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所在平台: Udemy |
课程主页: https://www.udemy.com/course/formal-logic-propositional-predicate-modal-logic/
课程评论：没有评论
## 课程总结：形式逻辑：命题逻辑、谓词逻辑与模态逻辑 本课程全面深入地探讨了形式逻辑的理论原则与证明技术，旨在为您构建扎实的逻辑推理基础。 **第一部分：命题逻辑** * **基础概念：** 学习如何构建良式公式，包括原子命题和逻辑联结词。 * **语义解释：** 通过真值赋值和真值表，识别重言式、矛盾式和可控式。 * **逻辑等价与范式：** 掌握交换律、分配律、德摩根定律等基本等价律，将复杂公式化简并转换为合取范式（CNF）和析取范式（DNF）。 * **证明系统：** 学习自然演绎规则和推理规则（如肯定前件、否定后件、假言三段论），并在命题逻辑中构建结构化的证明。深入理解可靠性与完备性定理，揭示证明与有效性之间的关键联系。 **第二部分：谓词逻辑（一阶逻辑）** * **基本要素：** 学习谓词、函数、变量和量词（全称量词与存在量词）的定义。 * **解释与性质：** 掌握在一阶语言的域和赋值上进行解释，理解辖域、自由变量与约束变量的概念，以及量化公式的逻辑性质。 * **自然语言翻译：** 练习将自然语言陈述精确翻译为一阶公式，解决辖域歧义和嵌套量词问题，并能将日常和哲学论断形式化为逻辑符号。 * **谓词逻辑证明：** 应用自然演绎技术，包括量词引入和消去规则，以及同一性、等词公理及其代换性质。 **第三部分：模态逻辑** * **模态概念：** 研究必然性与可能性算子，定义可能世界模型中的可达性关系。 * **公理系统与证明：** 分析模态公理系统（如K, T, S4, S5），学习模态相继演算和标记推理等证明方法，并通过对应理论连接模态公理与框架条件。 **最终回顾与应用** * **进阶主题：** 概述不可判定性结果、勒文海姆—斯科勒姆定理，以及模态逻辑的扩展（时间逻辑、义务逻辑、认知逻辑）。 * **实际应用：** 探索形式逻辑在计算机科学、语言学和哲学中的实际应用，并为进一步学习提供指导。 通过详尽的讲解、丰富的实例和挑战性的练习，本课程将为您提供在命题逻辑、谓词逻辑和模态逻辑方面的坚实理论基础，助您在科研、软件验证或高等学术研究中有效地运用形式推理。
Welcome to Formal Logic: Propositional, Predicate & Modal Logic! This rigorous course offers a comprehensive exploration of theoretical logic principles and proof techniques. You will begin with the foundations of propositional logic, learning how to construct well-formed formulas using atomic propositions and logical connectives. You will delve into semantic interpretation by building truth assignments and designing truth tables to identify tautologies, contradictions, and contingencies.Next, you will master logical equivalences and normal forms. Through clear explanations and step-by-step algorithms, you will learn to apply commutativity, distributivity, De Morgan's laws, and other fundamental equivalence laws to simplify complex formulas and convert them into Conjunctive and Disjunctive Normal Forms.The course then guides you through robust proof systems. You will study natural deduction rules and common inference rules-such as modus ponens, modus tollens, and hypothetical syllogism-to construct structured proofs in propositional logic. You will also explore the soundness and completeness theorems, demonstrating the essential relationship between provable and valid formulas.Building on propositional logic, you will transition to first-order predicate logic. You will define predicates, functions, variables, and quantifiers (universal and existential), and learn how to interpret first-order languages over domains and assignments. You will tackle the intricacies of scope, free and bound variables, and logical properties that govern quantified formulas.You will practice translating natural language statements into precise first-order formulas, resolving scope ambiguities and nested quantifiers. Through guided examples, you will develop the skills to formalize everyday and philosophical assertions in logical notation. You will also apply natural deduction techniques with quantifier introduction and elimination rules, and explore identity, equality axioms, and their substitutive properties in proofs.In the final module, you will study modal logic and Kripke semantics. You will examine necessity and possibility operators, define accessibility relations in possible-world models, and analyze axiomatic systems such as K, T, S4, and S5. You will learn proof methods including modal sequent calculus and labeled deduction, and explore correspondence theory to connect modal axioms with frame conditions.The course concludes with an overview of advanced topics-undecidability results, Löwenheim-Skolem theorems, and modal logic extensions (temporal, deontic, epistemic). You will discover practical applications in computer science, linguistics, and philosophy, and receive guidance on next steps for further study.Throughout this course, you will engage with detailed lectures, worked examples, and challenging exercises to solidify your understanding. By the end, you will possess a strong theoretical foundation in propositional, predicate, and modal logic, ready to apply formal reasoning in research, software verification, or advanced academic study.
