Chapter one: Introduction Calculus is the study of variation, and it is also the central subject in mathematics (Boyer, 1959; Goldstine, 2012; Tall, 1990). The concept of calculus is applied in statistics, science, economics, and engineering to study the concepts of gravity, speed, velocity, variations, growth or decay function, and maximum or minimum of profit and cost function (Boyer, 1959, Goldstine, 2012; Tall, 1992). Many of scientiﬁc and technological growth since 1900s to the current time are linked with the...
Modern AI Systems have seen some major advancements and breakthroughs in recent years. However, almost all of them use a bottom-down approach where machines are heavily trained in as many situations as possible to increase accuracy and minimize their margin or error. This is a rather inefficient and at times untrustworthy way to teach machines. This approach requires large amounts of ‘good data’ and even with that, it is always uncertain that AI can be trusted in abstract situations. Abductive...
In addition to conditional reasoning, the other key type of deductive reasoning is syllogistic reasoning, which is based on the use of syllogisms. Syllogisms are deductive arguments that involve drawing conclusions from two premises (Maxwell, 2005; Rips, 1994, 1999). All syllogisms comprise a major premise, a minor premise, and a conclusion. Categorical syllogism comprise of two premises and a conclusion. the premises state something about the category memberships of the terms. In fact, each term represents all, none, or some...
Legal reasoning is an old concept, capable of being found way back in the Roman times. Decisions were justified by reference to exemplar factual situations and reasoning of other jurists, often seemingly guided by own views. The current age decision-making contains slight differences. To understand why a judge argues a case in a certain way, it is necessary to consider the reasons used to justify his reasoning. As Hunh suggests, a judicial decision is capable of being reduced into a...
Philosophy is a perspective about the world, the universe, and society. It works by posing fundamental inquiries about the idea of human idea, the nature of the universe, and the associations between them. The thoughts in reasoning are regularly broad and dynamic. However, this doesn’t imply that way of thinking isn’t about this present reality. Morals, for instance, gets some information about how to be great in our everyday lives. Mysticism gets some information about how the world functions and...
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“The role of analogy is to aid understanding rather than to provide justification.” To what extent do you agree with this statement? Human beings share a strong intuition that analogical justification forces us to better understand and interpret the situations that we face in our everyday lives. These analogies are widely recognized as playing an important role as a mental shortcut that allows people to solve problems and make judgments quickly and efficiently. Analogies provide insight and formulate possible solutions...
The reasoning is the process where the information is given and is compared with the known information or knowledge and come up with a reasoned conclusion. Reasoning skills can help in decision making, distinguishing situations and problems solving. To have agents involved in reasoning, they have to equipped with higher-level cognitive functions. For examples, beliefs and goals, actions, perception, plan coordination, the mental states of other agents and collaborative task execution. The belief-desire-intention (BDI) model is an approach that contains...
There are many reasons why a student can demonstrate their understanding to core related content. External factors in a child life, such as reading or exposure to technology can expand the student’s prior knowledge to assist them in learning core-related material. As well as internal factors, such as the student’s mental capability of understanding content. These are a few explanations to support the theory of a student’s ability to grasp materials in a classroom. However, students can also show their...