | -- | + | + | + | - | + | ± | + | +| Evaluating | -- | + | -- | -- | -- | -- | ± | -- | +| Creating | -- | -- | -- | -- | -- | -- | ± | -- | + +### Exercise 1 Deduction and induction + +In this questions, students should remember the meaning of deduction, induction, validity and inferences. They should recognize and understand what makes an inference valid or not and how the form of the inference looks like, depending on induction or deduction. This involves knowledge, comprehension of the concepts and application of the knowledge to new examples. Therefore, the remembering, understand and application levels of Bloom's taxonomy are used. + +### Exercise 2 Monotonicity + +First, students are asked to analyse the structural principle of monotonicity and explain why this is logical demanding within a deductive system. This requires insight in the relation between premises and the conclusion for deductive validity. Thus, this question is on the understanding and analysing level. + +Secondly, students should analyse why the principle of monotonicity fails in inductive logic, concerning the probabilistic structure of induction. This requires understanding, analysis and evaluation of the differences. + +### Exercise 3 Validity + +The question about validity demands a certain level of knowledge and understanding of the concepts. Moreover, the students should reflect on the possibility of making the inference valid by adding a premise. This requires judgements about conditions for validity. Consequently, this is a question at the level over remembering, understanding and analyzing. + +### Exercise 4 Truth-Preservation + +This exercise asks students to apply concepts such as truth-preservation to various hypothetical scenarios (involving true or false premises and conclusions), and to analyze the structural conditions under which deductive or inductive validity is preserved. To do this, a certain level of knowledge and comprehension is needed, in addition to the ability to apply and analyse the concepts. + +### Exercise 5 Malfunctioning systems + +In this exercise, students are asked to explain why the systems result in the wrong outcome. They need to understand that the system makes an invalid inference and therefore concludes the wrong thing. To explain this, students need to understand the difference between valid en invalid inferences. They should recognize the parts that determinate the invalidity of the inference and hopefully they can come up with a method to fix the inference. The examples mentioned in the exercise are all symbolic AI systems, this recalls knowledge from the previous chapter. + +### Exercise 6 Semantic tools + +Firstly, the students should remember the subset relation and its property. The symbols should be a part of the student's knowledge in order to understand the symbols and their meaning. The understanding of transitivity is required. Therefore this question is at the level of knowledge, comprehension and analysis. + +The second part is an understanding question, since students are expected to demonstrate that they understand the basic concept of set intersection and can relate it to logical conjunction. The focus here is on the comprehension. + +### Exercise 7 Research + +The research question might be at all levels of the taxonomy, depending on how serious the students take this exercise. The students should, with the help of academic sources, form a judgement about whether deductive and inductive logic exhaust all forms of `good' reasoning as a classification system. If students go further and propose alternative classifications or develop integrative perspectives, they may reach the level of creation. + +### Exercise 8 Discussion + +The discussion question requires a well-considered view about specific forms of limited monotonicity in inductive logic. It involves weighing arguments, assessing plausibility, and taking a position within a theoretical framework. Therefore, decent knowledge, comprehension and analysis is needed.