logic
关于Logic的十个问题
1、Logic的推荐配置是什么？Logic的推荐配置分为移动工作站系统和工作室系统。
在移动工作站中，我们推荐采用Logic＋PowerBook G4 17寸＋Fireface800.工作室系统的配置方式是Pro T ools HD2(核心卡)＋Apogee Rosetta800(AD/DA接口)＋Millennia HV-3D-4(顶级四通道话放).2. Pro Tools用户有必要使用Logic么？Pro T ools是非常优秀的使用广泛的录音、音频编辑和混音平台。
但遗憾的是，Pro T ools 编曲和音乐制作相关功能非常薄弱，国内很多人认为Pro Tools是全能的音乐音频工作站，这是错误的，Pro Tools在国内存在被过分美化的现象。
Logic在5版本之前，一直是音乐制作方面的首选平台，一条来自Apple公司的官方信息说，美国Billboard排行榜前100位，都是使用苹果平台在进行音乐制作，其中绝大多数又是使用Logic进行编曲和制作工作。
但是，Logic的第7个版本，已经不仅仅是一款编曲和音乐制作软件了，音频功能非常强大，不然目前也不会有很多电视台选用Logic作为他们的录音和编辑平台。
（上海卫视、湖南卫视音乐频道和快乐大本营栏目以及内蒙古电视台影视剧译制中心等）Logic区别于Pro Tools的第一个方面，就是真正的功能集合，而不仅仅是一个平台。
很多Logic用户在进行录音、制作、编辑、混音的过程里，完全使用Logic自带的效果器就制作出了商业标准的作品，以这次Logic巡演所请的Henrik为例，他给Co CO Lee制作的两首歌，在Logic 6里制作时，还使用了UAD-1和PowerCore的效果器，但在Logic 7进行最后的混音时，全部使用Logic自带的效果器、合成器、采样器等等。
Logic不仅仅完全提供了所有制作环节里需要使用的效果器，还提供了名为Channel Strip3、Logic的音质如何？就是他们发现用Logic录制管弦乐要比Pro Tools更好。
WhatisLogic（什么是逻辑）
LogicThis article is about reasoning and its study. For other uses, see Logic (disambiguation).Logic (from the Ancient Greek: λογική, logike)[1] is the use and study of valid reasoning.[2][3] The study of logic features most prominently in the subjects of philosophy, mathematics, and computer science.Logic was studied in several ancient civilizations, includingIndia,[4] China,[5] Persia and Greece. In the West, logic was established as a formal discipline by Aristotle, who gave it a fundamental place in philosophy. The study of logic was part of the classical trivium, which also included grammar and rhetoric. Logic was further extended by Al-Farabi who categorized it into two separate groups (idea and proof). Later, Avicenna revived the study of logic and developed relationship between temporalis and the implication. In the East, logic was developed by Buddhists and Jains.Logic is often divided into three parts: inductive reasoning, abductive reasoning, and deductive reasoning.The study of logic“Upon this first, and in one sense this sole, rule of reason, that in order to learn you must desire to learn, and in so desiring not be satisfied with what you alreadyincline to think, there follows one corollary which itself deserves to be inscribed upon every wall of the city of philosophy: Do not block the way of inquiry.”—Charles Sanders Peirce, "First Rule of Logic" The concept of logical form is central to logic, it being held that the validity of an argument is determined by its logical form, not by its content. Traditional Aristotelian syllogistic logic and modern symbolic logic are examples of formal logics.∙Informal logic is the study of natural language arguments. The study of fallacies is an especially important branch of informal logic. The dialogues of Plato[6] are goodexamples of informal logic.∙Formal logic is the study of inference with purely formal content. An inference possessesa purely formal content if it can be expressed as a particular application of a whollyabstract rule, that is, a rule that is not about any particular thing or property. The worksof Aristotle contain the earliest known formal study of logic. Modern formal logic followsand expands on Aristotle.[7] In many definitions of logic, logical inference and inferencewith purely formal content are the same. This does not render the notion of informallogic vacuous, because no formal logic captures all of the nuances of natural language.∙Symbolic logic is the study of symbolic abstractions that capture the formal features of logical inference.[8][9] Symbolic logic is often divided into two branches: propositionallogic and predicate logic.∙Mathematical logic is an extension of symbolic logic into other areas, in particular to the study of model theory, proof theory, set theory, and recursion theory.Logical formMain article: Logical formLogic is generally considered formal when it analyzes and represents the form of any valid argument type. The form of an argument is displayed by representing its sentences in the formal grammar and symbolism of a logical language to make its content usable in formal inference. If one considers the notion of form too philosophically loaded, one could say that formalizing simply means translating English sentences into the language of logic.This is called showing the logical form of the argument. It is necessary because indicative sentences of ordinary language show a considerable variety of form and complexity that makes their use in inference impractical. It requires, first, ignoring those grammatical features irrelevant to logic (such as gender and declension, if the argument is in Latin), replacing conjunctions irrelevant to logic (such as "but") with logical conjunctions like "and" and replacing ambiguous, or alternative logical expressions ("any", "every", etc.) with expressions of a standard type (such as "all", or the universalquantifier ∀).Second, certain parts of the sentence must be replaced with schematic letters. Thus, for example, the expression "all As are Bs" shows the logical form common to the sentences "all men are mortals", "all cats are carnivores", "all Greeks are philosophers", and so on.That the concept of form is fundamental to logic was already recognized in ancient times. Aristotle uses variable letters to represent valid inferences in Prior Analytics, leading JanŁukasiewicz to say that the introduction of variables was "one of Aristotle's greatest inventions".[10] According to the followers of Aristotle (such as Ammonius), only the logical principles stated inschematic terms belong to logic, not those given in concrete terms. The concrete terms "man", "mortal", etc., are analogous to the substitution values of the schematic placeholders A, B, C, which were called the "matter" (Greek hyle) of the inference.The fundamental difference between modern formal logic and traditional, or Aristotelian logic, lies in their differing analysis of the logical form of the sentences they treat.∙In the traditional view, the form of the sentence consists of (1) a subject (e.g., "man") plus a sign of quantity ("all" or "some" or "no"); (2) the copula, which is of the form "is"or "is not"; (3) a predicate (e.g., "mortal"). Thus: all men are mortal. The logicalconstants such as "all", "no" and so on, plus sentential connectives such as "and" and"or" were called "syncategorematic" terms (from the Greek kategorei – to predicate,and syn – together with). This is a fixed scheme, where each judgment has an identifiedquantity and copula, determining the logical form of the sentence.∙According to the modern view, the fundamental form of a simple sentence is given by a recursive schema, involving logical connectives, such as a quantifier with its boundvariable, which are joined by juxtaposition to other sentences, which in turn may havelogical structure.∙The modern view is more complex, since a single judgement of Aristotle's system involves two or more logical connectives. For example, the sentence "All men aremortal" involves, in term logic, two non-logical terms "is a man" (here M) and "is mortal"(here D): the sentence is given by the judgement A(M,D). In predicate logic, the sentenceinvolves the same two non-logical concepts, here analyzed as and , and thesentence is given by , involving the logical connectives foruniversal quantification and implication.∙But equally, the modern view is more powerful. Medieval logicians recognized the problem of multiple generality, where Aristotelian logic is unable to satisfactorily render such sentences as "Some guys have all the luck", because both quantities "all" and"some" may be relevant in an inference, but the fixed scheme that Aristotle used allowsonly one to govern the inference. Just as linguists recognize recursive structure innatural languages, it appears that logic needs recursive structure.Deductive and inductive reasoning, and abductive inferenceDeductive reasoning concerns what follows necessarily from given premises (if a, then b). However, inductive reasoning—the process of deriving a reliable generalization from observations—has sometimes been included in the study of logic. Similarly, it is important to distinguish deductive validity and inductive validity (called "cogency"). An inference is deductively valid if and only if there isno possible situation in which all the premises are true but the conclusion false. An inductive argument can be neither valid nor invalid; its premises give only some degree of probability, but not certainty, to its conclusion.The notion of deductive validity can be rigorously stated for systems of formal logic in terms of the well-understood notions of semantics. Inductive validity on the other hand requires us to define a reliable generalization of some set of observations. The task of providingthis definition may be approached in various ways, some less formal than others; some of these definitions may use mathematical models of probability. For the most part this discussion of logic deals only with deductive logic.Abduction[11] is a form of logical inference that goes from observation to a hypothesis that accounts for the reliable data (observation) and seeks to explain relevant evidence. The American philosopher Charles Sanders Peirce (1839–1914) first introduced the term as "guessing".[12] Peirce said that to abduce a hypothetical explanation from an observed surprising circumstance is to surmise that may be true because then would be a matter of course.[13] Thus, to abduce from involves determining that is sufficient (or nearly sufficient), but not necessary, for .Consistency, validity, soundness, and completenessAmong the important properties that logical systems can have:∙Consistency, which means that no theorem of the system contradicts another.[14]∙Validity, which means that the system's rules of proof never allow a false inference from true premises. A logical system has the property of soundness when the logical systemhas the property of validity and uses only premises that prove true (or, in the case ofaxioms, are true by definition).[14]∙Completeness, of a logical system, which means that if a formula is true, it can be proven (if it is true, it is a theorem of the system).∙Soundness, the term soundness has multiple separate meanings, which creates a bit of confusion throughout the literature. Most commonly, soundness refers to logicalsystems, which means that if some formula can be proven in a system, then it is true inthe relevant model/structure (if A is a theorem, it is true). This is the converse ofcompleteness. A distinct, peripheral use of soundness refers to arguments, which means that the premises of a valid argument are true in the actual world.Some logical systems do not have all four properties. As an example, Kurt Gödel's incompleteness theorems show that sufficiently complexformal systems of arithmetic cannot be consistent and complete;[9] however, first-order predicate logics not extended by specific axioms to be arithmetic formal systems with equality can be complete and consistent.[15]Rival conceptions of logicMain article: Definitions of logicLogic arose (see below) from a concern with correctness of argumentation. Modern logicians usually wish to ensure that logic studies just those arguments that arise from appropriately general forms of inference. For example, Thomas Hofweber writes in the Stanford Encyclopedia of Philosophy that logic "does not, however, cover good reasoning as a whole. That is the job of the theory of rationality. Rather it deals with inferences whose validity can be traced back to the formal features of the representations that are involved in that inference, be they linguistic, mental, or other representations".[16]By contrast, Immanuel Kant argued that logic should be conceived as the science of judgement, an idea taken up in Gottlob Frege's logical and philosophical work. But Frege's work is ambiguous in the sense that it is both concerned with the "laws of thought" as well as with the "laws of truth", i.e. it both treats logic in the context of a theory of the mind, and treats logic as the study of abstract formal structures.HistoryMain article: History of logicAristotle, 384–322 BCE.In Europe, logic was first developed by Aristotle.[17] Aristotelian logic became widely accepted in science and mathematics and remained in wide use in the West until the early 19th century.[18] Aristotle's system of logic was responsible for the introduction of hypothetical syllogism,[19] temporal modal logic,[20][21] and inductive logic,[22] as well as influential terms such as terms, predicables, syllogisms and propositions. In Europe during the later medieval period, major efforts were made to show that Aristotle's ideas were compatible with Christian faith. During the High Middle Ages, logic became a main focus of philosophers, who would engage in critical logical analyses of philosophical arguments, often using variations of the methodology of scholasticism. In 1323, William of Ockham's influential Summa Logicae was released. By the 18th century, the structured approach to arguments had degenerated and fallen out of favour, as depicted in Holberg's satirical play Erasmus Montanus.The Chinese logical philosopher Gongsun Long (c. 325–250 BCE) proposed the paradox "One and one cannot become two, since neither becomes two."[23] In China, the tradition of scholarly investigation into logic, however, was repressed by the Qin dynasty following the legalist philosophy of Han Feizi.In India, innovations in the scholastic school, called Nyaya, continued from ancient times into the early 18th century with the Navya-Nyaya school. By the 16th century, it developed theories resembling modern logic, such as Gottlob Frege's "distinction between sense and reference of proper names" and his "definition of number", as well as the theory of "restrictive conditions for universals" anticipating some of the developments in modern set theory.[24] Since 1824, Indian logic attracted the attention of many Western scholars, and has had an influence on important 19th-century logicians such as Charles Babbage, Augustus De Morgan, and George Boole.[25] In the20th century, Western philosophers like Stanislaw Schayer and Klaus Glashoff have explored Indian logic more extensively.The syllogistic logic developed by Aristotle predominated in the West until the mid-19th century, when interest in the foundations of mathematics stimulated the development of symbolic logic (now called mathematical logic). In 1854, George Boole published An Investigation of the Laws of Thought on Which are Founded the Mathematical Theories of Logic and Probabilities, introducing symbolic logic and the principles of what is now known as Boolean logic. In 1879, Gottlob Frege published Begriffsschrift, which inaugurated modern logic with the invention of quantifier notation. From 1910 to 1913, Alfred North Whitehead and Bertrand Russell published Principia Mathematica[8] onthe foundations of mathematics, attempting to derive mathematical truths from axioms and inference rules in symbolic logic. In 1931,Gödel raised serious problems with the foundationalist program and logic ceased to focus on such issues.The development of logic since Frege, Russell, and Wittgenstein had a profound influence on the practice of philosophy and the perceived nature of philosophical problems (see Analytic philosophy), and Philosophy of mathematics. Logic, especially sentential logic, is implemented in computer logic circuits and is fundamental to computer science. Logic is commonly taught by university philosophy departments, often as a compulsory discipline.Types of logicSyllogistic logicMain article: Aristotelian logicThe Organon was Aristotle's body of work on logic, with the Prior Analytics constituting the first explicit work in formal logic, introducing the syllogistic.[26] The parts of syllogistic logic, also known by the name term logic, are the analysis of the judgements into propositions consisting of two terms that are related by one of a fixed number of relations, and the expression of inferences by means of syllogisms that consist of two propositions sharing a common term as premise, and a conclusion that is a proposition involving the two unrelated terms from the premises.Aristotle's work was regarded in classical times and from medieval times in Europe and the Middle East as the very picture of a fully worked out system. However, it was not alone: the Stoics proposed a system of propositional logic that was studied by medieval logicians. Also, the problem of multiple generality was recognized in medieval times. Nonetheless, problems with syllogistic logic were not seen as being in need of revolutionary solutions.Today, some academics claim that Aristotle's system is generally seen as having little more than historical value (though there is some current interest in extending term logics), regarded as made obsolete by the advent of propositional logic and the predicate calculus. Others use Aristotle in argumentation theory to help develop andcritically question argumentation schemes that are used in artificial intelligence and legal arguments.Propositional logic (sentential logic)Main article: Propositional calculusA propositional calculus or logic (also a sentential calculus) is a formal system in which formulae representing propositions can be formed by combining atomic propositions using logical connectives, and in which a system of formal proof rules establishes certain formulae as "theorems".Predicate logicMain article: Predicate logicPredicate logic is the generic term for symbolic formal systems such as first-order logic, second-order logic, many-sorted logic, and infinitary logic.Predicate logic provides an account of quantifiers general enough to express a wide set of arguments occurring in natural language. Aristotelian syllogistic logic specifies a small number of forms that the relevant part of the involved judgements may take. Predicatelogic allows sentences to be analysed into subject and argument in several additional ways—allowing predicate logic to solve the problem of multiple generality that had perplexed medieval logicians.The development of predicate logic is usually attributed to Gottlob Frege, who is also credited as one of the founders of analytical philosophy, but the formulation of predicate logic most often used today is the first-order logic presented in Principles of Mathematical Logic by David Hilbert and Wilhelm Ackermann in 1928. The analytical generality of predicate logic allowed theformalization of mathematics, drove the investigation of set theory, and allowed the development of Alfred Tarski's approach to model theory. It provides the foundation of modern mathematical logic.Frege's original system of predicate logic was second-order, rather than first-order. Second-order logic is most prominently defended (against the criticism of Willard Van Orman Quine and others) by George Boolos and Stewart Shapiro.Modal logicMain article: Modal logicIn languages, modality deals with the phenomenon that sub-parts of a sentence may have their semantics modified by special verbs or modal particles. For example, "We go to the games" can be modified to give "We should go to the games", and "We can go to the games" and perhaps "We will go to the games". More abstractly, we might say that modality affects the circumstances in which we take an assertion to be satisfied.Aristotle's logic is in large parts concerned with the theory of non-modalized logic. Although, there are passages in his work, such as the famous sea-battle argument in De Interpretatione § 9, that are now seen as anticipations of modal logic and its connection with potentiality and time, the earliest formal system of modal logic was developed by Avicenna, whom ultimately developed a theory of "temporally modalized" syllogistic.[27]While the study of necessity and possibility remained important to philosophers, little logical innovation happened until the landmark investigations of Clarence Irving Lewis in 1918, who formulated a family of rival axiomatizations of the alethic modalities. His work unleashed a torrent of new work on the topic, expanding the kinds of modality treated to include deontic logic and epistemic logic. The seminal work of Arthur Prior applied the same formal language totreat temporal logic and paved the way for the marriage of the two subjects. Saul Kripke discovered (contemporaneously with rivals) his theory of frame semantics, which revolutionized the formal technology available to modal logicians and gave a new graph-theoretic way of looking at modality that has driven many applications in computational linguistics and computer science, such as dynamic logic.Informal reasoningMain article: Informal logicThe motivation for the study of logic in ancient times was clear: it is so that one may learn to distinguish good from bad arguments, and so become more effective in argument and oratory, and perhaps also to become a better person. Half of the works of Aristotle's Organontreat inference as it occurs in an informal setting, side by sidewith the development of the syllogistic, and in the Aristotelian school, these informal works on logic were seen as complementary to Aristotle's treatment of rhetoric.This ancient motivation is still alive, although it no longer takes centre stage in the picture of logic; typically dialectical logic forms the heart of a course in critical thinking, a compulsory course at many universities.Argumentation theory is the study and research of informal logic, fallacies, and critical questions as they relate to every day and practical situations. Specific types of dialogue can be analyzed and questioned to reveal premises, conclusions, and fallacies. Argumentation theory is now applied in artificial intelligence and law.Mathematical logicMain article: Mathematical logicMathematical logic really refers to two distinct areas of research: the first is the application of the techniques of formal logic to mathematics and mathematical reasoning, and the second, in the other direction, the application of mathematical techniques to the representation and analysis of formal logic.[28]The earliest use of mathematics and geometry in relation to logic and philosophy goes back to the ancient Greeks such as Euclid, Plato, and Aristotle.[29] Many other ancient and medieval philosophers applied mathematical ideas and methods to their philosophical claims.[30]One of the boldest attempts to apply logic to mathematics was undoubtedly the logicism pioneered by philosopher-logicians such as Gottlob Frege and Bertrand Russell: the idea was that mathematical theories were logical tautologies, and the programme was to show this by means to a reduction of mathematics to logic.[8] The various attempts to carry this out met with a series of failures, from the crippling of Frege's project in his Grundgesetze by Russell's paradox, to the defeat of Hilbert's program by Gödel's incompleteness theorems.Both the statement of Hilbert's program and its refutation by Gödel depended upon their work establishing the second area of mathematical logic, the application of mathematics to logic in the form of proof theory.[31] Despite the negative nature of the incompleteness theorems,Gödel's completeness theorem, a result in model theory and another application of mathematics to logic, can be understood as showing how close logicism came to being true: every rigorously defined mathematical theory can be exactly captured by a first-order logical theory; Frege's proof calculus is enough to describe the whole of mathematics, though not equivalent to it. Thus we see how complementary the two areas of mathematical logic have been.[citation needed]If proof theory and model theory have been the foundation of mathematical logic, they have been but two of the four pillars of the subject. Set theory originated in the study of the infinite by Georg Cantor, and it has been the source of many of the most challenging and important issues in mathematical logic, from Cantor's theorem, through the status of the Axiom of Choice and the question of the independence of the continuum hypothesis, to the modern debate on large cardinal axioms.Recursion theory captures the idea of computation in logical and arithmetic terms; its most classical achievements are the undecidability of the Entscheidungsproblem by Alan Turing, and his presentation of the Church–Turing thesis.[32] Today recursion theory is mostly concerned with the more refined problem of complexity classes—when is a problem efficiently solvable?—and the classification of degrees of unsolvability.[33]Philosophical logicMain article: Philosophical logicPhilosophical logic deals with formal descriptions of ordinary, non-specialist ("natural") language. Most philosophers assume that the bulk of everyday reasoning can be captured in logic if a method or methods to translate ordinary language into that logic can be found. Philosophical logic is essentially a continuation of the traditional discipline called "logic" before the invention of mathematical logic. Philosophical logic has a much greater concern with the connection between natural language and logic. As a result, philosophical logicians have contributed a great deal to the development of non-standard logics (e.g. free logics, tense logics) as well as various extensions of classical logic (e.g. modal logics) and non-standard semantics for such logics (e.g. Kripke's supervaluationism in the semantics of logic).Logic and the philosophy of language are closely related. Philosophy of language has to do with the study of how our language engages and interacts with our thinking. Logic has an immediate impact on other areas of study. Studying logic and the relationship between logic and ordinary speech can help a person better structure his own arguments and critique the arguments of others. Many popular arguments arefilled with errors because so many people are untrained in logic and unaware of how to formulate an argument correctly.Computational logicMain article: Logic in computer scienceLogic cut to the heart of computer science as it emerged as a discipline: Alan Turing's work on the Entscheidungsproblem followed from Kurt Gödel's work on the incompleteness theorems. The notion of the general purpose computer that came from this work was of fundamental importance to the designers of the computer machinery in the 1940s.In the 1950s and 1960s, researchers predicted that when human knowledge could be expressed using logic with mathematical notation, it would be possible to create a machine that reasons, or artificial intelligence. This was more difficult than expected because of the complexity of human reasoning. In logic programming, a program consists of a set of axioms and rules. Logic programming systems such as Prolog compute the consequences of the axioms and rules in order to answer a query.Today, logic is extensively applied in the fields of Artificial Intelligence, and Computer Science, and these fields provide a rich source of problems in formal and informal logic. Argumentation theory is one good example of how logic is being applied to artificial intelligence. The ACM Computing Classification System in particular regards:∙Section F.3 on Logics and meanings of programs and F.4 on Mathematical logic and formal languages as part of the theory of computer science: this work covers formalsemantics of programming languages, as well as work of formal methods such as Hoarelogic;∙Boolean logic as fundamental to computer hardware: particularly, the system's sectionB.2 on Arithmetic and logic structures, relating to operatives AND, NOT, and OR;。
Logic操作入门手册
Logic 操作入门手册Logic操作入门手册目录部分：前言：Logic简介什么是Logic关于本操作手册第一章：Logic配置MIDI和音频连接Logic配置助手模板第二章：什么是Logic装载并打开Tutorial Song(演示曲指南)了解和熟悉Logic的项目编辑（Arrange）窗口轨道和区域项目编辑区域（Arrange Area）参数区域（Parameters Area）键盘命令第三章：演示曲引导传输窗口第四章：区域编辑区域大小的重新调整区域的移动撤销和重试区域的复制区域的剪切循环循环浏览器第五章：MIDI区域MIDI区域的调换量化MIDI录音歌曲保存MIDI事件的编辑第六章：音频区域在项目编辑（Arrangement）项下创建音频轨道采样编辑器音频录音第七章：调音台、乐器以及效果器轨道调音台环境（Environment）中的调音台和音频目标（Audio Objects）调音台和插件的使用自动化混音并轨——最后混音第八章：环境概念MIDI通道外部控制从琶音器到分步音序器附录A：音频和MIDI基础知识MIDI音频附录B：Mac OS X系统中的音频和MIDI核心音频核心MIDI附录C：如何实现Logic同调音台的连接将Logic用作调音台没有编组输出功能（Sub Groups）的桌面混音系统（Mixing Desk）带有编组输出功能（Sub Groups）的桌面混音系统（Mixing Desk）附录D：如何对音频电脑系统进行优化故障排除方案前言：Logic简介近年来，随着个人电脑的风行和普及，音乐制作领域正在经受着一场重大变革。
以前需要大量专业工作室设备的音乐项目，现在只需通过一台个人电脑，再加上一些软件资源，就可以在家庭工作室或者项目工作室中完成！一台配有快速处理器和足够内存的个人电脑，就可以作为一个工作站，来完成对整套音乐项目的录音、编辑、混音以及制作，最后，制作好的音乐还可以在电脑中播放、烧录成CD/DVD或者上传到因特网。
logic使用手册
logic使用手册摘要：一、Logic概述二、Logic的使用方法1.安装与配置2.项目创建与编辑3.音频编辑与处理4.音乐创作工具5.混合与音效处理6.导出与分享三、Logic的高级技巧与实战案例四、常见问题与解决方案五、Logic的升级与未来发展正文：Logic是一款由苹果公司开发的专业音频和音乐创作软件，广泛应用于音乐制作、音频编辑、录音等领域。
本文将为大家介绍Logic的使用方法、高级技巧以及常见问题解决方案，帮助大家更好地掌握这款软件。
一、Logic概述Logic是一款强大的音频和音乐创作软件，具有丰富的音源、效果器和乐器库，适用于Mac操作系统。
相较于其他音频编辑软件，Logic具备更强大的音乐创作功能，可以让用户在同一个环境下完成音乐的制作、编辑、混音等过程。
二、Logic的使用方法1.安装与配置在使用Logic之前，首先需要确保您的计算机安装了最新版本的MacOS 操作系统。
然后下载并安装Logic Pro X，按照提示完成安装过程。
安装完成后，建议对软件进行基本设置，如音源、界面语言等。
2.项目创建与编辑在Logic中，项目是音乐创作的基本单位。
新建项目时，可以根据需求选择不同的项目模板。
编辑项目时，可以通过拖拽、复制、粘贴等方式调整音轨、音源和效果器的位置，实现音乐的创意组合。
3.音频编辑与处理Logic提供了丰富的音频编辑功能，包括裁剪、粘贴、删除、淡入淡出等。
此外，还可以对音频进行处理，如降噪、均衡、压缩等，以提高音乐品质。
4.音乐创作工具Logic内置了多种音乐创作工具，如虚拟键盘、鼓机、弦乐合奏等。
用户可以根据自己的创作需求，选择合适的工具进行音乐创作。
5.混合与音效处理Logic具有专业的混音功能，可以实现多轨音频的混合。
此外，还提供了丰富的音效库，如压缩、限幅、延迟、混响等，让用户轻松实现音乐制作的专业效果。
6.导出与分享当音乐创作完成后，可以通过Logic导出成品。
verilog logic类型
verilog logic类型Verilog Logic类型Verilog是一种硬件描述语言，用于描述数字电路和系统。
Verilog 中有多种数据类型，其中之一是Logic类型。
Logic类型是一种用于表示数字电路中的逻辑值的数据类型。
在Verilog中，逻辑值可以是0或1，也可以是X、Z或不确定的值。
Logic类型可以用于描述数字电路中的信号和寄存器。
在数字电路中，信号可以是输入、输出或内部信号。
输入信号是从外部输入到电路中的信号，输出信号是从电路中输出到外部的信号，而内部信号是在电路中使用的信号。
寄存器是一种存储器件，用于存储数字电路中的数据。
在Verilog中，Logic类型可以用于描述数字电路中的逻辑运算。
逻辑运算包括AND、OR、NOT、XOR等。
例如，下面的代码描述了一个AND门：module and_gate(input a, input b, output c);assign c = a & b;endmodule在这个代码中，a和b是输入信号，c是输出信号。
&是AND运算符，用于计算a和b的逻辑与，并将结果赋值给c。
除了逻辑运算，Logic类型还可以用于描述数字电路中的比较运算。
比较运算包括等于、不等于、大于、小于等。
例如，下面的代码描述了一个比较器：module comparator(input [7:0] a, input [7:0] b, output equal, output greater, output less);assign equal = (a == b);assign greater = (a > b);assign less = (a < b);endmodule在这个代码中，a和b是输入信号，equal、greater和less是输出信号。
==是等于运算符，>是大于运算符，<是小于运算符。
Logic类型还可以用于描述数字电路中的状态机。
logic使用手册
logic使用手册
我很高兴帮助你找到关于Logic软件的使用手册。
在这里，你
可以找到一些关于Logic软件的基本信息和常见操作的说明。
1. 了解Logic软件界面：了解Logic的布局和各个部分的功能，包括工具栏、编辑器窗口、控制面板等。
你可以通过查看
Logic的官方文档或在线教程来了解更多。
2. 创建新项目：学习如何在Logic中创建新的音频或MIDI项目。
这包括选择适当的项目设置、添加轨道和配置输入/输出。
3. 录制音频和MIDI：学习如何在Logic中录制音频和MIDI。
了解如何设置音频接口、选择输入源和音频设置，并学习如何使用Logic的录音功能。
4. 编辑音频和MIDI：了解如何在Logic中编辑音频和MIDI。
包括剪切、复制、粘贴、修剪、淡入淡出和变速等操作。
5. 添加效果和插件：学习如何在Logic中添加效果和插件来调
整音频和MIDI。
了解如何添加插件、调整参数和创建效果链。
6. 混音和母带处理：学习如何在Logic中进行混音和母带处理。
了解如何使用音频总线、插件和混响来调整声音。
7. 导出和分享音频：了解如何在Logic中将项目导出为音频文件。
包括选择导出格式、调整设置和保存。
以上是一些关于Logic软件使用手册的主要内容，希望对你有帮助。
请记住，你可以通过阅读Logic的官方文档、参加Logic的培训课程或寻求在线教程来进一步深入了解。
祝你使用Logic软件愉快！。
What is Logic(什么是逻辑)
LogicThis article is about reasoning and its study. For other uses, see Logic (disambiguation).Logic (from the Ancient Greek: λογική, logike)[1] is the use and study of valid reasoning.[2][3]The study of logic features most prominently in the subjects of philosophy, mathematics, and computer science.Logic was studied in several ancient civilizations, including India,[4] China,[5]Persia and Greece. In the West, logic was established as a formal discipline by Aristotle, who gave it a fundamental place in philosophy. The study of logic was part of the classical trivium, which also included grammar and rhetoric. Logic was further extended by Al-Farabi who categorized it into two separate groups (idea and proof). Later, Avicenna revived the study of logic and developed relationship between temporalis and the implication. In the East, logic was developed by Buddhists and Jains.Logic is often divided into three parts: inductive reasoning, abductive reasoning, and deductive reasoning.The study of logic“Upon this first, and in one sense this sole, rule of reason, that in order to learn you must desire to learn, and in so desiring not be satisfied with what you alreadyincline to think, there follows one corollary which itself deserves to be inscribed upon every wall of the city of philosophy: Do not block the way of inquiry.”—Charles Sanders Peirce, "First Rule of Logic"The concept of logical form is central to logic, it being held that the validity of an argument is determined by its logical form, not by its content. Traditional Aristotelian syllogistic logic and modern symbolic logic are examples of formal logics.•Informal logic is the study of natural language arguments. The study of fallacies is an especially important branch of informal logic. The dialogues of Plato[6] are goodexamples of informal logic.•Formal logic is the study of inference with purely formal content. An inference possessesa purely formal content if it can be expressed as a particular application of a whollyabstract rule, that is, a rule that is not about any particular thing or property. The worksof Aristotle contain the earliest known formal study of logic. Modern formal logic followsand expands on Aristotle.[7] In many definitions of logic, logical inference and inferencewith purely formal content are the same. This does not render the notion of informallogic vacuous, because no formal logic captures all of the nuances of natural language.•Symbolic logic is the study of symbolic abstractions that capture the formal features of logical inference.[8][9] Symbolic logic is often divided into two branches: propositionallogic and predicate logic.•Mathematical logic is an extension of symbolic logic into other areas, in particular to the study of model theory, proof theory, set theory, and recursion theory.Logical formMain article: Logical formLogic is generally considered formal when it analyzes and represents the form of any valid argument type. The form of an argument is displayed by representing its sentences in the formal grammar and symbolism of a logical language to make its content usable in formal inference. If one considers the notion of form too philosophically loaded, one could say that formalizing simply means translating English sentences into the language of logic.This is called showing the logical form of the argument. It is necessary because indicative sentences of ordinary language show a considerable variety of form and complexity that makes their use in inference impractical. It requires, first, ignoring those grammatical features irrelevant to logic (such as gender and declension, if the argument is in Latin), replacing conjunctions irrelevant to logic (such as "but") with logical conjunctions like "and" and replacing ambiguous, or alternative logical expressions ("any", "every", etc.) with expressions of a standard type (such as "all", or the universal quantifier ∀).Second, certain parts of the sentence must be replaced with schematic letters. Thus, for example, the expression "all As are Bs" shows the logical form common to the sentences "all men are mortals", "all cats are carnivores", "all Greeks are philosophers", and so on.That the concept of form is fundamental to logic was already recognized in ancient times. Aristotle uses variable letters to represent valid inferences in Prior Analytics, leading Jan Łukasiewicz to say that the introduction of variables was "one of Aristotle's greatest inventions".[10] According to the followers of Aristotle (such as Ammonius), only the logical principles stated in schematic terms belong to logic, not those given in concrete terms. The concrete terms "man", "mortal", etc., are analogous to the substitution values of the schematic placeholders A, B, C, which were called the "matter" (Greek hyle) of the inference.The fundamental difference between modern formal logic and traditional, or Aristotelian logic, lies in their differing analysis of the logical form of the sentences they treat.•In the traditional view, the form of the sentence consists of (1) a subject (e.g., "man") plus a sign of quantity ("all" or "some" or "no"); (2) the copula, which is of the form "is"or "is not"; (3) a predicate (e.g., "mortal"). Thus: all men are mortal. The logical constants such as "all", "no" and so on, plus sentential connectives such as "and" and "or" werecalled "syncategorematic" terms (from the Greek kategorei – to predicate, and syn –together with). This is a fixed scheme, where each judgment has an identified quantityand copula, determining the logical form of the sentence.•According to the modern view, the fundamental form of a simple sentence is given by a recursive schema, involving logical connectives, such as a quantifier with its boundvariable, which are joined by juxtaposition to other sentences, which in turn may havelogical structure.•The modern view is more complex, since a single judgement of Aristotle's system involves two or more logical connectives. For example, the sentence "All men aremortal" involves, in term logic, two non-logical terms "is a man" (here M) and "is mortal"(here D): the sentence is given by the judgement A(M,D). In predicate logic, the sentence involves the same two non-logical concepts, here analyzed as and , andthe sentence is given by , involving the logical connectives for universal quantification and implication.•But equally, the modern view is more powerful. Medieval logicians recognized the problem of multiple generality, where Aristotelian logic is unable to satisfactorily rendersuch sentences as "Some guys have all the luck", because both quantities "all" and"some" may be relevant in an inference, but the fixed scheme that Aristotle used allowsonly one to govern the inference. Just as linguists recognize recursive structure in natural languages, it appears that logic needs recursive structure.Deductive and inductive reasoning, and abductive inferenceDeductive reasoning concerns what follows necessarily from given premises (if a, then b). However, inductive reasoning—the process of deriving a reliable generalization from observations—has sometimes been included in the study of logic. Similarly, it is important to distinguish deductive validity and inductive validity (called "cogency"). An inference is deductively valid if and only if there is no possible situation in which all the premises are true but the conclusion false. An inductive argument can be neither valid nor invalid; its premises give only some degree of probability, but not certainty, to its conclusion.The notion of deductive validity can be rigorously stated for systems of formal logic in terms of the well-understood notions of semantics. Inductive validity on the other hand requires us to define a reliable generalization of some set of observations. The task of providing this definition may be approached in various ways, some less formal than others; some of these definitions may use mathematical models of probability. For the most part this discussion of logic deals only with deductive logic.Abduction[11]is a form of logical inference that goes from observation to a hypothesis that accounts for the reliable data (observation) and seeks to explain relevant evidence. The American philosopher Charles Sanders Peirce (1839–1914) first introduced the term as "guessing".[12] Peirce said that to abduce a hypothetical explanation from an observed surprising circumstance is to surmise that may be true because then would be a matter of course.[13] Thus, to abduce from involves determining that is sufficient (or nearly sufficient), but not necessary, for .Consistency, validity, soundness, and completenessAmong the important properties that logical systems can have:•Consistency, which means that no theorem of the system contradicts another.[14]•Validity, which means that the system's rules of proof never allow a false inference from true premises. A logical system has the property of soundness when the logical systemhas the property of validity and uses only premises that prove true (or, in the case ofaxioms, are true by definition).[14]•Completeness, of a logical system, which means that if a formula is true, it can be proven (if it is true, it is a theorem of the system).•Soundness, the term soundness has multiple separate meanings, which creates a bit of confusion throughout the literature. Most commonly, soundness refers to logical systems,which means that if some formula can be proven in a system, then it is true in therelevant model/structure (if A is a theorem, it is true). This is the converse ofcompleteness. A distinct, peripheral use of soundness refers to arguments, which meansthat the premises of a valid argument are true in the actual world.Some logical systems do not have all four properties. As an example, Kurt Gödel's incompleteness theorems show that sufficiently complex formal systems of arithmetic cannot be consistent and complete;[9] however, first-order predicate logics not extended by specific axioms to be arithmetic formal systems with equality can be complete and consistent.[15]Rival conceptions of logicMain article: Definitions of logicLogic arose (see below) from a concern with correctness of argumentation. Modern logicians usually wish to ensure that logic studies just those arguments that arise from appropriately general forms of inference. For example, Thomas Hofweber writes in the Stanford Encyclopedia of Philosophy that logic "does not, however, cover good reasoning as a whole. That is the job of the theory of rationality. Rather it deals with inferences whose validity can be traced back to the formal features of the representations that are involved in that inference, be they linguistic, mental, or other representations".[16]By contrast, Immanuel Kant argued that logic should be conceived as the science of judgement, an idea taken up in Gottlob Frege's logical and philosophical work. But Frege's work is ambiguous in the sense that it is both concerned with the "laws of thought" as well as with the "laws of truth", i.e. it both treats logic in the context of a theory of the mind, and treats logic as the study of abstract formal structures.HistoryMain article: History of logicAristotle, 384–322BCE.In Europe, logic was first developed by Aristotle.[17] Aristotelian logic became widely accepted in science and mathematics and remained in wide use in the West until the early 19th century.[18] Aristotle's system of logic was responsible for the introduction of hypothetical syllogism,[19] temporal modal logic,[20][21] and inductive logic,[22] as well as influential terms such as terms, predicables, syllogisms and propositions. In Europe during the later medieval period, major efforts were made to show thatAristotle's ideas were compatible with Christian faith. During the High Middle Ages, logic became a main focus of philosophers, who would engage in critical logical analyses of philosophical arguments, often using variations of the methodology of scholasticism. In 1323, William of Ockham's influential Summa Logicae was released. By the 18th century, the structured approach to arguments had degenerated and fallen out of favour, as depicted in Holberg's satirical play Erasmus Montanus.The Chinese logical philosopher Gongsun Long (c. 325–250 BCE) proposed the paradox "One and one cannot become two, since neither becomes two."[23] In China, the tradition of scholarly investigation into logic, however, was repressed by the Qin dynasty following the legalist philosophy of Han Feizi.In India, innovations in the scholastic school, called Nyaya, continued from ancient times into the early 18th century with the Navya-Nyaya school. By the 16th century, it developed theories resembling modern logic, such as Gottlob Frege's "distinction between sense and reference of proper names" and his "definition of number", as well as the theory of "restrictive conditions for universals" anticipating some of the developments in modern set theory.[24] Since 1824, Indian logic attracted the attention of many Western scholars, and has had an influence on important 19th-century logicians such as Charles Babbage, Augustus De Morgan, and George Boole.[25] In the 20th century, Western philosophers like Stanislaw Schayer and Klaus Glashoff have explored Indian logic more extensively.The syllogistic logic developed by Aristotle predominated in the West until the mid-19th century, when interest in the foundations of mathematics stimulated the development of symbolic logic (now called mathematical logic). In 1854, George Boole published An Investigation of the Laws of Thought on Which are Founded the Mathematical Theories of Logic and Probabilities, introducing symbolic logic and the principles of what is now known as Boolean logic. In 1879, Gottlob Frege published Begriffsschrift, which inaugurated modern logic with the invention of quantifier notation. From 1910 to 1913, Alfred North Whitehead and Bertrand Russell published Principia Mathematica[8]on the foundations of mathematics, attempting to derive mathematical truths from axioms and inference rules in symbolic logic. In 1931, Gödel raised serious problems with the foundationalist program and logic ceased to focus on such issues.The development of logic since Frege, Russell, and Wittgenstein had a profound influence on the practice of philosophy and the perceived nature of philosophical problems (see Analytic philosophy), and Philosophy of mathematics. Logic, especially sentential logic, is implemented incomputer logic circuits and is fundamental to computer science. Logic is commonly taught by university philosophy departments, often as a compulsory discipline.Types of logicSyllogistic logicMain article: Aristotelian logicThe Organon was Aristotle's body of work on logic, with the Prior Analytics constituting the first explicit work in formal logic, introducing the syllogistic.[26]The parts of syllogistic logic, also known by the name term logic, are the analysis of the judgements into propositions consisting of two terms that are related by one of a fixed number of relations, and the expression of inferences by means of syllogisms that consist of two propositions sharing a common term as premise, and a conclusion that is a proposition involving the two unrelated terms from the premises.Aristotle's work was regarded in classical times and from medieval times in Europe and the Middle East as the very picture of a fully worked out system. However, it was not alone: the Stoics proposed a system of propositional logic that was studied by medieval logicians. Also, the problem of multiple generality was recognized in medieval times. Nonetheless, problems with syllogistic logic were not seen as being in need of revolutionary solutions.Today, some academics claim that Aristotle's system is generally seen as having little more than historical value (though there is some current interest in extending term logics), regarded as made obsolete by the advent of propositional logic and the predicate calculus. Others use Aristotle in argumentation theory to help develop and critically question argumentation schemes that are used in artificial intelligence and legal arguments.Propositional logic (sentential logic)Main article: Propositional calculusA propositional calculus or logic (also a sentential calculus) is a formal system in which formulae representing propositions can be formed bycombining atomic propositions using logical connectives, and in which a system of formal proof rules establishes certain formulae as "theorems".Predicate logicMain article: Predicate logicPredicate logic is the generic term for symbolic formal systems such as first-order logic, second-order logic, many-sorted logic, and infinitary logic.Predicate logic provides an account of quantifiers general enough to express a wide set of arguments occurring in natural language. Aristotelian syllogistic logic specifies a small number of forms that the relevant part of the involved judgements may take. Predicate logic allows sentences to be analysed into subject and argument in several additional ways—allowing predicate logic to solve the problem of multiple generality that had perplexed medieval logicians.The development of predicate logic is usually attributed to Gottlob Frege, who is also credited as one of the founders of analytical philosophy, but the formulation of predicate logic most often used today is thefirst-order logic presented in Principles of Mathematical Logic by David Hilbert and Wilhelm Ackermann in 1928. The analytical generality of predicate logic allowed the formalization of mathematics, drove the investigation of set theory, and allowed the development of Alfred Tarski's approach to model theory. It provides the foundation of modern mathematical logic.Frege's original system of predicate logic was second-order, rather than first-order. Second-order logic is most prominently defended (against the criticism of Willard Van Orman Quine and others) by George Boolos and Stewart Shapiro.Modal logicMain article: Modal logicIn languages, modality deals with the phenomenon that sub-parts of a sentence may have their semantics modified by special verbs or modal particles. For example, "We go to the games" can be modified to give "We should go to the games", and "We can go to the games" and perhaps "We willgo to the games". More abstractly, we might say that modality affects the circumstances in which we take an assertion to be satisfied.Aristotle's logic is in large parts concerned with the theory ofnon-modalized logic. Although, there are passages in his work, such as the famous sea-battle argument in De Interpretatione§ 9, that are now seen as anticipations of modal logic and its connection with potentiality and time, the earliest formal system of modal logic was developed by Avicenna, whom ultimately developed a theory of "temporally modalized" syllogistic.[27]While the study of necessity and possibility remained important to philosophers, little logical innovation happened until the landmark investigations of Clarence Irving Lewis in 1918, who formulated a family of rival axiomatizations of the alethic modalities. His work unleashed a torrent of new work on the topic, expanding the kinds of modality treated to include deontic logic and epistemic logic. The seminal work of Arthur Prior applied the same formal language to treat temporal logic and paved the way for the marriage of the two subjects. Saul Kripke discovered (contemporaneously with rivals) his theory of frame semantics, which revolutionized the formal technology available to modal logicians and gave a new graph-theoretic way of looking at modality that has driven many applications in computational linguistics and computer science, such as dynamic logic.Informal reasoningMain article: Informal logicThe motivation for the study of logic in ancient times was clear: it is so that one may learn to distinguish good from bad arguments, and so become more effective in argument and oratory, and perhaps also to become a better person. Half of the works of Aristotle's Organon treat inference as it occurs in an informal setting, side by side with the development of the syllogistic, and in the Aristotelian school, these informal works on logic were seen as complementary to Aristotle's treatment of rhetoric.This ancient motivation is still alive, although it no longer takes centre stage in the picture of logic; typically dialectical logic forms the heart of a course in critical thinking, a compulsory course at many universities.Argumentation theory is the study and research of informal logic, fallacies, and critical questions as they relate to every day andpractical situations. Specific types of dialogue can be analyzed and questioned to reveal premises, conclusions, and fallacies. Argumentation theory is now applied in artificial intelligence and law.Mathematical logicMain article: Mathematical logicMathematical logic really refers to two distinct areas of research: the first is the application of the techniques of formal logic to mathematics and mathematical reasoning, and the second, in the other direction, the application of mathematical techniques to the representation and analysis of formal logic.[28]The earliest use of mathematics and geometry in relation to logic and philosophy goes back to the ancient Greeks such as Euclid, Plato, and Aristotle.[29] Many other ancient and medieval philosophers applied mathematical ideas and methods to their philosophical claims.[30]One of the boldest attempts to apply logic to mathematics was undoubtedly the logicism pioneered by philosopher-logicians such as Gottlob Frege and Bertrand Russell: the idea was that mathematical theories were logical tautologies, and the programme was to show this by means to a reduction of mathematics to logic.[8]The various attempts to carry this out met with a series of failures, from the crippling of Frege's project in his Grundgesetze by Russell's paradox, to the defeat of Hilbert's program by Gödel's incompleteness theorems.Both the statement of Hilbert's program and its refutation by Gödel depended upon their work establishing the second area of mathematical logic, the application of mathematics to logic in the form of proof theory.[31] Despite the negative nature of the incompleteness theorems, Gödel's completeness theorem, a result in model theory and another application of mathematics to logic, can be understood as showing how close logicism came to being true: every rigorously defined mathematical theory can be exactly captured by a first-order logical theory; Frege's proof calculus is enough to describe the whole of mathematics, though not equivalent to it. Thus we see how complementary the two areas of mathematical logic have been.[citation needed]If proof theory and model theory have been the foundation of mathematical logic, they have been but two of the four pillars of the subject. Set theory originated in the study of the infinite by Georg Cantor, and it has been the source of many of the most challenging and important issues inmathematical logic, from Cantor's theorem, through the status of the Axiom of Choice and the question of the independence of the continuum hypothesis, to the modern debate on large cardinal axioms.Recursion theory captures the idea of computation in logical and arithmetic terms; its most classical achievements are the undecidability of the Entscheidungsproblem by Alan Turing, and his presentation of the Church–Turing thesis.[32]Today recursion theory is mostly concerned with the more refined problem of complexity classes—when is a problem efficiently solvable?—and the classification of degrees of unsolvability.[33]Philosophical logicMain article: Philosophical logicPhilosophical logic deals with formal descriptions of ordinary,non-specialist ("natural") language. Most philosophers assume that the bulk of everyday reasoning can be captured in logic if a method or methods to translate ordinary language into that logic can be found. Philosophical logic is essentially a continuation of the traditional discipline called "logic" before the invention of mathematical logic. Philosophical logic has a much greater concern with the connection between natural language and logic. As a result, philosophical logicians have contributed a great deal to the development of non-standard logics (e.g. free logics, tense logics) as well as various extensions of classical logic (e.g. modal logics) and non-standard semantics for such logics (e.g. Kripke's supervaluationism in the semantics of logic).Logic and the philosophy of language are closely related. Philosophy of language has to do with the study of how our language engages and interacts with our thinking. Logic has an immediate impact on other areas of study. Studying logic and the relationship between logic and ordinary speech can help a person better structure his own arguments and critique the arguments of others. Many popular arguments are filled with errors because so many people are untrained in logic and unaware of how to formulate an argument correctly.Computational logicMain article: Logic in computer scienceLogic cut to the heart of computer science as it emerged as a discipline: Alan Turing's work on the Entscheidungsproblem followed from Kurt Gödel's work on the incompleteness theorems. The notion of the general purpose computer that came from this work was of fundamental importance to the designers of the computer machinery in the 1940s.In the 1950s and 1960s, researchers predicted that when human knowledge could be expressed using logic with mathematical notation, it would be possible to create a machine that reasons, or artificial intelligence. This was more difficult than expected because of the complexity of human reasoning. In logic programming, a program consists of a set of axioms and rules. Logic programming systems such as Prolog compute the consequences of the axioms and rules in order to answer a query.Today, logic is extensively applied in the fields of Artificial Intelligence, and Computer Science, and these fields provide a rich source of problems in formal and informal logic. Argumentation theory is one good example of how logic is being applied to artificial intelligence. The ACM Computing Classification System in particular regards:•Section F.3 on Logics and meanings of programs and F.4 on Mathematical logic and formal languages as part of the theory of computer science: this work covers formalsemantics of programming languages, as well as work of formal methods such as Hoarelogic;•Boolean logic as fundamental to computer hardware: particularly, the system's sectionB.2 on Arithmetic and logic structures, relating to operatives AND, NOT, and OR;•Many fundamental logical formalisms are essential to section I.2 on artificial intelligence, for example modal logic and default logic in Knowledge representation formalisms andmethods, Horn clauses in logic programming, and description logic.Furthermore, computers can be used as tools for logicians. For example, in symbolic logic and mathematical logic, proofs by humans can be computer-assisted. Using automated theorem proving the machines can find and check proofs, as well as work with proofs too lengthy to write out by hand.Bivalence and the law of the excluded middleMain article: Principle of bivalenceThe logics discussed above are all "bivalent" or "two-valued"; that is, they are most naturally understood as dividing propositions into true and false propositions. Non-classical logics are those systems that reject bivalence.。
logic pro x教学案例
Logic Pro X教学案例Logic Pro X是一款强大的数字音频工作站软件，被广泛应用于音乐制作、录音混音和音乐创作等领域。
它拥有丰富的音频处理功能和强大的乐器库，可以满足各种不同音乐人的创作需求。
本文将通过一些具体的案例来介绍Logic Pro X的教学方法和技巧，帮助读者更好地了解和掌握这款软件。
一、入门基础1.1 安装和界面介绍我们需要对Logic Pro X进行安装，并对其界面进行简单介绍。
在安装完成后，打开软件，可以看到主界面分为顶部的菜单栏、左侧的浏览区、中间的编辑区以及底部的传输栏等部分。
熟悉这些界面元素将有助于我们更好地使用软件进行音频处理和音乐创作。
1.2 基本操作和快捷键接下来，我们可以介绍一些Logic Pro X的基本操作和常用快捷键，如新建工程、导入音频、调整音轨等。
熟练掌握这些操作将大大提高我们的工作效率，同时也可以通过快捷键来简化操作流程。
二、音频处理技巧2.1 录音和编曲在音频处理方面，Logic Pro X提供了丰富的录音和编曲功能，包括录音、剪辑、混音等。
我们可以通过案例来介绍如何进行音频录制，如何进行编曲和如何添加各种音效效果等。
从简单的乐器演奏到复杂的编曲，都可以在Logic Pro X中得到很好的实现。
2.2 混音和母带处理Logic Pro X还提供了强大的混音和母带处理功能，可以对音频进行各种调音和效果处理。
我们可以通过案例来介绍如何进行混音处理，如何使用插件来增强音频效果，以及如何进行最终的母带处理等。
这些技巧对于提升音频质量和制作专业音乐作品至关重要。
三、乐器库和效果插件3.1 乐器库的应用Logic Pro X内置了丰富的乐器库，包括各种虚拟乐器和采样乐器，如钢琴、吉他、合成器等。
我们可以通过案例来介绍如何使用乐器库进行音乐创作，如何通过MIDI键盘进行演奏录制，以及如何调整乐器参数以达到理想的音色效果等。
3.2 效果插件的使用在效果处理方面，Logic Pro X也提供了丰富的效果插件，如均衡器、压缩器、混响等。
logic使用快捷键使用方法
l o g i c使用快捷键使用方法本页仅作为文档封面，使用时可以删除This document is for reference only-rar21year.March以前用过NUENDO等软件，Logic Pro 9的快捷键适应不了，怎么设置快捷键？启动Logic Pro 9，点击桌面左上角Logic Pro菜单，找到Preferences,找到key commands，在这里设置。
这里有一个我已经改好的快捷键预设，仿NUENDO的，可下载导入。
方法：在key commands窗口左上角，找到Option下拉菜单。
选择Import....，完成即可。
Logic Pro 9录音以后再录音，怎么会“顿”一下？在Logic Pro 9底部，transport (传送条）上，在录音按钮上单击鼠标右键，勾选“punch on the fly",好了，整个世界清净了。
我想对单个音频/MIDI事件进行非破坏性的移调处理怎么做？选择你要处理的音频/MIDI事件，在界面最左边Inspctor区域找到Transposition，输入数值：移高半音输入1，降低半音输入-1，以此类推。
在Logic Pro 9中怎样精细制作渐快、渐慢速度a 首先在刻度尺上选择你要变速的范围。
b将播放光标定位到范围的最右边c按键盘上的“T”键，打开LIST窗口d点击Create，程序将在播放光标位置，创建新的速度标记e在TEMPO栏下，输入你想要的新速度f在这个窗口上方，找到Options下来菜单，找到Tempo operations，在curve type出选择适合的渐变模式，如果从此以后就用新的速度，那么勾选“Continue with New Tempo",如果变速后还想马上回到原有速度则不要勾选，注意density这个下拉菜单，它可以让你的变速曲线像楼梯一样有棱有角，也可让曲线像丝绸一般顺滑。
g调整完了，点”Apply”，试听。
Logic操作入门手册
11） 能够按照不同的拍速和按键对 Apple Loops 进行混音：Logic 能够根据项目的拍速和 按键来自动调整循环，因此，使用者可以在同一个项目中对不同声源的循环进行自由组合。 2、 关于本操作手册 本操作手册的撰写目的是帮助 Logic 用户尽快组装和使用系统，因此，它不是对 Logic 所有 内容的最终测评，不会对 Logic 程序的各个部分都进行详尽的介绍。 在本手册里，我们只为您详细介绍 Logic 的接口、命令以及菜单等最重要的内容。此外，随 同这些详细介绍，我们还配有对如何完成某项特定任务的逐步讲解和指导。我们建议您利用 系统中自带的演示曲教程（Tutorial Song），跟从这些讲解和指导进行大量的练习和实例 观摩，以快速掌握 MIDI 和音频信息的处理方法和技巧。 本手册的第一章主要为您讲述如何安装配置 Logic。如果您已经完成这一步，想直接进入应 用的学习阶段，那么您可以转跳到第二章——Logic 入门。然后，在接下来的几章，您将学 到很多关于 Logic 概念和设备的简介。 本手册的设计初衷不是为使用者提供利用电脑进行音乐创作的综合指南，因此，通常使用较 多的技术术语都被安排在附录部分。 如果您想了解更多关于数字音频和音乐项目组成元素的内容，可以阅读本手册的附录 A—— 音频和 MIDI 基础知识；而附录 B 则主要讲述 Mac OS X 操作系统中音频和 MIDI 的有关信息； 附录 C 则主要教您如何将 Logic 接入调音台并将作为调音台使用；最后，在附录 D 中，您将 学到如何对电脑进行优化，以用于音乐制作。 此外，通过 Logic 的参考手册以及在线帮助系统，您还可以获得更多更全面有关 Logic 的各 种信息。因此，除了本手册，我们建议您阅读更多相关的参考手册。 其中，在线帮助系统可以通过 Logic 的“帮助”菜单进入，它基本上相当于一款电子版的参 考手册。它的优点在于使用方便，可以随时查找。 无论您再怎么不喜欢阅读使用手册，我们还是建议您读完下一部分，因为它将为您提供 Logic、XSK 所涉及的版权保护硬件的有关信息。 最后，请注意，这里我们为您提供的所有信息在付诸打印时都是最权威的。对于此后发生的 任何有关功能增减的升级信息，请参照 Logic DVD 中的“后继信息”或者每一款 Logic 升级 版本中所附带的“升级信息”。 3、 本手册中所使用的有关规则 在教您从 DVD 中载入演示曲教程之前，我们认为有必要向您介绍一下本手册所使用的所关规 则。 1）菜单功能 Logic 中大多数功能都可以通过等级菜单来实现，其中菜单的等级设置如下：菜单>菜单页 面>功能 2）重要页面 在本手册中，部分文本中标有“重要”字样，指的主要是有关功能或者参数的信息。这些页 面讲述的都是一些应该或者必须阅读并且牢记的重要概念或者技术信息。建议您对这种页面 格外留心。 3）注解 在本手册中，您会发现有的地方标有“注解”字样，这些部分主要为您提供一些能够帮助您 更好地使用 Logic 的额外信息或者技巧。 4）键盘命令 Logic 中的很多功能都可以通过键盘命令（也就是电脑键盘的快捷键）来激活或者打开。本 手册中所提到的快捷键设置都是基于 Logic 设置助手中所分配的标准快捷键设置。另外，我
常用逻辑用语(Logic)
试判断上面命题的真假.
练一练 1.判断下列说法是否正确。 1）一个命题的逆命题为真，它的逆否命题不一定为真； （对）
2）一个命题的否命题为真，它的逆命题一定为真。 （对） 3）一个命题的原命题为假，它的逆命题一定为假。 （错） 4）一个命题的逆否命题为假，它的否命题为假。
（错）
2.原命题：若A∪B=A, 则A∩B=φ。 逆命题：若A∩B=φ，则A∪B=A。 否命题：若A∪B≠A，则A∩B≠φ。 逆否命题：若A∩B≠φ，则A∪B≠A。
原命题 若p则q 逆命题 若q则p
互 否 命 题
互 否 命 题
否命题 若﹁ p则﹁ q
逆否命题 若﹁ q则﹁p
探究：四种命题的真假关系
试写出下列命题的逆命题，否命题，逆否命题，并判断真假 填入下表 (1) 若x=2 ，则x² -3x+2=0. （3）若x是无理数，则x+1是无理数
(2) 若a² =b²，则a=b.
对所有x, 存在某x， 对任何x， 不成立 成立 不成立 所有的 某些
练习1:写出下列命题的逆命题、否命题、逆否命题。 (1)原命题： 若 则 2 2 a b 则 a b 真命题 答:逆命题： 若 2 2 否命题： 若 a b 则 a2 b 2 假命题 a b 则 a b 假命题 逆否命题： 若 2 2 a b 真命题 a b 假 (2)原命题：若一个数是负数，则它的平方是0； 假 逆命题：若一个数的平方是0，则它是负数； 否命题：若一个数不是负数，则它的平方不是0；假 逆否命题：若一个数的平方不是0，则它不是负数. 假 试判断上面命题的真假.
┐p
┐q
原命题:若p,则q 否命题:若┐p,则┐q
例如，命题“同位角相等，两直线平行”的否命题是 “同位角不相等，两直线不平行”。
关于逻辑
[编辑] 本质
形式是逻辑的核心，但在“形式逻辑”中对“形式”使用时常不很明确，因而使其阐述变得很费解。其中，符号逻辑仅为形式逻辑的一种类型，而和形式逻辑的另一种类型－只处理直言命题的三段论不同。
非形式逻辑是研究自然语言论证的一门学科。对谬论的研究是非形式逻辑中尤其重要的一个分支。柏拉图的作品[3]是非形式逻辑的一重要例子。
传统上，逻辑被作为哲学的一个分支来研究。自从十九世纪中期，逻辑经常在数学和最近的计算机科学中研究。作为一门形式科学，通过对推论的形式系统和自然语言论证二者的研究，逻辑研究和分类语句和论证的结构。因此逻辑的范围是非常广阔的，从核心主题如对谬论和悖论的研究，到专门的推理分析如或然正确的推理和涉及因果关系的论证。
W. Hodges, 2001. Logic. An introduction to elementary logic. Penguin Books.
G. Birkhoff and J. von Neumann, 1936. 'The Logic of Quantum Mechanics'. Annals of Mathematics, 37:823-843.
D. Finkelstein, 1969. 'Matter, Space and Logic'. In R. S. Cohen and M. W. Wartofsky, (eds.), Proceedings of the Boston Colloquium for the Philosophy of Science, Boston Studies in the Philosophy of Science, vol 13. ISBN 90-277-支，和文法与修辞一同被称为古典三学科。自十九世纪中叶，“形式逻辑”已被作为数学基础而被研究，当中经常被称之为符号逻辑。1903年，阿弗烈·诺夫·怀海德与伯特兰·罗素写成了《Principia Mathematica》，试图将逻辑形式地建立成数学的基石。[2]不过，除了些基本的以外，当时的系统已不再被使用，大部份都被集合论所取代掉了。当对形式逻辑的研究渐渐地扩张了之后，研究也不再只局限于基础的议题，之后的各个数学领域被合称为数理逻辑。形式逻辑的发展和其在电脑上的应用是计算机科学的基础。
Logic
Diagram representing Classical Definition of Knowledge
Criteria of truth
• In epistemology, criteria of truth (or tests of truth) are standards and rules used to judge the accuracy of statements and claims. They are tools of verification. Understanding a philosophy's criteria of truth is fundamental to a clear evaluation of that philosophy. This necessity is driven by the varying, and conflicting, claims of different philosophies. The rules of logic have no ability to distinguish truth on their own. An individual must determine what standards distinguish truth from falsehood. Not all criteria are equally valid. Some standards are sufficient, while
Truth
• Whether someone's belief is true is not a prerequisite for its belief. On the other hand, if something is actually known, then it categorically cannot be false. For example, a person believes that a particular bridge is safe enough to support him, and attempts to cross it; unfortunately, the bridge collapses under his weight. It could be said that he believed that the bridge was safe, but that this belief was mistaken. It would not be accurate to say that he knew that the bridge was safe, because plainly it was not. By contrast, if the bridge actually supported his weight then he might be justified in subsequently holding that
教你使用LogicPro进行音乐编曲与制作
教你使用LogicPro进行音乐编曲与制作第一章：LogicPro的介绍LogicPro是一款专业的音乐编曲与制作软件，由苹果公司开发。
它为音乐制作人提供了各种功能和工具，帮助他们创作、录制和混合音乐。
LogicPro具有直观的用户界面和强大的功能，使得它成为音乐制作领域最受欢迎的工具之一。
第二章：界面和工作流程在开始使用LogicPro之前，首先要了解它的界面和工作流程。
LogicPro的界面由多个面板组成，包括音频编辑器、MIDI编辑器、混音器和效果器等。
用户可以自定义界面布局，以适应各种创作和编辑任务。
工作流程主要包括录制、编辑、编曲和混音等步骤，每个步骤都有相应的工具和功能。
第三章：录制音频和MIDILogicPro支持多种录制方式，包括直接录制、导入音频文件和使用虚拟乐器等。
用户可以通过插入音频轨道或MIDI轨道来录制音频或MIDI。
在录制过程中，LogicPro提供了实时监视、定位和循环播放等功能，方便用户进行精确的录制。
第四章：编辑音频和MIDILogicPro提供了丰富的音频和MIDI编辑功能，使用户可以对录制的音频和MIDI进行精确的编辑。
音频编辑器可以实现剪切、复制、粘贴和淡入淡出等操作。
MIDI编辑器则可以编辑音符、控制器数据和音色等。
此外，LogicPro还提供了一些高级编辑功能，如时间和音高校正等。
第五章：编曲和打击乐LogicPro内置了多个虚拟乐器和音色库，使用户可以轻松进行编曲。
用户可以使用虚拟键盘或外接MIDI控制器进行演奏，也可以使用MIDI编辑器直接编辑音符。
此外，LogicPro还提供了丰富的打击乐音色和鼓组合，供用户创作节奏部分。
第六章：编辑和应用效果器LogicPro提供了多种效果器，如均衡器、压缩器、混响和合唱等。
用户可以在音频轨道或总线上插入效果器，并调整其参数来实现各种音效。
此外，LogicPro还支持插件效果器，用户可以通过安装第三方插件来扩展音频处理和音色设计功能。
Logic全攻略
Logic 全攻略前言：Logic简介近年来，随着个人电脑的风行和普及，音乐制作领域正在经受着一场重大变革。
以前需要大量专业工作室设备的音乐项目，现在只需通过一台个人电脑，再加上一些软件资源，就可以在家庭工作室或者项目工作室中完成！一台配有快速处理器和足够内存的个人电脑，就可以作为一个工作站，来完成对整套音乐项目的录音、编辑、混音以及制作，最后，制作好的音乐还可以在电脑中播放、烧录成CD/DVD或者上传到因特网。
1、什么是Logic？Logic是一套专门为Mac OS X操作系统设计的用来进行音乐创作、制作、谱曲的高性能集成系统。
通过它，可以谱写出专业水准的原创音乐作品；通过它，可以为Final Cut Pro视频项目配置版税全免的声音轨道；当然，它的功能远不止此！它允许使用者通过MIDI和软件乐器、声学乐器和人声演唱的音频录音材料以及预先录制好的音频文件，来创建音乐项目编排！使用者可以先在Logic的项目编辑（Arrange）窗口对音频和MIDI数据进行自由组合和编排，然后为编辑文件添加各种极具专业品质的音效，并在立体声或者环绕声（仅限于Logic Pro）环境中对其进行混音，最后将完成的音乐转换成一个或者多个标准的音频文件或者一张音频CD，放在任何一台多媒体电脑或者家庭立体声上播放，或者传入Final Cut Pro或其它应用程序。
与其它同类音频程序相比，Logic主要具有如下特点：1）能够通过与之相连的键盘等MIDI输入设备记录MIDI信息，然后再通过任何一件相连的MIDI设备或者Logic自带的软件乐器对这些信息进行回放。
2）能够对MIDI项目进行创建、编排和编辑，并通过与电脑相连的打印机打印出乐谱。
3）能够对声学乐器、电乐器以及人声演唱等进行数字化录音，并能够通过系统内置的各种实时效果器对这些音频录音材料进行处理。
4）可以使用系统自带的各种软件乐器或者第三方厂家Audio Units乐器。
logic使用手册
logic使用手册摘要：1.Logic 使用手册概述2.Logic 的功能与特点3.Logic 的安装与配置4.Logic 的基本操作与使用方法5.Logic 的高级功能与应用6.Logic 的故障排除与维护7.Logic 的升级与更新正文：【Logic 使用手册概述】Logic 是一款功能强大的知识库管理工具，适用于个人、团队和企业。
它可以帮助用户高效地组织、管理和分享知识，提高工作效率和协同能力。
本手册将为您详细介绍Logic 的功能、安装配置、使用方法和注意事项等内容。
【Logic 的功能与特点】1.多维度知识管理：Logic 支持文档、图片、音频、视频等多种格式的知识资料，并提供标签、分类、评分等管理功能，方便用户建立个性化的知识库。
2.强大的搜索功能：Logic 提供实时搜索功能，用户可以快速找到所需知识资料。
同时，Logic 还支持全文搜索、关键词搜索等多种搜索方式。
3.便捷的协同功能：Logic 支持多人实时协作，团队成员可以共同编辑、评论和分享知识，提高团队协作效率。
4.自动备份与同步：Logic 支持自动备份和多设备同步功能，确保用户知识资料的安全和便捷访问。
5.灵活的权限管理：Logic 提供多种权限设置，管理员可以灵活分配权限，确保知识资料的安全和隐私。
【Logic 的安装与配置】1.下载与安装：用户可以从Logic 官网下载最新版本的安装包，按照提示进行安装。
2.注册与登录：安装完成后，用户需要注册一个账户并登录，方可使用Logic 的功能。
3.配置个人信息：用户可以配置个人信息，如昵称、头像、联系方式等，以便更好地展示个人身份和知识领域。
【Logic 的基本操作与使用方法】1.创建知识库：用户可以创建多个知识库，对不同领域的知识进行分类管理。
2.添加知识资料：用户可以添加文档、图片、音频、视频等多种格式的知识资料，并为其添加标签、分类、评分等信息。
3.编辑与删除知识资料：用户可以编辑和删除知识资料，以及对知识库进行排序和整理。
logic全局命令
-------- logic全局命令--------R 录音⌅播放⌘⌅暂停↩停止˽播放或停止, 倒回. 向前⇧, 倒回⇧. 快进J 左右定位符互换⇧⌅•从选择位置播放⇧↩•跳到选定部分开头⌃K 创建标记⇧K 按片段创建标记⌘⌫删除标记⌃, 跳到上一个标记⌃. 跳到下一个标记⌘↩给标记重新命名C 循环模式S 独奏模式⌥S •设定独奏锁定模式⌥⇧S •再次选择锁定独奏的片段⇧T •拍子速度K MIDI/监视节拍器咔嗒声⇧⌘L 锁定/解锁当前的屏幕设置1 恢复屏幕设置12 恢复屏幕设置23 恢复屏幕设置34 恢复屏幕设置45 恢复屏幕设置56 恢复屏幕设置67 恢复屏幕设置78 恢复屏幕设置89 恢复屏幕设置9⌃1 恢复屏幕设置1x⌃2 恢复屏幕设置2x⌃3 恢复屏幕设置3x⌃4 恢复屏幕设置4x⌃5 恢复屏幕设置5x⌃6 恢复屏幕设置6x⌃7 恢复屏幕设置7x⌃8 恢复屏幕设置8x ⌃9 恢复屏幕设置9x⌥R 片段检查器浮动⌥⌘I 导入项目设置... ⌘, 打开偏好设置...⌘0 打开事件列表...⌘1 打开编配窗口...⌘2 打开调音台...⌘3 打开乐谱编辑器...⌘4 打开变换⌘5 打开HyperEditor...⌘6 打开钢琴卷帘窗...⌘7 打开走带窗口...⌘8 打开环境...⌘9 打开媒体夹...⌥E 开关事件浮动窗口E 开关事件列表X 开关调音台N 开关乐谱编辑器Y 开关Hyper EditorP 开关钢琴卷帘窗B 开关媒体夹O 开关循环浏览器⌥L 开关资源库F 开关文件浏览器W 开关样本编辑器⌥M 开关标记列表T 开关速度列表⌥⌘T 使用节拍检测来调整速度U 切换拍号列表⇧W 在外部样本编辑器中打开⌥X 打开系统性能...⌥⇧T 打开速度操作...⌥K 打开键盘命令...⌥C 打开调色板...⌥⌘O 打开影片...⌃⌘O 开关当前轨道自动化关闭/读⌃⌘A 开关当前轨道自动化闩锁/读⌃⌥⌘A 开关自动化快速访问⌘G 开关组离合器⌥⌘G 打开组设置... ⌘W 关闭窗口⌘` 循环显示窗口↑ •选定上一个轨道↓ •选定下一个轨道⌘N 新建...⌘O 打开...⌥P 项目设置... ⌥⌘W 关闭项目⌘S 存储⇧⌘S 将项目存储为...⌘P 打印⌘I 导入...⌥⌘E 将选定部分导出为MIDI 文件... ⌘E 将轨道导出为音频文件...⇧⌘E 将所有轨道导出为音频文件... ⌘B 并轨...⌘Q 退出⌘Z 撤销⇧⌘Z 重做⌥Z 撤销历史记录...⌘X 剪切⌘C 拷贝⌘V 粘贴⌘A 全选⌘M 最小化窗口⇧⌘M 缩放窗口⇧⌘I 导入音频文件...⌘→下一个插件设置或EXS 乐器⌘←上一个插件设置或EXS 乐器⌥⌘→所选轨道的下一个通道条设置⌥⌘←所选轨道的上一个通道条设置⌥⌘C 拷贝通道条设置⌥⌘V 粘贴通道条设置V 隐藏/显示所有插件窗口-------- 全局控制表面命令-------- ⌘K 打开控制器分配⌘L 学习新的控制器分配-------- 不同窗口--------⎋•显示工具菜单⌃⇟•设定下一个工具⌃⇞•设定上一个工具G 开关全局轨道⌥G 配置全局轨道⌃⌥←水平缩小⌃⌥→水平放大⌃⌥↑垂直缩小⌃⌥↓垂直放大Z 切换缩放以适合所选内容或所有内容⌃⌥Z 导航:向后⇞向上翻页⇟向下翻页↖页左↘页右示走带控制I 隐藏/显示检查器⌃O MIDI 输出开关M 让音符/片段/折叠夹静音打开/关闭⇧⌘Y 超级画笔:停用⌘Y 超级画笔:自动定义+ •将上一个点按的参数增大1- •将上一个点按的参数减小1⇧+ •将上一个点按的参数增大10⇧- •将上一个点按的参数减小10-------- 显示音频文件的窗口-------- ⇧⌘R 在Finder 中显示文件˽播放/停止选定部分-------- 编配和各种编辑器--------⇧⌘A 取消全选⇧I 反选⇧F 选定以下全部⌥⇧F 选定所有后面的相同轨道/音高⇧L 选定定位符以内的⇧G 取消选定全局轨道⇧U 选定空片段⇧P 选定同等子位置⇧M 选定静音的片段/事件⇧C 选定同等着色的片段/事件⇧↖•选择第一个或将选取框选择范围左移⇧↘•选择最后一个或将选取框选择范围右移← •选择上一个片段/事件,或者将选取框末端(或点/其他边)设定到上一个瞬变→ •选择下一个片段/事件,或者将选取框末端(或点/其他边)设定到下一个瞬变⇧←•切换上一个片段/事件,或者将选取框末端(或延伸点)设定到上一个瞬变⇧→•切换下一个片段/事件,或者将选取框末端(或延伸点)设定到下一个瞬变L 循环片段/折叠夹打开/关闭Q 量化选定事件⌃⌥Q 撤销量化⇧↑选定最高音符⇧↓选定最低音符D 删除重复事件⌘R 重复片段/事件...⌘↖•将片段/事件/选取框开头设定到播放头位置⌘↘•将片段/事件/选取框末端设定到播放头位置⌥→•将片段/事件位置向右挪动1 个挪动值的距离⌥←•将片段/事件位置向左挪动1 个挪动值的距离⌥⇧→•将片段/事件长度向右挪动1 个挪动值的距离⌥⇧←•将片段/事件长度向左挪动1 个挪动值的距离⌃⌥T 将挪动值设定为音位⌃⌥D 将挪动值设定为等份⌃⌥B 将挪动值设定为节拍⌃⌥M 将挪动值设定为小节⌃⌥F 将挪动值设定为SMPTE 帧⌥↑•事件移调+1⌥↓•事件移调-1⌥⇧↑事件移调+12⌥⇧↓事件移调-12⌘⇞解锁SMPTE位置⌘⇟锁定SMPTE位置⌃⇧S 吸附模式:敏捷⌃⇧M 吸附模式:小节⌃⇧B 吸附模式:节拍⌃⇧D 吸附模式:等份⌃⇧T 吸附模式:音位⌃⇧F 吸附模式:帧⌃⇧W 吸附模式:样本⌃⇧A 吸附自动化⌃⇧V 吸附到绝对值⌃⇧O 拖移模式:重叠⌃⇧N 拖移模式:无重叠⌃⇧X 拖移模式:交叉渐入渐出⌃⇧L拖移模式:左靠齐⌃⇧R 拖移模式:右靠齐-------- 编配窗口--------← •在所选轨道上选定上一个片段→ •在所选轨道上选定下一个片段⇧⌘F 打包折叠夹⇧⌘U 将折叠夹解开到新轨道⌃⌘⌫删除所选轨道上可见的自动化⌃⇧⌘⌫删除所选轨道上的所有自动化⌃⌘↑将可见的片段数据移到轨道自动化⌃⌘↓将可见的轨道自动化移到片段⌃⇧⌘↑将所有片段数据移到轨道自动化⌃⇧⌘↓将所有轨道自动化移到片段⌃⌘F 打包汇整折叠夹⌃⌘U 解开汇整折叠夹⌃⇧⌘U 将汇整折叠夹解开成新轨道⌃F 隐藏/显示汇整折叠夹⌘D 使用重复设置新建轨道⌥⌘N 新建轨道...⌃B 原位并轨片段⌃⌘B 原位并轨轨道⌃D 鼓替换/重叠H 开关隐藏视图⌃H 隐藏当前轨道并选定下一个轨道⌃⇧H 取消隐藏所有轨道⌃M 开关轨道静音⌃R 录音启用的轨道⌃S 开关轨道独奏⌃⌥⌘↓单轨放大⌃⌥⌘↑单轨缩小⌃⌥⌘Z 开关单轨缩放⌃Z 自动轨道缩放⌃⌥⌘⌫还原单轨缩放⌃⌥⌫还原所有轨道的单轨缩放⇧A 选定片段的所有替身⌃⌘X 剪开:剪切定位符之间的部分(全局)⌃⌘Z 在定位符之间插入无声片段(全局)⌃⌘V 接合:在播放头处插入剪开的部分(全局) ⌃⌘R 重复定位符之间的部分(全局)⌘T 使用片段长度和定位符来调整速度⌃E 将片段转换成新的采样器轨道⌥⌘L 到定位符的时间伸展片段长度⌥⌘B 到最近小节的时间伸展片段长度⌃X 剥离无声...⌃N 正常化片段参数⌃Q 破坏性地应用量化⌃L 将循环转换成真实拷贝⇧⌘B 设定最适宜的片段大小(按小节取整)⌥, 在选择范围内向左随机播放片段⌥. 在选择范围内向右随机播放片段⌃C 裁剪定位符或选取框所选内容以外的片段A 隐藏/显示轨道自动化⌘F 隐藏/显示伸缩视图⌃⌥- 波形垂直缩小⌃⌥+ 波形垂直放大⌃⌥W 切换波形垂直缩放⌥T 配置轨道头-------- 调音台--------⇧X 在调音台模式之间循环(单个、编配、全部) ⇧⌘A 取消全选⇧C 选择同等着色的通道条⇧M 选择已静音的通道条← 选择上一个(左侧)通道条→ 选择下一个(右侧)通道条⌥⌘N 创建新的辅助通道条⌃T 为选定的通道条创建编配轨道-------- 环境窗口-------- ⌃⌫仅清除电缆⌃C 隐藏/显示电缆⌃P 保护连线/位置⇧I 反选⇧U 选定未使用的乐器⇧→选定电缆的目的位置⇧←选定电缆的起始位置⌃V 发送所选的推子值⌃S 串接-------- 乐谱窗口-------- ⌃P 页面视图⌃F 显示文件夹⌃X 显示复音⌃N 隐藏/显示乐器名称⌃R 隐藏/显示页面标尺→ •下一个事件← •上一个事件↓ •下一个五线谱↑ •上一个五线谱⌃↑符干:上⌃↓符干:下⌃⇧↑延音线:上⌃⇧↓延音线:下⌃B 给所选音符加符杠⌃U 去掉所选音符的符杠⇧⇟等音移动:#⇧⇞等音移动:b⌃C 基于乐谱分离来分配通道-------- 事件窗口--------↑ •选定上一个事件↓ •选定下一个事件⌃A 长度为绝对位置⇧V •将值拷贝到接下来的所有事件-------- Hyper Editor -------- ⌥⌘N 创建事件定义⌃⌫删除事件定义⌃C 拷贝事件定义⌃V 粘贴事件定义⌃A 开关自动定义↓ 选择下一个超级定义↑ 选择上一个超级定义-------- 音频媒体夹-------- ↑ 选定上一个音频文件↓ 选定下一个音频文件⌃F 添加音频文件...⌃R 添加片段⌃⌫删除文件⌃C 拷贝/转换文件... ⇧U 选定未使用的⌃X 剥离无声...⌃G 创建组...-------- 样本编辑窗口-------- ⌃B 创建备份⌥⌘S 将选定部分存储为... ← 跳到选定部分开头→ 跳到选定部分末尾↓ 跳到片段锚点⌘T 切换瞬变编辑模式⌘+ 增加瞬变数量⌘- 减少瞬变数量⌃N 正常化⌃G 更改增益... ⌃I 淡入⌃O 淡出⌃⌫无声⌃T 修剪⌃D 去掉直流偏移⌃P Time and Pitch Machine... ⌃S 音频到乐谱...⇧P 搜索峰值⇧S 搜索无声片段⌃A 移动锚点时锁定编配位置-------- EXS24 乐器编辑器-------- ⇧I 反选⌃F 载入音频样本...⌃Z 新区域⌃G 新组的音频文件...⌥←•将选定的区域/组向左移动⌥→•将选定的区域/组向右移动⌥⇧←•将选定的区域/组向左移动(区域包括调的主音) ⌥⇧→•将选定的区域/组向右移动(区域包括调的主音) ⌥⌘S 存储乐器⌃O 载入多个样本...⌃W 在样本编辑器中打开。
Logic逻辑上课用
前提是作为推理根据的已知判断； 结论是根据已知判断所推出的新判断； 推理的联项是前提与结论之间的逻辑联结项，是 推理的逻辑常项。
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2、形式：
推理中常见的有三段论推理和二难推理
❖ （1）三段论推理是由两个包含着一个共同项的 性质判断作前提，推出另一个性质判断为结论的 间接推理。
小说和侦探小说等。 读书笔记和摘要、心得体会是包含关
系，非反对或矛盾关系，不能并列
2、每读一篇好文章，他都要写
读书笔记，写摘要“晚和上/来心”还得是“晚体/上会。 来”概念命题不明确，有 3、这里经常干旱歧，义 山上的水非
常宝贵，我们把它留给晚上来的人喝。
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二、命题
定义：是运用概念进行判 断的语言形式，是断定 或陈述事物情况的思维 单位。
不能算作命题，即 不能下定义的情况：
①否定句②比喻句 ③描述句④循环定义
这里的语句②是疑问句，它仅仅提出问题。语句③是祈 使句，它表达一种要求、愿望。语句④是感叹句，它只是 抒发情感。这几类语句都没有直接描述事件，也这就无所 谓真假，因此它们不表达命题。
语句①则不同，它作为陈述句，描述了红豆生长的客观 情况。这个描述是符合事实的，因此它是一个真的陈述 句，语句①有所描述并且可精选区ppt 分真假，它表达了命题。15
a b关
ab
之
间
矛盾关系
反对关系
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判断下列各对概念的关系：
❖阿Q——老舍 反对关系
❖文学作品——小说 包含关系
❖鲁迅——《孔乙己》的作者 全同关系
❖教师——作家 交叉关系
❖真理——谬误 矛盾关系
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Introduction Introduction
Syntax
Model Semantics
Boolean Algebra
Proof Semantics
Biconditional (or equivalence) p⇔q a natural number is odd if and only if it is divisible by 2. being divisible by 2 is a necessary and sufficient condition for being odd. A natural number is odd if it is divisible by 2, and conversely.
“It is not possible to have a dispute with someone who denies the principles”
a
Introduction Introduction
Syntax
Model Semantics
Boolean Algebra
Proof Semantics
Proof Semantics
Different Notations ⊥ (p ∧ q) (p ∨ q) (p ⊕ q) (p ⇔ q) (p ⇒ q) ¬p (p) T , true, 1 F , false, 0 (p.q), p × q, (p&q), (p&&q) (p + q), (p | q), (p q) (p ˆq) (p ↔ q), (p ≡ q) (p → q), (p ⊃ q) ∼ p, p, !p [p]
Introduction Introduction
Syntax
Model Semantics
Boolean Algebra
Proof Semantics
Disjunction and Exclusive Disjunction p ∨ q, p ⊕ q Alexander invaded Bactria or Persia This material is useful for for studying discrete mathematics or databases. Tea or coffee. It is a boy or a girl. 3 is odd or even.
Introduction Syntax
Syntax
Model Semantics
Boolean Algebra
Proof Semantics
2.2. Syntax of Propositional Calculus
Definition 2.2.1 Let us consider a collection of symbols called propositions or statements. Let us consider the collection of symbols { , ⊥, ∨, ∧, ¬, ⇒, ⇔, ⊕}a . Let us consider the two parenthesis symbols ( and ). F is a well formed formula (wff) (or atomic statementb ) if F is a proposition. The following are wff (or compound statements) iff F1 and F2 are wff. , ⊥, (F1 ∧ F2 ), (F1 ∨ F2 ), ¬(F1 ), (F1 ⇒ F2 ), (F1 ⇔ F2 ), (F1 ⊕ F2 ). the above are the only wff.
Negation ¬p Alexander is not Persian. 3 is not odd. It is not a fact that 3 is odd. 3 is odd is not true. 3 is odd is false.
Introduction Introduction
a b
These are the standard connectives. There are more. p and ¬p are sometimes refer to as unit statements.
Introduction Syntax
Syntax
Model Semantics
Boolean Algebra
Introduction Precedence
Syntax
Model Semantics
Boolean Algebra
Proof Semantics
Precedence We may assume this precedence (from lowest to highest) ⇔ ⇒ ∧ ∨ ⊕ ¬
Introduction
Syntax
Model Semantics
Boolean Algebra
Proof Semantics
2. Propositional Logic
St´phane Bressan e
August 27, 2010
Introduction Introduction
Syntax
Introduction Introduction
Syntax
Model Semantics
Boolean Algebra
Proof Semantics
Colin Farrell in the role of Alexander the Great in Oliver Stone’s Alexander.
Introduction Introduction
Syntax
Model Semantics
Boolean Algebra
Proof Semantics
Conditional Cont. p⇒q Being a perfect square is a sufficient condition for a natural number to be composite. Being composite is a necessary condition for a natural number to be a perfect square. If a natural number is not composite then it is not a perfect square (contrapositive). a natural number is perfect square only if it it is composite.
Introduction Precedence
Syntax
Model Semantics
Boolean Algebra
Proof Semantics
Precedence and Parenthesis q ∨ p ∧ p is ambiguous, q ∧ p reads (q ∧ p), ¬q ⇒ p reads (¬(q) ⇒ p), p ∨ q ∨ q reads ((p ∨ q) ∨ q), [(p ∨ (q)) ∧ q] reads ((p ∨ q) ∧ q).
Introduction Introduction
Syntax
Model Semantics
Boolean Algebra
Proof Semantics
Angelina Jolie in the role of Queen Olympia in Oliver Stone’s Alexander.
Conditional Cont. p⇒q If Olympia is Greek and the mother of Alexander then Alexander is Greek. Anyone who has a Greek mother is Greek.
Introduction Introduction
Syntax
Model Semantics
Boolean Algebra
Proof Semantics
Conditional p⇒q If a natural number is a perfect square then it is composite. If a natural number is a perfect square, it is composite. A natural number is a perfect square implies that it is composite. A natural number is composite if it is a perfect square. A natural number is composite when it is a perfect square. A natural number is composite whenever it is a perfect square. A natural number is composite follows from the fact that it is a perfect square.
Introduction Introduction
Syntax
Model Semantics
Boolean Algebra
Proof Semantics
Conditional Cont. p⇒q If a natural number is a perfect square then it is composite. q ⇒ p is the converse. If a natural number is composite then it is a perfect square.